r1c1: 1

{"version":1,"calcs":[{"id":"1031-exchange-timeline","title":"1031 Exchange Timeline","description":"Track critical identification and exchange deadlines for 1031 tax swaps.","category":"real-estate","icon":"calendar","tags":["real-estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"saleClosingDate = 0 // day","label":null,"prefix":null,"suffix":"day","section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"identificationPeriodDays = 45 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"exchangePeriodDays = 180 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"identificationDeadline = saleClosingDate + identificationPeriodDays // days from sale @hero","label":null,"prefix":null,"suffix":"days from sale","section":null,"hidden":false,"hero":true,"slider":null,"value":45,"display":"45"},{"text":"exchangeDeadline = saleClosingDate + exchangePeriodDays","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"}]},{"id":"401k-contribution","title":"401k Contribution","description":"Estimate annual 401(k) contributions, employer match, and 30-year growth at 7% return.","category":"finance","icon":"dollar-sign","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Salary and Contribution","label":null,"prefix":null,"suffix":null,"section":"Salary and Contribution","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual salary = 80000 // 20k..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Salary and Contribution","hidden":false,"hero":false,"slider":{"min":20000,"max":500000,"step":1000},"value":80000,"display":"$80,000.00"},{"text":"contribution percent = 10 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Salary and Contribution","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":10,"display":"10"},{"text":"$employer match percent = 50 // % of your contribution 0..100","label":null,"prefix":"$","suffix":"% of your contribution","section":"Salary and Contribution","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":50,"display":"$50.00"},{"text":"employer match limit = 6 // % of salary 0..15 by 0.5","label":null,"prefix":null,"suffix":"% of salary","section":"Salary and Contribution","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.5},"value":6,"display":"6"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_your_annual_contribution = annual salary * (contribution percent / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":8000,"display":"$8,000.00"},{"text":"_match_threshold = if(contribution percent < employer match limit, contribution percent, employer match limit)","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"$_employer_annual_match = annual salary * (match_threshold / 100) * (employer match percent / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2400,"display":"$2,400.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$total annual contribution = your_annual_contribution + employer_annual_match // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":10400,"display":"$10,400.00"},{"text":"$monthly contribution = total annual contribution / 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":866.6666666666666,"display":"$866.67"},{"text":"percent of salary matched = (employer_annual_match / annual salary) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"$total after 30 years at 7 percent return = total annual contribution * ((1.07^30 - 1) / 0.07)","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":982392.1777669319,"display":"$982,392.18"}]},{"id":"__kitchen-sink","title":"Kitchen Sink","description":"Every working decorator + row type — the canonical reference. Visit with ?lab to flip styles and check coverage.","category":"other","icon":"beaker","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-28T04:36:03.514Z"},"rows":[{"text":"# 1. Hero + suffix","label":null,"prefix":null,"suffix":null,"section":"1. Hero + suffix","hero":false,"slider":null,"value":null,"display":null},{"text":"weight = 180 // lbs 80..400","label":null,"prefix":null,"suffix":"lbs","section":"1. Hero + suffix","hidden":false,"hero":false,"slider":{"min":80,"max":400,"step":1},"value":180,"display":"180"},{"text":"height = 70 // inches 48..84","label":null,"prefix":null,"suffix":"inches","section":"1. Hero + suffix","hidden":false,"hero":false,"slider":{"min":48,"max":84,"step":1},"value":70,"display":"70"},{"text":"_weight_kg = weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"1. Hero + suffix","hidden":true,"hero":false,"slider":null,"value":81.64656,"display":"81.65"},{"text":"_height_m = height * 0.0254","label":null,"prefix":null,"suffix":null,"section":"1. Hero + suffix","hidden":true,"hero":false,"slider":null,"value":1.778,"display":"1.778"},{"text":"body mass index = weight_kg / (height_m^2) // @hero @label(BMI) @suffix(kg/m²)","label":"BMI","prefix":null,"suffix":null,"section":"1. Hero + suffix","hidden":false,"hero":true,"slider":null,"value":25.82702471527392,"display":"25.83"},{"text":"# 2. Prefix + suffix","label":null,"prefix":null,"suffix":null,"section":"2. Prefix + suffix","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual income = $80000 // 20k..200k by 1k","label":null,"prefix":"$","suffix":null,"section":"2. Prefix + suffix","hidden":false,"hero":false,"slider":{"min":20000,"max":200000,"step":1000},"value":80000,"display":"$80,000.00"},{"text":"$annual expenses = $45000 // 10k..150k by 1k","label":null,"prefix":"$","suffix":null,"section":"2. Prefix + suffix","hidden":false,"hero":false,"slider":{"min":10000,"max":150000,"step":1000},"value":45000,"display":"$45,000.00"},{"text":"$annual savings = annual_income - annual_expenses","label":null,"prefix":"$","suffix":null,"section":"2. Prefix + suffix","hidden":false,"hero":false,"slider":null,"value":35000,"display":"$35,000.00"},{"text":"# 3. Hidden + advanced","label":null,"prefix":null,"suffix":null,"section":"3. Hidden + advanced","hero":false,"slider":null,"value":null,"display":null},{"text":"$_compound_seed = 100000","label":null,"prefix":"$","suffix":null,"section":"3. Hidden + advanced","hidden":true,"hero":false,"slider":null,"value":100000,"display":"$100,000.00"},{"text":"return rate = 7 // % 1..15 @advanced","label":null,"prefix":null,"suffix":"%","section":"3. Hidden + advanced","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.2},"value":7,"display":"7"},{"text":"years = 30 // 1..50 @advanced","label":null,"prefix":null,"suffix":null,"section":"3. Hidden + advanced","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":30,"display":"30"},{"text":"# 4. Long suffix — phrase","label":null,"prefix":null,"suffix":null,"section":"4. Long suffix — phrase","hero":false,"slider":null,"value":null,"display":null},{"text":"billable rate = 150 // dollars per hour","label":null,"prefix":null,"suffix":"dollars per hour","section":"4. Long suffix — phrase","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"output capacity = 145 // cubic feet per minute","label":null,"prefix":null,"suffix":"cubic feet per minute","section":"4. Long suffix — phrase","hidden":false,"hero":false,"slider":null,"value":145,"display":"145"},{"text":"monthly burn = 28500 // dollars per month","label":null,"prefix":null,"suffix":"dollars per month","section":"4. Long suffix — phrase","hidden":false,"hero":false,"slider":null,"value":28500,"display":"28,500"},{"text":"# 5. Hint-shaped suffix","label":null,"prefix":null,"suffix":null,"section":"5. Hint-shaped suffix","hero":false,"slider":null,"value":null,"display":null},{"text":"sex = 1 // 1 for male, 0 for female","label":null,"prefix":null,"suffix":"1 for male, 0 for female","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"material factor = 0.15 // Hard cheese: 0.1, Soft: 0.2","label":null,"prefix":null,"suffix":"Hard cheese: 0.1, Soft: 0.2","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"scope ratio = 7 // 7:1 is standard for overnight anchoring","label":null,"prefix":null,"suffix":"7:1 is standard for overnight anchoring","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"beam stress = 30000 // psi (steel)","label":null,"prefix":null,"suffix":"psi (steel)","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":30000,"display":"30,000"},{"text":"# 6. Note decorator","label":null,"prefix":null,"suffix":null,"section":"6. Note decorator","hero":false,"slider":null,"value":null,"display":null},{"text":"$shipping cost = 9.99 // @note(Free over $50)","label":null,"prefix":"$","suffix":null,"section":"6. Note decorator","hidden":false,"hero":false,"slider":null,"value":9.99,"display":"$9.99"},{"text":"$tax rate = 8.25 // @suffix(%) @note(Varies by ZIP — verify before checkout)","label":null,"prefix":"$","suffix":null,"section":"6. Note decorator","hidden":false,"hero":false,"slider":null,"value":8.25,"display":"$8.25"},{"text":"# 7. Tooltip","label":null,"prefix":null,"suffix":null,"section":"7. Tooltip","hero":false,"slider":null,"value":null,"display":null},{"text":"sample size = 30 // @tooltip(Larger samples reduce confidence interval width)","label":null,"prefix":null,"suffix":null,"section":"7. Tooltip","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"confidence = 95 // % @tooltip(Standard for academic publication)","label":null,"prefix":null,"suffix":"%","section":"7. Tooltip","hidden":false,"hero":false,"slider":null,"value":95,"display":"95"},{"text":"# 8. Section + nested subsection","label":null,"prefix":null,"suffix":null,"section":"8. Section + nested subsection","hero":false,"slider":null,"value":null,"display":null},{"text":"# Group A — Inputs","label":null,"prefix":null,"suffix":null,"section":"Group A — Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"group_a_input_1 = 10","label":null,"prefix":null,"suffix":null,"section":"Group A — Inputs","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"group_a_input_2 = 20","label":null,"prefix":null,"suffix":null,"section":"Group A — Inputs","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"## Subsection","label":null,"prefix":null,"suffix":null,"section":"Subsection","hero":false,"slider":null,"value":null,"display":null},{"text":"nested_value = group_a_input_1 + group_a_input_2","label":null,"prefix":null,"suffix":null,"section":"Subsection","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# 9. Collapsed section","label":null,"prefix":null,"suffix":null,"section":"9. Collapsed section","hero":false,"slider":null,"value":null,"display":null},{"text":"# Advanced settings @collapsed","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hero":false,"slider":null,"value":null,"display":null},{"text":"fudge factor = 1.05","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hidden":false,"hero":false,"slider":null,"value":1.05,"display":"1.05"},{"text":"overhead = 0.12","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"margin = 0.25","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"# 10. Accent row","label":null,"prefix":null,"suffix":null,"section":"10. Accent row","hero":false,"slider":null,"value":null,"display":null},{"text":"$emergency reserve = 50000 // @accent","label":null,"prefix":"$","suffix":null,"section":"10. Accent row","hidden":false,"hero":false,"slider":null,"value":50000,"display":"$50,000.00"},{"text":"# 11. Readonly","label":null,"prefix":null,"suffix":null,"section":"11. Readonly","hero":false,"slider":null,"value":null,"display":null},{"text":"constant_pi = 3.14159 // @readonly","label":null,"prefix":null,"suffix":null,"section":"11. Readonly","hidden":false,"hero":false,"slider":null,"value":3.14159,"display":"3.142"},{"text":"# 12. Slider min..max syntax (inline range)","label":null,"prefix":null,"suffix":null,"section":"12. Slider min..max syntax (inline range)","hero":false,"slider":null,"value":null,"display":null},{"text":"slider quick = 50 // 0..100 by 5","label":null,"prefix":null,"suffix":null,"section":"12. Slider min..max syntax (inline range)","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":5},"value":50,"display":"50"},{"text":"slider with units = 250 // ml 0..1k by 25","label":null,"prefix":null,"suffix":"ml","section":"12. Slider min..max syntax (inline range)","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":25},"value":250,"display":"250"},{"text":"# 13. Dropdown","label":null,"prefix":null,"suffix":null,"section":"13. Dropdown","hero":false,"slider":null,"value":null,"display":null},{"text":"plan = {price: 9, name: 'Hobby'} // dropdown({Hobby: {price: 9, name: 'Hobby'}, Pro: {price: 29, name: 'Pro'}, Team: {price: 99, name: 'Team'}})","label":null,"prefix":null,"suffix":null,"section":"13. Dropdown","hidden":false,"hero":false,"slider":null,"value":{"price":9,"name":"Hobby"},"display":null},{"text":"$plan price = plan.price // @label(Selected price) @prefix($)","label":"Selected price","prefix":"$","suffix":null,"section":"13. Dropdown","hidden":false,"hero":false,"slider":null,"value":9,"display":"$9.00"},{"text":"# 14. Toggle","label":null,"prefix":null,"suffix":null,"section":"14. Toggle","hero":false,"slider":null,"value":null,"display":null},{"text":"includes_premium = false // @label(Premium add-on) toggle()","label":"Premium add-on","prefix":null,"suffix":null,"section":"14. Toggle","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"$base price = 49.99 // @prefix($)","label":null,"prefix":"$","suffix":null,"section":"14. Toggle","hidden":false,"hero":false,"slider":null,"value":49.99,"display":"$49.99"},{"text":"$total = base_price + (includes_premium ? 20 : 0) // @hero @prefix($)","label":null,"prefix":"$","suffix":null,"section":"14. Toggle","hidden":false,"hero":true,"slider":null,"value":49.99,"display":"$49.99"},{"text":"# 15. @icon on row","label":null,"prefix":null,"suffix":null,"section":"15. on row","hero":false,"slider":null,"value":null,"display":null},{"text":"fuel = 12.5 // @icon(droplet) gal","label":null,"prefix":null,"suffix":"gal","section":"15. on row","hidden":false,"hero":false,"slider":null,"value":12.5,"display":"12.5"},{"text":"distance = 320 // @icon(map-pin) mi","label":null,"prefix":null,"suffix":"mi","section":"15. on row","hidden":false,"hero":false,"slider":null,"value":320,"display":"320"},{"text":"# 16. Calc title @icon + @category in the first heading at the top of this file","label":null,"prefix":null,"suffix":null,"section":"16. Calc title + in the first heading at the top of this file","hero":false,"slider":null,"value":null,"display":null},{"text":"# 17. Layout: grid (peer outputs)","label":null,"prefix":null,"suffix":null,"section":"17. Layout: grid (peer outputs)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Color breakdown @layout(grid)","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"red = 255","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":255,"display":"255"},{"text":"green = 128","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":128,"display":"128"},{"text":"blue = 64","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":64,"display":"64"},{"text":"alpha = 1.0","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# 18. Layout: split (inputs left, outputs right)","label":null,"prefix":null,"suffix":null,"section":"18. Layout: split (inputs left, outputs right)","hero":false,"slider":null,"value":null,"display":null},{"text":"# I/O scenario @layout(split)","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hero":false,"slider":null,"value":null,"display":null},{"text":"revenue = 150000","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":150000,"display":"150,000"},{"text":"expenses = 90000","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":90000,"display":"90,000"},{"text":"profit = revenue - expenses","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":60000,"display":"60,000"},{"text":"margin pct = (profit / revenue) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"# 19. @wide — row spans full grid width","label":null,"prefix":null,"suffix":null,"section":"19. — row spans full grid width","hero":false,"slider":null,"value":null,"display":null},{"text":"$total quarterly revenue = 600000 // @wide @prefix($) @label(Q4 total revenue across all regions)","label":"Q4 total revenue across all regions","prefix":"$","suffix":null,"section":"19. — row spans full grid width","hidden":false,"hero":false,"slider":null,"value":600000,"display":"$600,000.00"},{"text":"# 20. Format: percent and currency","label":null,"prefix":null,"suffix":null,"section":"20. Format: percent and currency","hero":false,"slider":null,"value":null,"display":null},{"text":"percent rate = 0.075 // @format(percent)","label":null,"prefix":null,"suffix":null,"section":"20. Format: percent and currency","hidden":false,"hero":false,"slider":null,"value":0.075,"display":"7.5%"},{"text":"$compact dollars = 12345.67 // @format(currency) @decimals(0)","label":null,"prefix":"$","suffix":null,"section":"20. Format: percent and currency","hidden":false,"hero":false,"slider":null,"value":12345.67,"display":"$12.3K"},{"text":"raw count = 1234567 // @format(raw)","label":null,"prefix":null,"suffix":null,"section":"20. Format: percent and currency","hidden":false,"hero":false,"slider":null,"value":1234567,"display":"1,234,567"},{"text":"# 20b. Suppress unit on dimensioned results","label":null,"prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hero":false,"slider":null,"value":null,"display":null},{"text":"_w_kg = 82","label":null,"prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hidden":true,"hero":false,"slider":null,"value":82,"display":"82"},{"text":"_h_m = 1.78","label":null,"prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hidden":true,"hero":false,"slider":null,"value":1.78,"display":"1.78"},{"text":"body mass index = _w_kg / (_h_m^2) // @hero @label(BMI) @suffix()","label":"BMI","prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hidden":false,"hero":true,"slider":null,"value":25.88057063502083,"display":"25.88"},{"text":"# 21. Inline variable interpolation in prose","label":null,"prefix":null,"suffix":null,"section":"21. Inline variable interpolation in prose","hero":false,"slider":null,"value":null,"display":null},{"text":"# 22. Narrative row (markdown-friendly)","label":null,"prefix":null,"suffix":null,"section":"22. Narrative row (markdown-friendly)","hero":false,"slider":null,"value":null,"display":null},{"text":"# 23. Plain comment","label":null,"prefix":null,"suffix":null,"section":"23. Plain comment","hero":false,"slider":null,"value":null,"display":null},{"text":"# 24. Divider","label":null,"prefix":null,"suffix":null,"section":"24. Divider","hero":false,"slider":null,"value":null,"display":null},{"text":"# 25. Quoted string narrative","label":null,"prefix":null,"suffix":null,"section":"25. Quoted string narrative","hero":false,"slider":null,"value":null,"display":null},{"text":"# 26. Comment heading (level 3)","label":null,"prefix":null,"suffix":null,"section":"26. Comment heading (level 3)","hero":false,"slider":null,"value":null,"display":null},{"text":"### A level-3 sub-label","label":null,"prefix":null,"suffix":null,"section":"A level-3 sub-label","hero":false,"slider":null,"value":null,"display":null},{"text":"# 27. End cap — one final hero so the calc has a clear payoff","label":null,"prefix":null,"suffix":null,"section":"27. End cap — one final hero so the calc has a clear payoff","hero":false,"slider":null,"value":null,"display":null},{"text":"$grand total = annual_savings * years // @hero @label(Total saved over horizon) @prefix($)","label":"Total saved over horizon","prefix":"$","suffix":null,"section":"27. End cap — one final hero so the calc has a clear payoff","hidden":false,"hero":true,"slider":null,"value":1050000,"display":"$1,050,000.00"}]},{"id":"_feature-showcase-charts","title":"📊 Chart Showcase","description":"Every visualization Instacalc draws — each from a one-line function call over plain data.","category":"demo","icon":"chart-bar","tags":["demo"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-27T17:24:15.270Z"},"rows":[{"text":"# 📊 Bars @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"📊 Bars","hero":false,"slider":null,"value":null,"display":null},{"text":"revenue = bars([42, 58, 71, 65, 89, 103], [\"Q1\", \"Q2\", \"Q3\", \"Q4\", \"Q5\", \"Q6\"])","label":null,"prefix":null,"suffix":null,"section":"📊 Bars","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# 📈 Line @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"📈 Line","hero":false,"slider":null,"value":null,"display":null},{"text":"trend = line([10, 25, 18, 40, 35, 55, 48, 70], [\"Jan\", \"Feb\", \"Mar\", \"Apr\", \"May\", \"Jun\", \"Jul\", \"Aug\"], {ylabel: \"Users (k)\"})","label":null,"prefix":null,"suffix":null,"section":"📈 Line","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# 🌄 Area @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"🌄 Area","hero":false,"slider":null,"value":null,"display":null},{"text":"filled = area([10, 25, 18, 40, 35, 55, 48, 70], [\"Jan\", \"Feb\", \"Mar\", \"Apr\", \"May\", \"Jun\", \"Jul\", \"Aug\"])","label":null,"prefix":null,"suffix":null,"section":"🌄 Area","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# 〰️ Plot f(x) @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"〰️ Plot 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@skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"🍩 Donut","hero":false,"slider":null,"value":null,"display":null},{"text":"budget = donut([45, 28, 17, 10], [\"Rent\", \"Food\", \"Transport\", \"Fun\"])","label":null,"prefix":null,"suffix":null,"section":"🍩 Donut","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# 🎯 Gauge @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"🎯 Gauge","hero":false,"slider":null,"value":null,"display":null},{"text":"progress = gauge(72, 0, 100)","label":null,"prefix":null,"suffix":null,"section":"🎯 Gauge","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# 🕸️ Radar @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"🕸️ Radar","hero":false,"slider":null,"value":null,"display":null},{"text":"character = radar([80, 65, 92, 70, 55, 88], [\"Speed\", \"Power\", \"Range\", 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coefficient = 0.3","label":null,"prefix":null,"suffix":null,"section":"Aero Settings","hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"frontal area square meters = 2.2","label":null,"prefix":null,"suffix":null,"section":"Aero Settings","hidden":false,"hero":false,"slider":null,"value":2.2,"display":"2.2"},{"text":"air density = 1.225","label":null,"prefix":null,"suffix":null,"section":"Aero Settings","hidden":false,"hero":false,"slider":null,"value":1.225,"display":"1.225"},{"text":"speed meters per second = 30","label":null,"prefix":null,"suffix":null,"section":"Aero Settings","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"drag force newtons = 0.5 * air density * (speed meters per second ^ 2) * drag coefficient * frontal area square 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dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":295000,"display":"295,000"},{"text":"arv = (comparablePropertySale1 + comparablePropertySale2 + comparablePropertySale3) / 3 // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":301666.6666666667,"display":"301,666.67"}]},{"id":"age-calculator","title":"Age Calculator","description":"See your age in months, weeks, days, hours, and heartbeats.","category":"everyday","icon":"calendar","tags":["age","birthday","life"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Your Age","label":null,"prefix":null,"suffix":null,"section":"Your Age","hero":false,"slider":null,"value":null,"display":null},{"text":"age in years = 30 // years 1..120","label":null,"prefix":null,"suffix":"years","section":"Your 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25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":375,"display":"375"},{"text":"air_fryer_time_minutes = oven_time_minutes * 0.8 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":16,"display":"16"}]},{"id":"air-fuel-ratio-afr","title":"Air Fuel Ratio AFR","description":"Calculate air fuel ratio from mass.","category":"engineering","icon":"settings","tags":["automotive","engine","fuel"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Mass Stats","label":null,"prefix":null,"suffix":null,"section":"Mass Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"air mass grams = 14.7","label":null,"prefix":null,"suffix":null,"section":"Mass Stats","hidden":false,"hero":false,"slider":null,"value":14.7,"display":"14.7"},{"text":"fuel mass grams = 1.0","label":null,"prefix":null,"suffix":null,"section":"Mass Stats","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"air fuel ratio = air mass grams / fuel mass grams","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":14.7,"display":"14.7"}]},{"id":"air-quality-index-from-pm25","title":"Air Quality Index From Pm25","description":"Calculate the EPA Air Quality Index from a PM2.5 concentration reading.","category":"other","icon":"calculator","tags":["air","index"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"pm25_concentration = 35","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"aqi_low = 51","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":51,"display":"51"},{"text":"aqi_high = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"conc_low = 12.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12.1,"display":"12.1"},{"text":"conc_high = 35.4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":35.4,"display":"35.4"},{"text":"aqi = ((aqi_high - aqi_low) / (conc_high - conc_low)) * (pm25_concentration - conc_low) + aqi_low // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":99.15879828326179,"display":"99.16"}]},{"id":"alcohol-by-volume-brix","title":"Alcohol By Volume Brix","description":"Estimate alcohol by volume from original and final Brix 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= 100","label":null,"prefix":null,"suffix":null,"section":"Electrical Load","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"base vehicle load amps = 30","label":null,"prefix":null,"suffix":null,"section":"Electrical Load","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"accessories load amps = 20","label":null,"prefix":null,"suffix":null,"section":"Electrical Load","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"remaining capacity amps = alternator output amps - (base vehicle load amps + accessories load amps)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"}]},{"id":"altman-z-score-bankruptcy-risk","title":"Altman Z Score Bankruptcy Risk","description":"Calculate the Altman Z-score to estimate corporate bankruptcy risk.","category":"finance","icon":"dollar-sign","tags":["risk","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"working_capital_assets = 0.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"retained_earnings_assets = 0.3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"ebit_assets = 0.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"market_value_equity_debt = 2.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"sales_assets = 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100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"aluminum_scrap_valuation = aluminum_weight_pounds * aluminum_price_per_pound","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"amazon-fba-fee-estimate","title":"Amazon Fba Fee Estimate","description":"Estimate Amazon FBA referral and fulfillment fees and net proceeds per sale.","category":"other","icon":"calculator","tags":["fee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"item_price = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"item_weight_pounds = 1.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"fulfillment_fee_per_pound = 3.22","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.22,"display":"3.22"},{"text":"referral_fee_percentage = 0.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"referral_fee = item_price * referral_fee_percentage","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7.5,"display":"7.5"},{"text":"total_fees = referral_fee + fulfillment_fee_per_pound","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10.72,"display":"10.72"},{"text":"net_proceeds = item_price - total_fees","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":39.28,"display":"39.28"}]},{"id":"aml-risk-score","title":"AML Risk Score","description":"Assess the anti-money laundering risk level of a transaction.","category":"other","icon":"shield","tags":["risk"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"transactionVolumeScore = 6 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"geographicRiskScore = 4 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"customerTypeScore = 7 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"combinedAMLScore = (transactionVolumeScore + geographicRiskScore + customerTypeScore) / 3 // scale 1-10 @hero","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":true,"slider":null,"value":5.666666666666667,"display":"5.667"}]},{"id":"among-us-imposter-probability","title":"Among Us Imposter Probability","description":"Calculate the probability of being assigned imposter or crewmate in Among Us.","category":"math","icon":"infinity","tags":["probability","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Game Settings","label":null,"prefix":null,"suffix":null,"section":"Game Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"total players = 10 // 4..15","label":null,"prefix":null,"suffix":null,"section":"Game Settings","hidden":false,"hero":false,"slider":{"min":4,"max":15,"step":0.2},"value":10,"display":"10"},{"text":"imposter count = 2 // 1..3","label":null,"prefix":null,"suffix":null,"section":"Game Settings","hidden":false,"hero":false,"slider":{"min":1,"max":3,"step":0.02},"value":2,"display":"2"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"imposter probability = (imposter count / total players) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":20,"display":"20"},{"text":"crewmate probability = 100 - imposter probability // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"amortization-schedule","title":"Amortization Schedule","description":"Calculate monthly payment, total interest, and total cost of a fixed-rate loan.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Loan Details","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = 250000 // 10k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Loan Details","hidden":false,"hero":false,"slider":{"min":10000,"max":1000000,"step":5000},"value":250000,"display":"$250,000.00"},{"text":"interest rate = 6.5 // % 1..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.1},"value":6.5,"display":"6.5"},{"text":"loan term = 30 // years 5..40","label":null,"prefix":null,"suffix":"years","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":5,"max":40,"step":1},"value":30,"display":"30"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_monthly_rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"_num_payments = loan term * 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly payment = loan amount * (monthly_rate * (1 + monthly_rate)^num_payments) / ((1 + monthly_rate)^num_payments - 1) // @hero","label":null,"prefix":"$","suffix":null,"section":"Results","hidden":false,"hero":true,"slider":null,"value":1580.1700587324135,"display":"$1,580.17"},{"text":"$total payments = monthly payment * num_payments","label":null,"prefix":"$","suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":568861.221143669,"display":"$568,861.22"},{"text":"$total interest = total payments - loan amount","label":null,"prefix":"$","suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":318861.221143669,"display":"$318,861.22"}]},{"id":"anchor-rode-scope-depth","title":"Anchor Rode Scope Depth","description":"Calculate the anchor rode length needed for a given water depth and scope ratio.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"water_depth_feet = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"freeboard_height_feet = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"scope_ratio = 7 // 7:1 is standard for overnight","label":null,"prefix":null,"suffix":"7:1 is standard for overnight","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"total_rode_length_feet = (water_depth_feet + freeboard_height_feet) * scope_ratio // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":168,"display":"168"}]},{"id":"anchoring-effect-strength","title":"Anchoring Effect Strength","description":"Estimate how much an anchor value biases a final numerical judgment.","category":"health","icon":"brain","tags":["effect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"anchor_value = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"actual_value = 500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"adjustment_percent = 0.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"final_estimate = anchor_value - (anchor_value - actual_value) * adjustment_percent // estimated value @hero","label":null,"prefix":null,"suffix":"estimated value","section":null,"hidden":false,"hero":true,"slider":null,"value":900,"display":"900"}]},{"id":"angle-conversion-degrees-radians","title":"Angle Conversion Degrees Radians","description":"Convert between degrees and radians: rad = deg × π/180.","category":"formulas","icon":"sigma","tags":["angle"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Inputs (you can use either)","label":null,"prefix":null,"suffix":null,"section":"Inputs (you can use either)","hero":false,"slider":null,"value":null,"display":null},{"text":"degrees = 180 // 0..360","label":null,"prefix":null,"suffix":null,"section":"Inputs (you can use either)","hidden":false,"hero":false,"slider":{"min":0,"max":360,"step":1},"value":180,"display":"180"},{"text":"radians = 3.14159 // 0..6.3","label":null,"prefix":null,"suffix":null,"section":"Inputs (you can use either)","hidden":false,"hero":false,"slider":{"min":0,"max":6.3,"step":0.1},"value":3.14159,"display":"3.142"},{"text":"# Conversions","label":null,"prefix":null,"suffix":null,"section":"Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"degrees_to_radians = degrees * pi / 180 // @hero @label(Degrees → Radians)","label":"Degrees → Radians","prefix":null,"suffix":null,"section":"Conversions","hidden":false,"hero":true,"slider":null,"value":3.141592653589793,"display":"3.142"},{"text":"radians_to_degrees = radians * 180 / pi // @hero @label(Radians → Degrees)","label":"Radians → Degrees","prefix":null,"suffix":null,"section":"Conversions","hidden":false,"hero":true,"slider":null,"value":179.99984796050433,"display":"180"}]},{"id":"annuity-payment-calculator","title":"Annuity Payment Calculator","description":"Calculate the periodic payment of an annuity from present value, rate, and term.","category":"finance","icon":"dollar-sign","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"present_value = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"annual_rate = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"years = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"payment = present_value * (annual_rate / (1 - (1 + annual_rate) ** -years))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8024.258719069128,"display":"8,024.26"}]},{"id":"aperture-depth-of-field-blur","title":"Aperture Depth Of Field Blur","description":"Calculate the near and far depth-of-field limits for a given aperture and focus distance.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"focal_length = 50 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"aperture_f_stop = 1.8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.8,"display":"1.8"},{"text":"distance_to_subject = 2000 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"circle_of_confusion = 0.03 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"_hyperfocal_distance = focal_length^2 / (aperture_f_stop * circle_of_confusion)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":46296.2962962963,"display":"46,296.3"},{"text":"near_limit = (distance_to_subject * (hyperfocal_distance - focal_length)) / (hyperfocal_distance + distance_to_subject - 2 * focal_length) // mm @hero","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":true,"slider":null,"value":1919.080919080919,"display":"1,919.08"},{"text":"far_limit = (distance_to_subject * (hyperfocal_distance - focal_length)) / (hyperfocal_distance - distance_to_subject) // mm @hero","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":true,"slider":null,"value":2088.0434782608695,"display":"2,088.04"}]},{"id":"app-store-take-home-pay","title":"App Store Take Home Pay","description":"Estimate take-home pay from app sales after Apple or Google commission and taxes.","category":"everyday","icon":"home","tags":["home","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"total_app_sales_revenue = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"apple_google_commission_percentage = 0.30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"applicable_taxes_percentage = 0.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"revenue_after_commission = total_app_sales_revenue * (1 - apple_google_commission_percentage)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7000,"display":"7,000"},{"text":"net_take_home_pay = revenue_after_commission * (1 - applicable_taxes_percentage)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5950,"display":"5,950"}]},{"id":"appreciation-rate-projector","title":"Appreciation Rate Projector","description":"Project future property value based on historical growth rates.","category":"real-estate","icon":"trending-up","tags":["real-estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"currentValue = 300000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"annualAppreciationRate = 3 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"yearsProjected = 10 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"futureValue = currentValue * (1 + (annualAppreciationRate / 100)) ^ yearsProjected // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":403174.9138032367,"display":"403,174.91"}]},{"id":"aquifer-recharge-time","title":"Aquifer Recharge Time","description":"Estimate how long it takes for an underground aquifer to refill.","category":"science","icon":"droplet","tags":["science","water","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"aquifer_volume_cubic_meters = 1000000 // m3","label":null,"prefix":null,"suffix":"m3","section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"annual_recharge_liters_per_m2 = 50 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"catchment_area_m2 = 500000 // m2","label":null,"prefix":null,"suffix":"m2","section":null,"hidden":false,"hero":false,"slider":null,"value":500000,"display":"500,000"},{"text":"annual_recharge_m3 = (annual_recharge_liters_per_m2 * catchment_area_m2) / 1000 // m3","label":null,"prefix":null,"suffix":"m3","section":null,"hidden":false,"hero":false,"slider":null,"value":25000,"display":"25,000"},{"text":"years_to_full_recharge = aquifer_volume_cubic_meters / annual_recharge_m3 // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":40,"display":"40"}]},{"id":"arc-length","title":"Arc Length","description":"Find the length of a circular arc: s = r × θ (θ in radians).","category":"formulas","icon":"circle","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Arc","label":null,"prefix":null,"suffix":null,"section":"Arc","hero":false,"slider":null,"value":null,"display":null},{"text":"radius = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Arc","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"angle_degrees = 60 // 0..360","label":null,"prefix":null,"suffix":null,"section":"Arc","hidden":false,"hero":false,"slider":{"min":0,"max":360,"step":1},"value":60,"display":"60"},{"text":"# Convert to radians and compute arc length","label":null,"prefix":null,"suffix":null,"section":"Convert to radians and compute arc length","hero":false,"slider":null,"value":null,"display":null},{"text":"_angle_radians = angle_degrees * pi / 180","label":null,"prefix":null,"suffix":null,"section":"Convert to radians and compute arc length","hidden":true,"hero":false,"slider":null,"value":1.0471975511965976,"display":"1.047"},{"text":"arc_length = radius * angle_radians","label":null,"prefix":null,"suffix":null,"section":"Convert to radians and compute arc length","hidden":false,"hero":true,"slider":null,"value":10.471975511965976,"display":"10.47"}]},{"id":"archery-kinetic-energy","title":"Archery Kinetic Energy","description":"Calculate arrow kinetic energy in foot-pounds from arrow weight and velocity.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"arrow_weight_grains = 400","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"arrow_velocity_feet_per_second = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"kinetic_energy_foot_pounds = (arrow_weight_grains * arrow_velocity_feet_per_second^2) / 450240 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":79.95735607675905,"display":"79.96"}]},{"id":"arithmetic-sequence-nth-term","title":"Arithmetic Sequence nth Term","description":"Find the nth term of an arithmetic sequence: aₙ = a₁ + (n−1)·d.","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Sequence parameters","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"d = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"n = 10 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# nth term","label":null,"prefix":null,"suffix":null,"section":"nth term","hero":false,"slider":null,"value":null,"display":null},{"text":"an = a1 + (n - 1) * d // @label(aₙ)","label":"aₙ","prefix":null,"suffix":null,"section":"nth term","hidden":false,"hero":true,"slider":null,"value":48,"display":"48"}]},{"id":"arithmetic-series-sum","title":"Arithmetic Series Sum","description":"Sum the first n terms of an arithmetic sequence: Sₙ = n/2 · (a₁ + aₙ).","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Sequence parameters","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"d = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"n = 10 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Sum of first n terms","label":null,"prefix":null,"suffix":null,"section":"Sum of first n terms","hero":false,"slider":null,"value":null,"display":null},{"text":"an = a1 + (n - 1) * d // @label(aₙ)","label":"aₙ","prefix":null,"suffix":null,"section":"Sum of first n terms","hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"sum_n = n / 2 * (a1 + an) // @label(Sₙ)","label":"Sₙ","prefix":null,"suffix":null,"section":"Sum of first n terms","hidden":false,"hero":true,"slider":null,"value":255,"display":"255"}]},{"id":"aspect-ratio","title":"Aspect Ratio","description":"Scale dimensions proportionally while maintaining aspect ratio.","category":"design","icon":"maximize","tags":["aspect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Original Dimensions","label":null,"prefix":null,"suffix":null,"section":"Original Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"original width = 1920 // 1..7680","label":null,"prefix":null,"suffix":null,"section":"Original Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":7680,"step":100},"value":1920,"display":"1,920"},{"text":"original height = 1080 // 1..4320","label":null,"prefix":null,"suffix":null,"section":"Original Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":4320,"step":50},"value":1080,"display":"1,080"},{"text":"# Resize","label":null,"prefix":null,"suffix":null,"section":"Resize","hero":false,"slider":null,"value":null,"display":null},{"text":"new width = 1280 // 1..7680","label":null,"prefix":null,"suffix":null,"section":"Resize","hidden":false,"hero":false,"slider":{"min":1,"max":7680,"step":100},"value":1280,"display":"1,280"},{"text":"# Calculated","label":null,"prefix":null,"suffix":null,"section":"Calculated","hero":false,"slider":null,"value":null,"display":null},{"text":"new height = round(original height * (new width / original width)) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculated","hidden":false,"hero":true,"slider":null,"value":720,"display":"720"},{"text":"scale factor = round(new width / original width * 10000) / 10000","label":null,"prefix":null,"suffix":null,"section":"Calculated","hidden":false,"hero":false,"slider":null,"value":0.6667,"display":"0.6667"},{"text":"# Ratio","label":null,"prefix":null,"suffix":null,"section":"Ratio","hero":false,"slider":null,"value":null,"display":null},{"text":"ratio decimal = round(original width / original height * 10000) / 10000 // @label(Ratio (decimal))","label":"Ratio (decimal)","prefix":null,"suffix":null,"section":"Ratio","hidden":false,"hero":false,"slider":null,"value":1.7778,"display":"1.778"},{"text":"# Common Checks","label":null,"prefix":null,"suffix":null,"section":"Common Checks","hero":false,"slider":null,"value":null,"display":null},{"text":"original megapixels = round((original width * original height) / 1000000 * 100) / 100","label":null,"prefix":null,"suffix":null,"section":"Common Checks","hidden":false,"hero":false,"slider":null,"value":2.07,"display":"2.07"},{"text":"new megapixels = round((new width * new height) / 1000000 * 100) / 100","label":null,"prefix":null,"suffix":null,"section":"Common Checks","hidden":false,"hero":false,"slider":null,"value":0.92,"display":"0.92"}]},{"id":"asset-turnover-ratio","title":"Asset Turnover Ratio","description":"Calculate the asset turnover ratio from revenue and average total assets.","category":"math","icon":"ratio","tags":["turnover","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"total_revenue = 5000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000000,"display":"5,000,000"},{"text":"average_assets = 2500000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2500000,"display":"2,500,000"},{"text":"asset_turnover = total_revenue / average_assets","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"asteroid-impact-energy","title":"Asteroid Impact Energy","description":"Estimate the impact energy of an asteroid in megatons of TNT from size, density, and velocity.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"diameter_meters = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"density_kg_per_m3 = 3000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"velocity_km_per_s = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"volume = (4/3) * pi * (diameter_meters / 2)^3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":523598.7755982988,"display":"523,598.78"},{"text":"mass_kg = volume * density_kg_per_m3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1570796326.7948964,"display":"1,570,796,326.79"},{"text":"energy_joules = 0.5 * mass_kg * (velocity_km_per_s * 1000)^2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":314159265358979260,"display":"314,159,265,358,979,260"},{"text":"megatons_tnt = energy_joules / 4.184e15 // Megatons of TNT 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45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"pressure_millibars = 1013","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1013,"display":"1,013"},{"text":"temperature_celsius = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"refraction_arcminutes = (1.02 / tan(apparent_altitude_degrees + 10.3 / (apparent_altitude_degrees + 5.11))) * (pressure_millibars / 1010) * (283 / (273 + temperature_celsius))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.9980817482748903,"display":"0.9981"}]},{"id":"attack-speed-frames-per-second","title":"Attack Speed Frames Per Second","description":"Calculate attack speed in frames per 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@hero","label":null,"prefix":null,"suffix":"ms","section":null,"hidden":false,"hero":true,"slider":null,"value":250,"display":"250"},{"text":"dotted_eighth_note_delay = eighth_note_delay * 1.5 // ms @hero","label":null,"prefix":null,"suffix":"ms","section":null,"hidden":false,"hero":true,"slider":null,"value":375,"display":"375"}]},{"id":"aurora-visibility-latitude","title":"Aurora Visibility Latitude","description":"Estimate the minimum latitude at which the aurora is visible for a given Kp index.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"kp_index = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"min_latitude = 67 - kp_index * 2 // minimum latitude for visibility @hero","label":null,"prefix":null,"suffix":"minimum latitude for 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Terms","hidden":false,"hero":false,"slider":{"min":12,"max":60,"step":1},"value":36,"display":"36"},{"text":"tax rate = 8 // % 0..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Lease Terms","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.1},"value":8,"display":"8"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_capitalized_cost = negotiated price - down payment","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":29000,"display":"$29,000.00"},{"text":"$_residual_value = msrp * (residual value percent / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":21000,"display":"$21,000.00"},{"text":"$_monthly_depreciation = (capitalized_cost - residual_value) / lease term","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":222.22222222222223,"display":"$222.22"},{"text":"$_monthly_finance_fee = (capitalized_cost + residual_value) * money factor","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":62.5,"display":"$62.50"},{"text":"$_base_monthly_payment = monthly_depreciation + monthly_finance_fee","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":284.72222222222223,"display":"$284.72"},{"text":"$_monthly_tax = base_monthly_payment * (tax rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":22.77777777777778,"display":"$22.78"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$total monthly lease payment = base_monthly_payment + monthly_tax // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":307.5,"display":"$307.50"},{"text":"$total cost of lease = total monthly lease payment * lease term + down payment","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":14070,"display":"$14,070.00"}]},{"id":"average-days-to-ship","title":"Average Days to Ship","description":"Calculate the average time from order receipt to shipping.","category":"business","icon":"clock","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"totalDaysForAllOrders = 450 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":450,"display":"450"},{"text":"totalOrdersShipped = 150 // orders","label":null,"prefix":null,"suffix":"orders","section":null,"hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"averageDaysToShip = totalDaysForAllOrders / totalOrdersShipped // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"avogadros-law-moles-volume","title":"Avogadros Law Moles Volume","description":"Calculate the final gas volume after changing moles at constant temperature and pressure.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"volume_initial = 22.4 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":22.4,"display":"22.4"},{"text":"moles_initial = 1.0 // mol","label":null,"prefix":null,"suffix":"mol","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"moles_final = 1.5 // mol","label":null,"prefix":null,"suffix":"mol","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"volume_final = volume_initial * (moles_final / moles_initial) // liters @hero","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":33.6,"display":"33.6"}]},{"id":"baby-name-randomizer","title":"Baby Name Randomizer","description":"Calculate the probability and 1-in-X odds of a baby name occurring among newborns.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Name Stats","label":null,"prefix":null,"suffix":null,"section":"Name Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"babies with name = 15000","label":null,"prefix":null,"suffix":null,"section":"Name Stats","hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"total babies born = 4000000","label":null,"prefix":null,"suffix":null,"section":"Name Stats","hidden":false,"hero":false,"slider":null,"value":4000000,"display":"4,000,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"probability of name = (babies with name / total babies born) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":0.375,"display":"0.375"},{"text":"odds = total babies born / babies with name // 1 in X @hero","label":null,"prefix":null,"suffix":"1 in X","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":266.6666666666667,"display":"266.67"}]},{"id":"back-end-load-impact","title":"Back End Load 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years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14025.517307000004,"display":"14,025.52"},{"text":"fee_amount = future_value_pre_fee * back_end_load_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":420.76551921000015,"display":"420.77"},{"text":"final_value = future_value_pre_fee - fee_amount","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":13604.751787790003,"display":"13,604.75"}]},{"id":"backorder-rate","title":"Backorder Rate","description":"Calculate the percentage of orders that cannot be filled immediately.","category":"business","icon":"list","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"backorderedOrders = 40 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"totalOrdersPlaced = 1000 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"backorderRatePercent = (backorderedOrders / totalOrdersPlaced) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"baking-ratio","title":"Baker's Percentage","description":"Calculate ingredient weights using baker's percentages relative to flour weight.","category":"cooking","icon":"egg-fried","tags":["baking"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Baker's Percentage (relative to flour)","label":null,"prefix":null,"suffix":null,"section":"Baker's Percentage (relative to flour)","hero":false,"slider":null,"value":null,"display":null},{"text":"flour = 500 // g 100..5k","label":null,"prefix":null,"suffix":"g","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":100,"max":5000,"step":50},"value":500,"display":"500"},{"text":"hydration = 65 // % 40..100","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":40,"max":100,"step":1},"value":65,"display":"65"},{"text":"salt pct = 2 // % 0..5 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.1},"value":2,"display":"2"},{"text":"yeast pct = 1 // % 0..5 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.1},"value":1,"display":"1"},{"text":"sugar pct = 5 // % 0..20","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":5,"display":"5"},{"text":"fat pct = 3 // % 0..20","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":3,"display":"3"},{"text":"# Ingredient Amounts","label":null,"prefix":null,"suffix":null,"section":"Ingredient Amounts","hero":false,"slider":null,"value":null,"display":null},{"text":"water = flour * hydration / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":325,"display":"325"},{"text":"salt = flour * salt_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"yeast = flour * yeast_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"sugar = flour * sugar_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"fat = flour * fat_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"# Total","label":null,"prefix":null,"suffix":null,"section":"Total","hero":false,"slider":null,"value":null,"display":null},{"text":"total dough weight = flour + water + salt + yeast + sugar + fat // g @hero","label":null,"prefix":null,"suffix":"g","section":"Total","hidden":false,"hero":true,"slider":null,"value":880,"display":"880"},{"text":"total in ounces = round(total_dough_weight / 28.35, 1) // oz","label":null,"prefix":null,"suffix":"oz","section":"Total","hidden":false,"hero":false,"slider":null,"value":31,"display":"31"}]},{"id":"baking-scale","title":"Baking Time Scale","description":"Adjusted bake time when scaling a recipe up or down (heat-conduction model).","category":"cooking","icon":"chef-hat","tags":["baking","recipe"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Original Recipe","label":null,"prefix":null,"suffix":null,"section":"Original Recipe","hero":false,"slider":null,"value":null,"display":null},{"text":"original servings = 8 // 1..50","label":null,"prefix":null,"suffix":null,"section":"Original Recipe","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":8,"display":"8"},{"text":"original bake minutes = 30 // min 5..240","label":null,"prefix":null,"suffix":"min","section":"Original 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0.12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"market_return = 0.10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"risk_free_rate = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"beta = (stock_return - risk_free_rate) / (market_return - risk_free_rate)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.2857142857142858,"display":"1.286"}]},{"id":"bicycle-cadence-to-speed","title":"Bicycle Cadence To Speed","description":"Calculate bicycle speed in mph from cadence, gear ratio, and wheel 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6.50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.5,"display":"6.5"},{"text":"price_big_mac_us = 5.60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5.6,"display":"5.6"},{"text":"actual_exchange_rate = 1.10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.1,"display":"1.1"},{"text":"implied_exchange_rate = price_big_mac_local / price_big_mac_us","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.1607142857142858,"display":"1.161"},{"text":"valuation = (actual_exchange_rate / implied_exchange_rate) - 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":-0.0523076923076924,"display":"-0.0523"}]},{"id":"big-o-complexity-growth","title":"Big O Complexity Growth","description":"Compare growth rates of common Big-O complexities at a given input size.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"# Input Size","label":null,"prefix":null,"suffix":null,"section":"Input Size","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 100 // size","label":null,"prefix":null,"suffix":"size","section":"Input Size","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"# Complexities","label":null,"prefix":null,"suffix":null,"section":"Complexities","hero":false,"slider":null,"value":null,"display":null},{"text":"o log n = log2(n) // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":6.643856189774725,"display":"6.644"},{"text":"o n = n // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":100,"display":"100"},{"text":"o n log n = n * log2(n) // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":664.3856189774725,"display":"664.39"},{"text":"o n squared = n^2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":10000,"display":"10,000"},{"text":"o 2 to the n = 2^n // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":1.2676506002282294e+30,"display":"1.2677e30"}]},{"id":"billable-hour-annual-income","title":"Billable Hour Annual Income","description":"Calculate gross annual income from hourly rate and weekly billable hours.","category":"productivity","icon":"clock","tags":["income"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.415Z"},"rows":[{"text":"hourly_rate = 100 // dollars per hour","label":null,"prefix":null,"suffix":"dollars per hour","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"billable_hours_per_week = 25 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"weeks_per_year = 48 // weeks","label":null,"prefix":null,"suffix":"weeks","section":null,"hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"gross_annual_income = hourly_rate * billable_hours_per_week * weeks_per_year // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":120000,"display":"120,000"}]},{"id":"binary-search-depth","title":"Binary Search Depth","description":"Calculate the maximum number of comparisons binary search needs for N elements.","category":"math","icon":"search","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Collection Size","label":null,"prefix":null,"suffix":null,"section":"Collection Size","hero":false,"slider":null,"value":null,"display":null},{"text":"number of elements = 1000000 // N","label":null,"prefix":null,"suffix":"N","section":"Collection Size","hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"max comparisons = ceil(log2(number of elements))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"binomial-distribution","title":"Binomial 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coefficient","label":null,"prefix":null,"suffix":null,"section":"Binomial coefficient","hero":false,"slider":null,"value":null,"display":null},{"text":"binomial = factorial(n) / (factorial(k) * factorial(n - k)) // @label(C(n,k))","label":"C(n,k)","prefix":null,"suffix":null,"section":"Binomial coefficient","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"# Probability","label":null,"prefix":null,"suffix":null,"section":"Probability","hero":false,"slider":null,"value":null,"display":null},{"text":"probability = binomial * p^k * (1 - p)^(n - k) // @label(P(X = k))","label":"P(X = k)","prefix":null,"suffix":null,"section":"Probability","hidden":false,"hero":true,"slider":null,"value":0.1171875,"display":"0.1172"}]},{"id":"binomial-expansion","title":"Binomial Coefficient","description":"Compute the binomial coefficient C(n, k) = n! / (k! · (n−k)!).","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# n choose k","label":null,"prefix":null,"suffix":null,"section":"n choose k","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 10 // 0..50","label":null,"prefix":null,"suffix":null,"section":"n choose k","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":10,"display":"10"},{"text":"k = 3 // 0..50","label":null,"prefix":null,"suffix":null,"section":"n choose k","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":3,"display":"3"},{"text":"# Binomial coefficient","label":null,"prefix":null,"suffix":null,"section":"Binomial coefficient","hero":false,"slider":null,"value":null,"display":null},{"text":"coefficient = factorial(n) / (factorial(k) * factorial(n - k)) // @label(C(n,k))","label":"C(n,k)","prefix":null,"suffix":null,"section":"Binomial coefficient","hidden":false,"hero":true,"slider":null,"value":120,"display":"120"}]},{"id":"biomass-energy-content","title":"Biomass Energy Content","description":"Calculate energy content of wood or biomass based on moisture.","category":"science","icon":"flame","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"wood_weight_kg = 100 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"moisture_percent = 20 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"energy_content_dry_mj_per_kg = 19 // MJ per kg","label":null,"prefix":null,"suffix":"MJ per kg","section":null,"hidden":false,"hero":false,"slider":null,"value":19,"display":"19"},{"text":"dry_weight = wood_weight_kg * (1 - moisture_percent / 100) // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"total_energy_content_mj = dry_weight * energy_content_dry_mj_per_kg // MJ @hero","label":null,"prefix":null,"suffix":"MJ","section":null,"hidden":false,"hero":true,"slider":null,"value":1520,"display":"1,520"},{"text":"energy_in_kwh = total_energy_content_mj / 3.6 // kWh","label":null,"prefix":null,"suffix":"kWh","section":null,"hidden":false,"hero":false,"slider":null,"value":422.22222222222223,"display":"422.22"}]},{"id":"bird-seed-mix-ratio","title":"Bird Seed Mix Ratio","description":"Calculate component weights for a bird seed mix from percentages and total weight.","category":"math","icon":"bird","tags":["seed","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"sunflower_seeds_percentage = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"millet_percentage = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"cracked_corn_percentage = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"total_mix_weight_kilograms = 5 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"sunflower_weight = total_mix_weight_kilograms * (sunflower_seeds_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"millet_weight = total_mix_weight_kilograms * (millet_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"corn_weight = total_mix_weight_kilograms * (cracked_corn_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"}]},{"id":"birthday-problem","title":"Birthday Problem","description":"Probability that two people in a group share a birthday.","category":"education","icon":"cake","tags":["probability","statistics","birthday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# People in the Room","label":null,"prefix":null,"suffix":null,"section":"People in the Room","hero":false,"slider":null,"value":null,"display":null},{"text":"people = 23 // 2..100","label":null,"prefix":null,"suffix":null,"section":"People in the Room","hidden":false,"hero":false,"slider":{"min":2,"max":100,"step":1},"value":23,"display":"23"},{"text":"# Probability Math","label":null,"prefix":null,"suffix":null,"section":"Probability Math","hero":false,"slider":null,"value":null,"display":null},{"text":"_days = 365","label":null,"prefix":null,"suffix":null,"section":"Probability Math","hidden":true,"hero":false,"slider":null,"value":365,"display":"365"},{"text":"_exponent = -people * (people - 1) / (2 * days)","label":null,"prefix":null,"suffix":null,"section":"Probability Math","hidden":true,"hero":false,"slider":null,"value":-0.6931506849315069,"display":"-0.6932"},{"text":"prob no match = E^exponent // @label(P(all unique))","label":"P(all unique)","prefix":null,"suffix":null,"section":"Probability Math","hidden":false,"hero":false,"slider":null,"value":0.49999824781728935,"display":"0.5"},{"text":"prob at least one match = 1 - prob no match // @hero @label(P(any 2 share birthday))","label":"P(any 2 share birthday)","prefix":null,"suffix":null,"section":"Probability Math","hidden":false,"hero":true,"slider":null,"value":0.5000017521827106,"display":"0.5"},{"text":"# Percentage","label":null,"prefix":null,"suffix":null,"section":"Percentage","hero":false,"slider":null,"value":null,"display":null},{"text":"match percent = round(prob at least one match * 100, 1) // % @label(Probability of a match)","label":"Probability of a match","prefix":null,"suffix":"%","section":"Percentage","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"# Reference Counts","label":null,"prefix":null,"suffix":null,"section":"Reference Counts","hero":false,"slider":null,"value":null,"display":null},{"text":"people for 50 percent = ceil(sqrt(2 * days * ln(2))) // @label(People needed for 50% odds)","label":"People needed for 50% odds","prefix":null,"suffix":null,"section":"Reference Counts","hidden":false,"hero":false,"slider":null,"value":23,"display":"23"},{"text":"people for 99 percent = ceil(sqrt(2 * days * ln(100))) // @label(People needed for 99% odds)","label":"People needed for 99% odds","prefix":null,"suffix":null,"section":"Reference Counts","hidden":false,"hero":false,"slider":null,"value":58,"display":"58"}]},{"id":"bits-to-terabytes-converter","title":"Bits To Terabytes Converter","description":"Convert a total number of bits to terabytes.","category":"everyday","icon":"home","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"total_bits = 10000000000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000000000000,"display":"10,000,000,000,000"},{"text":"terabytes = total_bits / (8 * 10^12) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.25,"display":"1.25"}]},{"id":"black-hole-event-horizon","title":"Black Hole Event Horizon","description":"Calculate a black hole's Schwarzschild radius in meters from its mass in solar masses.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"mass_solar_masses = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"solar_mass_kilograms = 1.989e30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.989e+30,"display":"1.989e30"},{"text":"gravitational_constant = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"speed_of_light = 299792458","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"schwarzschild_radius_meters = (2 * gravitational_constant * mass_solar_masses * solar_mass_kilograms) / speed_of_light^2 // meters @hero","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":true,"slider":null,"value":29539.93771397716,"display":"29,539.94"}]},{"id":"black-hole-schwarzschild-radius","title":"Black Hole Schwarzschild Radius","description":"Calculate the Schwarzschild radius of a black hole in kilometers from its mass.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"object_mass_kilograms = 1.989e30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.989e+30,"display":"1.989e30"},{"text":"gravitational_constant = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"speed_of_light = 299792458","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"schwarzschild_radius_meters = (2 * gravitational_constant * object_mass_kilograms) / (speed_of_light ** 2)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2953.993771397716,"display":"2,953.99"},{"text":"schwarzschild_radius_kilometers = schwarzschild_radius_meters / 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.953993771397716,"display":"2.954"}]},{"id":"black-jack-basic-strategy-odds","title":"Black Jack Basic Strategy Odds","description":"Estimate the house edge in blackjack from deck count and dealer soft-17 rules.","category":"other","icon":"calculator","tags":["strategy","odds"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Rules","label":null,"prefix":null,"suffix":null,"section":"Rules","hero":false,"slider":null,"value":null,"display":null},{"text":"number of decks = 6 // 1..8","label":null,"prefix":null,"suffix":null,"section":"Rules","hidden":false,"hero":false,"slider":{"min":1,"max":8,"step":0.1},"value":6,"display":"6"},{"text":"dealer hits soft 17 = 1 // toggle()","label":null,"prefix":null,"suffix":null,"section":"Rules","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Base Edge","label":null,"prefix":null,"suffix":null,"section":"Base Edge","hero":false,"slider":null,"value":null,"display":null},{"text":"base edge = 0.5 // % (typical)","label":null,"prefix":null,"suffix":"% (typical)","section":"Base Edge","hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_deck_penalty = (number of decks - 1) * 0.02","label":null,"prefix":null,"suffix":null,"section":"Base Edge","hidden":true,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"_rule_penalty = dealer hits soft 17 * 0.2","label":null,"prefix":null,"suffix":null,"section":"Base Edge","hidden":true,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"total house edge = base edge + deck_penalty + rule_penalty // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":true,"slider":null,"value":0.8,"display":"0.8"}]},{"id":"black-scholes-model","title":"Black Scholes Model","description":"Calculate Black-Scholes call and put option prices with intrinsic and time value.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Option Parameters","label":null,"prefix":null,"suffix":null,"section":"Option 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1..100","label":null,"prefix":null,"suffix":"%","section":"Option Parameters","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":20,"display":"20"},{"text":"# Intermediate Steps (Black-Scholes d1, d2)","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hero":false,"slider":null,"value":null,"display":null},{"text":"_s = share_price","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_k = strike_price","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_t = time_to_expiry","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_r = risk free rate / 100","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"_v = volatility / 100","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"_d1 = (ln(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t))","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.35,"display":"0.35"},{"text":"_d2 = d1 - v * sqrt(t)","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"# Normal CDF Approximation (Logistic)","label":null,"prefix":null,"suffix":null,"section":"Normal CDF Approximation (Logistic)","hero":false,"slider":null,"value":null,"display":null},{"text":"# N(x) approx 1 / (1 + exp(-1.6 * x))","label":null,"prefix":null,"suffix":null,"section":"N(x) approx 1 / (1 + exp(-1.6 * x))","hero":false,"slider":null,"value":null,"display":null},{"text":"_n_d1 = 1 / (1 + exp(-1.6 * d1))","label":null,"prefix":null,"suffix":null,"section":"N(x) approx 1 / (1 + exp(-1.6 * x))","hidden":true,"hero":false,"slider":null,"value":0.6364525402815664,"display":"0.6365"},{"text":"_n_d2 = 1 / (1 + exp(-1.6 * d2))","label":null,"prefix":null,"suffix":null,"section":"N(x) approx 1 / (1 + exp(-1.6 * x))","hidden":true,"hero":false,"slider":null,"value":0.5597136492671929,"display":"0.5597"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$call option price = s * n_d1 - k * exp(-r * t) * n_d2 // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":10.40364478039402,"display":"$10.40"},{"text":"$put option price = call option price + k * exp(-r * t) - s","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":5.52658723046542,"display":"$5.53"},{"text":"$intrinsic value = if(s > k, s - k, 0)","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":0,"display":"$0.00"},{"text":"$time value = call option price - intrinsic value","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":10.40364478039402,"display":"$10.40"}]},{"id":"block-wall-estimator","title":"Block Wall Estimator","description":"Estimate the number of standard CMU blocks needed for a wall, including waste.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Wall Dimensions","label":null,"prefix":null,"suffix":null,"section":"Wall Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"wall length = 30 // feet 1..500","label":null,"prefix":null,"suffix":"feet","section":"Wall Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":500,"step":1},"value":30,"display":"30"},{"text":"wall height = 4 // feet 1..20","label":null,"prefix":null,"suffix":"feet","section":"Wall Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":20,"step":0.2},"value":4,"display":"4"},{"text":"# Block Dimensions (Standard CMU 16x8)","label":null,"prefix":null,"suffix":null,"section":"Block Dimensions (Standard CMU 16x8)","hero":false,"slider":null,"value":null,"display":null},{"text":"block length = 16 // 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Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_federal_tax_withholding = bonus amount * (federal supplemental tax rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2200,"display":"$2,200.00"},{"text":"$_state_tax_withholding = bonus amount * (state tax rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":500,"display":"$500.00"},{"text":"$_social_security_withholding = bonus amount * (social security rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":620,"display":"$620.00"},{"text":"$_medicare_withholding = bonus amount * (medicare rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":145,"display":"$145.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$net bonus amount = bonus amount - federal_tax_withholding - state_tax_withholding - social_security_withholding - medicare_withholding // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":6535,"display":"$6,535.00"},{"text":"$total tax withheld = bonus amount - net bonus amount","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":3465,"display":"$3,465.00"},{"text":"effective tax rate = (total tax withheld / bonus amount) * 100 // 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@hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":45,"display":"$45.00"},{"text":"$market price per share = 65 // 1..1k","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":65,"display":"$65.00"},{"text":"price to book ratio = market price per share / book value per share","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":1.4444444444444444,"display":"1.444"}]},{"id":"boss-enrage-timer-countdown","title":"Boss Enrage Timer Countdown","description":"Calculate time remaining before boss enrages.","category":"math","icon":"alert-triangle","tags":["gaming","timer"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Timer Settings","label":null,"prefix":null,"suffix":null,"section":"Timer 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Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"bowling average = total pins / total games","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":179.16666666666666,"display":"179.17"}]},{"id":"bowling-score-projector","title":"Bowling Score Projector","description":"Project a final bowling score from current frame, current score, and season average.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Current Game","label":null,"prefix":null,"suffix":null,"section":"Current Game","hero":false,"slider":null,"value":null,"display":null},{"text":"current frame = 6 // 1..10","label":null,"prefix":null,"suffix":null,"section":"Current 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(including mortar joint)","label":null,"prefix":null,"suffix":null,"section":"Brick Dimensions (including mortar joint)","hero":false,"slider":null,"value":null,"display":null},{"text":"brick length = 8 // inches","label":null,"prefix":null,"suffix":"inches","section":"Brick Dimensions (including mortar joint)","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"brick height = 2.25 // inches","label":null,"prefix":null,"suffix":"inches","section":"Brick Dimensions (including mortar joint)","hidden":false,"hero":false,"slider":null,"value":2.25,"display":"2.25"},{"text":"mortar joint = 0.5 // inches","label":null,"prefix":null,"suffix":"inches","section":"Brick Dimensions (including mortar joint)","hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_effective_brick_length = brick length + 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bricks needed = roundup(wall_area_square_inches / brick_area_square_inches) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":986,"display":"986"},{"text":"waste factor percent = 10 // 0..25","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":{"min":0,"max":25,"step":1},"value":10,"display":"10"},{"text":"total bricks with waste = roundup(total bricks needed * (1 + waste factor percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":1085,"display":"1,085"}]},{"id":"brine-salt-percentage","title":"Brine Salt Percentage","description":"Calculate brine salt percentage from water volume and salt weight.","category":"health","icon":"activity","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"water_volume_milliliters = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"salt_weight_grams = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"salt_percentage = (salt_weight_grams / (water_volume_milliliters + salt_weight_grams)) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4.761904761904762,"display":"4.762"}]},{"id":"btu-air-conditioner-sizing","title":"Btu Air Conditioner Sizing","description":"Estimate BTU air conditioner size needed from room area, occupants, and sun exposure.","category":"other","icon":"calculator","tags":["air"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Room Info","label":null,"prefix":null,"suffix":null,"section":"Room 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inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"end_condition_factor_k = 1 // 1 for pinned-pinned","label":null,"prefix":null,"suffix":"1 for pinned-pinned","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"critical_buckling_load_lbs = (3.14159^2 * elastic_modulus_psi * moment_of_inertia_in4) / ((end_condition_factor_k * column_length_inches)^2) // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":true,"slider":null,"value":39752.50612706944,"display":"39,752.51"}]},{"id":"buff-duration-extension","title":"Buff Duration Extension","description":"Calculate extended buff duration.","category":"math","icon":"clock","tags":["gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Buff Settings","label":null,"prefix":null,"suffix":null,"section":"Buff 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balances.","category":"science","icon":"flame","tags":["burn","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Startup Cash","label":null,"prefix":null,"suffix":null,"section":"Startup Cash","hero":false,"slider":null,"value":null,"display":null},{"text":"$starting cash balance = 500000 // 10k..10M","label":null,"prefix":"$","suffix":null,"section":"Startup Cash","hidden":false,"hero":false,"slider":{"min":10000,"max":10000000,"step":100000},"value":500000,"display":"$500,000.00"},{"text":"$ending cash balance = 350000 // 0..10M","label":null,"prefix":"$","suffix":null,"section":"Startup Cash","hidden":false,"hero":false,"slider":{"min":0,"max":10000000,"step":100000},"value":350000,"display":"$350,000.00"},{"text":"number of months = 6 // months 1..24","label":null,"prefix":null,"suffix":"months","section":"Startup Cash","hidden":false,"hero":false,"slider":{"min":1,"max":24,"step":1},"value":6,"display":"6"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_cash_burned = starting cash balance - ending cash balance","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":150000,"display":"$150,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly burn rate = total_cash_burned / number of months // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":25000,"display":"$25,000.00"},{"text":"runway in months = ending cash balance / monthly burn rate","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"$annual burn = monthly burn rate * 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":300000,"display":"$300,000.00"}]},{"id":"burnout-risk-score","title":"Burnout Risk Score","description":"Estimate burnout risk from weekly work hours, stress, and autonomy levels.","category":"health","icon":"brain","tags":["risk"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"work_hours_per_week = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"stress_level_1_to_10 = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"autonomy_level_1_to_10 = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"risk_score = (work_hours_per_week * stress_level_1_to_10) / autonomy_level_1_to_10 // risk index @hero","label":null,"prefix":null,"suffix":"risk index","section":null,"hidden":false,"hero":true,"slider":null,"value":133.33333333333334,"display":"133.33"}]},{"id":"business-downtime-cost-per-minute","title":"Business Downtime Cost Per Minute","description":"Estimate the revenue cost of one hour of business downtime.","category":"productivity","icon":"clock","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"annual_revenue = 1000000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"business_hours_per_year = 2080 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":2080,"display":"2,080"},{"text":"_revenue_per_minute = annual_revenue / (business_hours_per_year * 60)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":8.012820512820513,"display":"8.013"},{"text":"downtime_cost_60_minutes = revenue_per_minute * 60 // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":480.7692307692308,"display":"480.77"}]},{"id":"buttons-and-controls","title":"⚡ Buttons & Controls — Instacalc","description":"A tour of the input controls — plus the new **action buttons** that set values (even a field inside an object) in one tap. Change anything; the readouts update live, and the whole state stays in the URL — nothing is hidden, so it's all shareable and undoable.","category":"demo","icon":"toggle-left","tags":["demo"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-27T19:43:20.603Z"},"rows":[{"text":"# 🎛️ Inputs @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"🎛️ Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"rate = 60 // 0..200 by 10 @suffix( /s) @label(🎚️ Slider)","label":"🎚️ Slider","prefix":null,"suffix":null,"section":"🎛️ Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":200,"step":10},"value":60,"display":"60"},{"text":"tier = \"Mk2\" // radio(Mk1, Mk2, Mk3) @label(🔘 Segmented)","label":"🔘 Segmented","prefix":null,"suffix":null,"section":"🎛️ Inputs","hidden":false,"hero":false,"slider":null,"value":"Mk2","display":"Mk2"},{"text":"boost = true // toggle() @label(🎛️ Toggle)","label":"🎛️ Toggle","prefix":null,"suffix":null,"section":"🎛️ Inputs","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"},{"text":"color = {r: 80, g: 120, b: 200} // @label(🎨 Color object)","label":"🎨 Color object","prefix":null,"suffix":null,"section":"🎛️ Inputs","hidden":false,"hero":false,"slider":null,"value":{"r":80,"g":120,"b":200},"display":null},{"text":"unit = \"Newton\" // combobox(Newton, Pascal, Joule, Watt, Kelvin, Ampere, Tesla, Henry, Ohm, Volt) @label(🔎 Combobox — type to filter)","label":"🔎 Combobox — type to filter","prefix":null,"suffix":null,"section":"🎛️ Inputs","hidden":false,"hero":false,"slider":null,"value":"Newton","display":"Newton"},{"text":"# ⚡ Action buttons @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"⚡ Action buttons","hero":false,"slider":null,"value":null,"display":null},{"text":"presets = \"\" // buttons({🐣 Min: {rate: 0, boost: false}, ⚖️ Mid: {rate: 100, boost: true}, 🚀 Max: {rate: 200, boost: true, tier: \"Mk3\"}}) @label(Presets — set many at once)","label":"Presets — set many at once","prefix":null,"suffix":null,"section":"⚡ Action buttons","hidden":false,"hero":false,"slider":null,"value":"","display":null},{"text":"fields = \"\" // buttons({🔴 Redder: {color.r: 255}, 🟢 Greener: {color.g: 255}, ↩️ Reset: {color.r: 80, color.g: 120, color.b: 200}}) @label(Set a field in an object)","label":"Set a field in an object","prefix":null,"suffix":null,"section":"⚡ Action buttons","hidden":false,"hero":false,"slider":null,"value":"","display":null},{"text":"step = \"\" // buttons({➖ Less: {rate: rate - 20}, ➕ More: {rate: rate + 20}, ✖️ Double: {rate: rate * 2}, ➗ Half: {rate: rate / 2}}) @label(Increment / decrement (relative to current))","label":"Increment / decrement (relative to current)","prefix":null,"suffix":null,"section":"⚡ Action buttons","hidden":false,"hero":false,"slider":null,"value":"","display":null},{"text":"# 📤 Live readouts @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"📤 Live readouts","hero":false,"slider":null,"value":null,"display":null},{"text":"throughput = rate*if(boost, 2, 1) // @label(⚙️ Throughput) @suffix( /s) @hero","label":"⚙️ Throughput","prefix":null,"suffix":null,"section":"📤 Live readouts","hidden":false,"hero":true,"slider":null,"value":120,"display":"120"},{"text":"red channel = color.r // @label(🎨 Red) @hero","label":"🎨 Red","prefix":null,"suffix":null,"section":"📤 Live readouts","hidden":false,"hero":true,"slider":null,"value":80,"display":"80"},{"text":"tier picked = tier // @label(🔘 Tier)","label":"🔘 Tier","prefix":null,"suffix":null,"section":"📤 Live readouts","hidden":false,"hero":false,"slider":null,"value":"Mk2","display":"Mk2"}]},{"id":"bystander-effect-probability","title":"Bystander Effect Probability","description":"Calculate the probability that at least one bystander helps in an emergency.","category":"health","icon":"brain","tags":["effect","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"number_of_bystanders = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"probability_of_help_per_person = 0.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"probability_anyone_helps = 1 - (1 - probability_of_help_per_person)^number_of_bystanders // probability @hero","label":null,"prefix":null,"suffix":"probability","section":null,"hidden":false,"hero":true,"slider":null,"value":0.4095099999999999,"display":"0.4095"}]},{"id":"cabinet-hardware-placement","title":"Cabinet Hardware Placement","description":"Calculate centering and offset for pulls and knobs.","category":"design","icon":"layout","tags":["design","woodworking"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"door_height_inches = 30 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"door_width_inches = 15 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"pull_length_inches = 4 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"offset_from_edge_inches = 2 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"vertical_center_position_from_bottom = door_height_inches - offset_from_edge_inches - (pull_length_inches / 2) // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":26,"display":"26"}]},{"id":"caffeine","title":"Caffeine Half-Life","description":"Track how much caffeine remains in your system over time based on your metabolism.","category":"health","icon":"coffee","tags":["coffee","sleep","half-life"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Caffeine Metabolism","label":null,"prefix":null,"suffix":null,"section":"Caffeine Metabolism","hero":false,"slider":null,"value":null,"display":null},{"text":"half life = 5 // hours 2..10 by 0.5","label":null,"prefix":null,"suffix":"hours","section":"Caffeine Metabolism","hidden":false,"hero":false,"slider":{"min":2,"max":10,"step":0.5},"value":5,"display":"5"},{"text":"initial dose = 100 // mg 10..500","label":null,"prefix":null,"suffix":"mg","section":"Caffeine Metabolism","hidden":false,"hero":false,"slider":{"min":10,"max":500,"step":1},"value":100,"display":"100"},{"text":"hours since dose = 10 // hours 0..24","label":null,"prefix":null,"suffix":"hours","section":"Caffeine Metabolism","hidden":false,"hero":false,"slider":{"min":0,"max":24,"step":1},"value":10,"display":"10"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"decay constant = ln(2) / half life","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":0.13862943611198905,"display":"0.1386"},{"text":"amount remaining = round(initial dose * E^(-decay constant * hours since dose) * 10) / 10 // mg @hero","label":null,"prefix":null,"suffix":"mg","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":25,"display":"25"},{"text":"percent remaining = round((amount remaining / initial dose) * 100) // %","label":null,"prefix":null,"suffix":"%","section":"Calculation","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"# Sleep Context","label":null,"prefix":null,"suffix":null,"section":"Sleep Context","hero":false,"slider":null,"value":null,"display":null},{"text":"midnight = 24","label":null,"prefix":null,"suffix":null,"section":"Sleep Context","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"dose time = 14 // 2pm","label":null,"prefix":null,"suffix":"2pm","section":"Sleep Context","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"hours to midnight = midnight - dose time","label":null,"prefix":null,"suffix":null,"section":"Sleep Context","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"amount at midnight = round(initial dose * E^(-decay constant * hours to midnight) * 10) / 10 // mg","label":null,"prefix":null,"suffix":"mg","section":"Sleep Context","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"half lives to midnight = hours to midnight / half life","label":null,"prefix":null,"suffix":null,"section":"Sleep Context","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"dose at 2pm remaining at midnight = 1 / 2^half_lives_to_midnight","label":null,"prefix":null,"suffix":null,"section":"Sleep Context","hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"}]},{"id":"calculus-explorer","title":"Calculus Explorer","description":"Differentiate and integrate any function — the engine's `derivative()` and `integral()` return results you can graph and evaluate.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# The function to study","label":null,"prefix":null,"suffix":null,"section":"The function to study","hero":false,"slider":null,"value":null,"display":null},{"text":"f(x) = x^2","label":null,"prefix":null,"suffix":null,"section":"The function to study","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["power",["parenExpr",{"type":"id","value":"x","text":"x","offset":17,"lineBreaks":0,"line":1,"col":18}],{"type":"decimal","value":"2","text":"2","offset":20,"lineBreaks":0,"line":1,"col":21}],"name":"f"},"display":null},{"text":"# Derivative as a callable: f'(x) = 2x","label":null,"prefix":null,"suffix":null,"section":"Derivative as a callable: f'(x) = 2x","hero":false,"slider":null,"value":null,"display":null},{"text":"slope = derivative(f)","label":null,"prefix":null,"suffix":null,"section":"Derivative as a callable: f'(x) = 2x","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"derive","text":"derive"},[["folded",{"type":"function","params":["x"],"body":["power",["parenExpr",{"type":"id","value":"x","text":"x","offset":17,"lineBreaks":0,"line":1,"col":18}],{"type":"decimal","value":"2","text":"2","offset":20,"lineBreaks":0,"line":1,"col":21}],"name":"f"}],{"type":"id","value":"x","text":"x"}]],"name":"slope"},"display":null},{"text":"# Slope at a specific point","label":null,"prefix":null,"suffix":null,"section":"Slope at a specific point","hero":false,"slider":null,"value":null,"display":null},{"text":"x0 = 3 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Slope at a specific point","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":3,"display":"3"},{"text":"slope_at_x0 = derivative(f, x0) // @hero @label(f'(x₀))","label":"f'(x₀)","prefix":null,"suffix":null,"section":"Slope at a specific point","hidden":false,"hero":true,"slider":null,"value":5.999999999994649,"display":"6"},{"text":"# See the derivative as a curve — the line 2x","label":null,"prefix":null,"suffix":null,"section":"See the derivative as a curve — the line 2x","hero":false,"slider":null,"value":null,"display":null},{"text":"# Definite integral: the area under x² from a to b","label":null,"prefix":null,"suffix":null,"section":"Definite integral: the area under x² from a to b","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 0 // -5..5","label":null,"prefix":null,"suffix":null,"section":"Definite integral: the area under x² from a to b","hidden":false,"hero":false,"slider":{"min":-5,"max":5,"step":0.1},"value":0,"display":"0"},{"text":"b = 1 // -5..5","label":null,"prefix":null,"suffix":null,"section":"Definite integral: the area under x² from a to b","hidden":false,"hero":false,"slider":{"min":-5,"max":5,"step":0.1},"value":1,"display":"1"},{"text":"area = integral(x^2, a, b) // @hero @label(∫ₐᵇ x² dx)","label":"∫ₐᵇ x² dx","prefix":null,"suffix":null,"section":"Definite integral: the area under x² from a to b","hidden":false,"hero":true,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"# Indefinite integral — the antiderivative x³/3, as a graphable curve","label":null,"prefix":null,"suffix":null,"section":"Indefinite integral — the antiderivative x³/3, as a graphable curve","hero":false,"slider":null,"value":null,"display":null},{"text":"# Fundamental theorem check: the antiderivative of x³ is x⁴/4,","label":null,"prefix":null,"suffix":null,"section":"Fundamental theorem check: the antiderivative of x³ is x⁴/4,","hero":false,"slider":null,"value":null,"display":null},{"text":"# so ∫₀² x³ dx should equal (2⁴ − 0)/4 = 4.","label":null,"prefix":null,"suffix":null,"section":"so ∫₀² x³ dx should equal (2⁴ − 0)/4 = 4.","hero":false,"slider":null,"value":null,"display":null},{"text":"cubic_area = integral(x^3, 0, 2) // @label(∫₀² x³ dx)","label":"∫₀² x³ dx","prefix":null,"suffix":null,"section":"so ∫₀² x³ dx should equal (2⁴ − 0)/4 = 4.","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"}]},{"id":"calorie-deficit","title":"Calorie Deficit","description":"Calculate your TDEE and calorie targets for weight loss using the Mifflin-St Jeor equation.","category":"health","icon":"utensils","tags":["calories"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Your Stats","label":null,"prefix":null,"suffix":null,"section":"Your Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"current weight = 180 // lbs 80..400","label":null,"prefix":null,"suffix":"lbs","section":"Your Stats","hidden":false,"hero":false,"slider":{"min":80,"max":400,"step":1},"value":180,"display":"180"},{"text":"height = 70 // inches 48..84","label":null,"prefix":null,"suffix":"inches","section":"Your Stats","hidden":false,"hero":false,"slider":{"min":48,"max":84,"step":1},"value":70,"display":"70"},{"text":"age = 30 // years 15..80","label":null,"prefix":null,"suffix":"years","section":"Your Stats","hidden":false,"hero":false,"slider":{"min":15,"max":80,"step":1},"value":30,"display":"30"},{"text":"activity factor = 1.55 // 1.2..1.9 by 0.05","label":null,"prefix":null,"suffix":null,"section":"Your Stats","hidden":false,"hero":false,"slider":{"min":1.2,"max":1.9,"step":0.05},"value":1.55,"display":"1.55"},{"text":"# Metabolic Rate","label":null,"prefix":null,"suffix":null,"section":"Metabolic Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"_weight_kg = current_weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"Metabolic Rate","hidden":true,"hero":false,"slider":null,"value":81.64656,"display":"81.65"},{"text":"_height_cm = height * 2.54","label":null,"prefix":null,"suffix":null,"section":"Metabolic Rate","hidden":true,"hero":false,"slider":null,"value":177.8,"display":"177.8"},{"text":"_basal_metabolic_rate = round(10 * weight_kg + 6.25 * height_cm - 5 * age + 5) // cal","label":null,"prefix":null,"suffix":"cal","section":"Metabolic Rate","hidden":true,"hero":false,"slider":null,"value":1783,"display":"1,783"},{"text":"total daily energy = round(basal_metabolic_rate * activity_factor) // cal @hero","label":null,"prefix":null,"suffix":"cal","section":"Metabolic Rate","hidden":false,"hero":true,"slider":null,"value":2764,"display":"2,764"},{"text":"# Weight Loss Targets @layout(grid)","label":null,"prefix":null,"suffix":null,"section":"Weight Loss Targets","hero":false,"slider":null,"value":null,"display":null},{"text":"mild loss = total_daily_energy - 250 // cal/day","label":null,"prefix":null,"suffix":"cal/day","section":"Weight Loss Targets","hidden":false,"hero":false,"slider":null,"value":2514,"display":"2,514"},{"text":"moderate loss = total_daily_energy - 500 // cal/day","label":null,"prefix":null,"suffix":"cal/day","section":"Weight Loss Targets","hidden":false,"hero":false,"slider":null,"value":2264,"display":"2,264"},{"text":"aggressive loss = total_daily_energy - 1000 // cal/day","label":null,"prefix":null,"suffix":"cal/day","section":"Weight Loss Targets","hidden":false,"hero":false,"slider":null,"value":1764,"display":"1,764"}]},{"id":"calories-burned-standing-desk","title":"Calories Burned Standing Desk","description":"Estimate extra calories burned standing instead of sitting at a desk.","category":"health","icon":"activity","tags":["calories","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"user_weight_pounds = 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"standing_hours = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"additional_calories_burned = standing_hours * 60 * 0.15 * (user_weight_pounds / 150) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":43.2,"display":"43.2"}]},{"id":"camera-iso-noise-estimate","title":"Camera Iso Noise Estimate","description":"Estimate camera noise increase as ISO rises above the base ISO.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"base_iso = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"current_iso = 3200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3200,"display":"3,200"},{"text":"base_noise_percent = 0.5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"estimated_noise_percent = base_noise_percent * (current_iso / base_iso)^0.5 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.8284271247461903,"display":"2.828"}]},{"id":"camera-sensor-crop-factor","title":"Camera Sensor Crop Factor","description":"Calculate a camera sensor's crop factor relative to full-frame 35mm.","category":"math","icon":"camera","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"sensor_width_millimeters = 23.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":23.5,"display":"23.5"},{"text":"sensor_height_millimeters = 15.6","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15.6,"display":"15.6"},{"text":"full_frame_diagonal = (36^2 + 24^2)^0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":43.266615305567875,"display":"43.27"},{"text":"sensor_diagonal = (sensor_width_millimeters^2 + sensor_height_millimeters^2)^0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":28.20655952079232,"display":"28.21"},{"text":"crop_factor = full_frame_diagonal / sensor_diagonal // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.5339203377027997,"display":"1.534"}]},{"id":"camshaft-lift-duration","title":"Camshaft Lift Duration","description":"Calculate valve lift from lobe lift and rocker 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@hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":13.333333333333334,"display":"13.33"}]},{"id":"canning-processing-time-altitude","title":"Canning Processing Time Altitude","description":"Adjust home canning processing time for altitude above sea level.","category":"productivity","icon":"clock","tags":["altitude","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"standard_time_minutes = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"altitude_feet = 4500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4500,"display":"4,500"},{"text":"time_increase = (altitude_feet > 6000) ? 15 : (altitude_feet > 3000) ? 10 : (altitude_feet > 1000) ? 5 : 0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"adjusted_time_minutes = standard_time_minutes + time_increase // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"cantilever-beam-stress","title":"Cantilever Beam Stress","description":"Calculate max bending stress for a cantilever beam.","category":"engineering","icon":"ruler","tags":["engineering","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"force_at_tip_lbs = 200 // lbs","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"beam_length_inches = 48 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"section_modulus_in3 = 2 // in^3","label":null,"prefix":null,"suffix":"in^3","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"max_bending_stress_psi = (force_at_tip_lbs * beam_length_inches) / section_modulus_in3 // psi @hero","label":null,"prefix":null,"suffix":"psi","section":null,"hidden":false,"hero":true,"slider":null,"value":4800,"display":"4,800"}]},{"id":"canvas-dpi-print-resolution","title":"Canvas Dpi Print Resolution","description":"Calculate pixel dimensions needed to print a canvas at a target DPI.","category":"design","icon":"palette","tags":["print"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"width_inches = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"height_inches = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"dpi = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"width_pixels = width_inches * dpi // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":2400,"display":"2,400"},{"text":"height_pixels = height_inches * dpi // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":3000,"display":"3,000"}]},{"id":"cap-rate-by-neighborhood","title":"Cap Rate by Neighborhood","description":"Calculate the capitalization rate for specific local real 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percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":true,"hero":false,"slider":null,"value":99.3,"display":"99.3"}]},{"id":"capital-expenditure-capex-reserve","title":"CapEx Reserve","description":"Calculate the recommended monthly reserve for major repairs.","category":"real-estate","icon":"archive","tags":["capital"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"grossMonthlyRent = 2000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"capexReservePercentage = 8 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"monthlyCapexReserve = grossMonthlyRent * (capexReservePercentage / 100) // @prefix($) @suffix(/mo) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":160,"display":"160"}]},{"id":"capital-gains-tax","title":"Capital Gains Tax","description":"Estimate capital gains tax owed and net proceeds after selling an asset.","category":"finance","icon":"dollar-sign","tags":["capital","tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Asset Sale","label":null,"prefix":null,"suffix":null,"section":"Asset Sale","hero":false,"slider":null,"value":null,"display":null},{"text":"$sale price = 50000 // 1k..1M","label":null,"prefix":"$","suffix":null,"section":"Asset Sale","hidden":false,"hero":false,"slider":{"min":1000,"max":1000000,"step":10000},"value":50000,"display":"$50,000.00"},{"text":"$purchase price = 30000 // 1k..1M","label":null,"prefix":"$","suffix":null,"section":"Asset 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adjusted_basis","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":18000,"display":"$18,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated capital gains tax = if(capital_gain > 0, capital_gain * (capital gains tax rate / 100), 0) // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":2700,"display":"$2,700.00"},{"text":"$net proceeds after tax = sale price - estimated capital gains tax","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":47300,"display":"$47,300.00"},{"text":"return on investment = (capital_gain / adjusted_basis) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":56.25,"display":"56.25"}]},{"id":"car-affordability","title":"Car Affordability","description":"Find the max car price you can afford from your monthly budget.","category":"finance","icon":"car","tags":["car","budget"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Budget","label":null,"prefix":null,"suffix":null,"section":"Budget","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly budget = 500 // 100..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Budget","hidden":false,"hero":false,"slider":{"min":100,"max":2000,"step":25},"value":500,"display":"$500.00"},{"text":"interest rate = 6 // % 0..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Budget","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.1},"value":6,"display":"6"},{"text":"loan term = 60 // months 12..84","label":null,"prefix":null,"suffix":"months","section":"Budget","hidden":false,"hero":false,"slider":{"min":12,"max":84,"step":1},"value":60,"display":"60"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":0.005,"display":"0.005"},{"text":"$max loan = round(monthly budget * ((1 + monthly rate)^loan term - 1) / (monthly rate * (1 + monthly rate)^loan term) * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":25862.78,"display":"$25,862.78"},{"text":"$down payment = 3000 // 0..30k","label":null,"prefix":"$","suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":{"min":0,"max":30000,"step":500},"value":3000,"display":"$3,000.00"},{"text":"# Affordability","label":null,"prefix":null,"suffix":null,"section":"Affordability","hero":false,"slider":null,"value":null,"display":null},{"text":"$max car price = max loan + down payment // @hero","label":null,"prefix":"$","suffix":null,"section":"Affordability","hidden":false,"hero":true,"slider":null,"value":28862.78,"display":"$28,862.78"},{"text":"$total paid = round((monthly budget * loan term + down payment) * 100) / 100 // @label(Total Cost Over Loan)","label":"Total Cost Over Loan","prefix":"$","suffix":null,"section":"Affordability","hidden":false,"hero":false,"slider":null,"value":33000,"display":"$33,000.00"},{"text":"$total interest = round((total paid - max car price) * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Affordability","hidden":false,"hero":false,"slider":null,"value":4137.22,"display":"$4,137.22"}]},{"id":"car-depreciation","title":"Car Depreciation","description":"Calculate a car's current value, total depreciation, and percent retained.","category":"other","icon":"car","tags":["car","depreciation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Car Value","label":null,"prefix":null,"suffix":null,"section":"Car Value","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchase price = 35000 // 5k..150k by 500","label":null,"prefix":"$","suffix":null,"section":"Car Value","hidden":false,"hero":false,"slider":{"min":5000,"max":150000,"step":500},"value":35000,"display":"$35,000.00"},{"text":"annual depreciation rate = 15 // % 5..30","label":null,"prefix":null,"suffix":"%","section":"Car Value","hidden":false,"hero":false,"slider":{"min":5,"max":30,"step":1},"value":15,"display":"15"},{"text":"age in years = 3 // years 0..20","label":null,"prefix":null,"suffix":"years","section":"Car Value","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":3,"display":"3"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"$current value = purchase price * (1 - annual depreciation rate / 100)^age in years // @hero","label":null,"prefix":"$","suffix":null,"section":"Results","hidden":false,"hero":true,"slider":null,"value":21494.374999999996,"display":"$21,494.37"},{"text":"$total depreciation = purchase price - current value","label":null,"prefix":"$","suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":13505.625000000004,"display":"$13,505.63"},{"text":"percent value retained = (current value / purchase price) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Results","hidden":false,"hero":false,"slider":null,"value":61.41249999999999,"display":"61.41"}]},{"id":"car-loan","title":"Car Loan","description":"Calculate monthly car payments, total cost, and interest.","category":"finance","icon":"car","tags":["car","loan"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Car Details","label":null,"prefix":null,"suffix":null,"section":"Car Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$car price = 35000 // 5k..100k","label":null,"prefix":"$","suffix":null,"section":"Car Details","hidden":false,"hero":false,"slider":{"min":5000,"max":100000,"step":1000},"value":35000,"display":"$35,000.00"},{"text":"$down payment = 5000 // 0..50k","label":null,"prefix":"$","suffix":null,"section":"Car Details","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":500},"value":5000,"display":"$5,000.00"},{"text":"interest rate = 5.5 // % 0..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Car Details","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.1},"value":5.5,"display":"5.5"},{"text":"loan term = 60 // months 12..84","label":null,"prefix":null,"suffix":"months","section":"Car Details","hidden":false,"hero":false,"slider":{"min":12,"max":84,"step":1},"value":60,"display":"60"},{"text":"# Loan Calculation","label":null,"prefix":null,"suffix":null,"section":"Loan Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = car price - down payment","label":null,"prefix":"$","suffix":null,"section":"Loan Calculation","hidden":false,"hero":false,"slider":null,"value":30000,"display":"$30,000.00"},{"text":"monthly rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Loan Calculation","hidden":false,"hero":false,"slider":null,"value":0.004583333333333333,"display":"0.004583"},{"text":"$monthly payment = loan amount * (monthly rate * (1 + monthly rate)^loan term) / ((1 + monthly rate)^loan term - 1) // @hero","label":null,"prefix":"$","suffix":null,"section":"Loan Calculation","hidden":false,"hero":true,"slider":null,"value":573.0348651534617,"display":"$573.03"},{"text":"# Total Cost","label":null,"prefix":null,"suffix":null,"section":"Total Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$total paid = round(monthly payment * loan term * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Total Cost","hidden":false,"hero":false,"slider":null,"value":34382.09,"display":"$34,382.09"},{"text":"$total interest = round((total paid - loan amount) * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Total Cost","hidden":false,"hero":false,"slider":null,"value":4382.09,"display":"$4,382.09"},{"text":"$total car cost = round((total paid + down payment) * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Total Cost","hidden":false,"hero":false,"slider":null,"value":39382.09,"display":"$39,382.09"}]},{"id":"car-rental-vs-own","title":"Car Rental vs Own","description":"Compare monthly cost of owning a car against renting one as needed.","category":"other","icon":"car","tags":["car","rental"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Ownership Costs","label":null,"prefix":null,"suffix":null,"section":"Ownership Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly car payment = 500 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Ownership Costs","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":500,"display":"$500.00"},{"text":"$monthly insurance = 150 // 0..500 by 10","label":null,"prefix":"$","suffix":null,"section":"Ownership Costs","hidden":false,"hero":false,"slider":{"min":0,"max":500,"step":10},"value":150,"display":"$150.00"},{"text":"$monthly maintenance and gas = 200 // 0..1k by 25","label":null,"prefix":"$","suffix":null,"section":"Ownership Costs","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":25},"value":200,"display":"$200.00"},{"text":"# Rental Costs","label":null,"prefix":null,"suffix":null,"section":"Rental Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$rental cost per day = 80 // 20..500","label":null,"prefix":"$","suffix":null,"section":"Rental Costs","hidden":false,"hero":false,"slider":{"min":20,"max":500,"step":1},"value":80,"display":"$80.00"},{"text":"days needed per month = 10 // days 0..31","label":null,"prefix":null,"suffix":"days","section":"Rental Costs","hidden":false,"hero":false,"slider":{"min":0,"max":31,"step":1},"value":10,"display":"10"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_monthly_ownership_cost = monthly car payment + monthly insurance + monthly maintenance and gas","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":850,"display":"$850.00"},{"text":"$_total_monthly_rental_cost = rental cost per day * days needed per month","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":800,"display":"$800.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly savings by renting = total_monthly_ownership_cost - total_monthly_rental_cost // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":50,"display":"$50.00"},{"text":"$annual ownership cost = total_monthly_ownership_cost * 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":10200,"display":"$10,200.00"},{"text":"$annual rental cost = total_monthly_rental_cost * 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":9600,"display":"$9,600.00"},{"text":"break even days per month = total_monthly_ownership_cost / rental cost per day","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":10.625,"display":"10.63"}]},{"id":"carbon-sequestration-per-tree","title":"Carbon Sequestration Per Tree","description":"Estimate annual CO2 sequestered by a tree from age and growth rate.","category":"health","icon":"activity","tags":["carbon","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"tree_age_years = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"growth_rate_factor = 1.0 // 1.0 for average, 1.5 for fast","label":null,"prefix":null,"suffix":"1.0 for average, 1.5 for fast","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"annual_co2_sequestered_pounds = 48 * growth_rate_factor * (min(tree_age_years, 25) / 25) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":38.4,"display":"38.4"}]},{"id":"carpet-area-calculator","title":"Carpet Area Calculator","description":"Calculate carpet square yardage and total cost from room dimensions and waste.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Room Dimensions","label":null,"prefix":null,"suffix":null,"section":"Room 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10..100","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":{"min":10,"max":100,"step":1},"value":30,"display":"$30.00"},{"text":"$total cost = round(total yards with waste * price per square yard, 2)","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":null,"value":660,"display":"$660.00"}]},{"id":"carpooling-emissions-savings","title":"Carpooling Emissions Savings","description":"Calculate annual CO2 savings by sharing your commute.","category":"science","icon":"users","tags":["eco","travel","emissions"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"commute_distance_km = 30 // km","label":null,"prefix":null,"suffix":"km","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"days_per_year = 240 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":240,"display":"240"},{"text":"carpool_members = 3 // people","label":null,"prefix":null,"suffix":"people","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"emissions_per_km = 0.15 // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"total_annual_emissions_solo = commute_distance_km * 2 * days_per_year * emissions_per_km // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":2160,"display":"2,160"},{"text":"annual_emissions_per_person_carpool = total_annual_emissions_solo / carpool_members // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":720,"display":"720"},{"text":"annual_co2_savings_per_person = total_annual_emissions_solo - annual_emissions_per_person_carpool // kg CO2 @hero","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":true,"slider":null,"value":1440,"display":"1,440"}]},{"id":"cash-conversion-cycle","title":"Cash Conversion Cycle","description":"Calculate the cash conversion cycle from inventory, receivable, and payable days.","category":"finance","icon":"dollar-sign","tags":["cash","cycle","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"days_inventory_outstanding = 60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"days_sales_outstanding = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"days_payable_outstanding = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"cash_conversion_cycle = days_inventory_outstanding + days_sales_outstanding - days_payable_outstanding","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":75,"display":"75"}]},{"id":"cash-on-cash-return-advanced","title":"Cash on Cash Return","description":"Calculate annual return based on the actual cash invested.","category":"real-estate","icon":"dollar-sign","tags":["cash"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"annualPreTaxCashFlow = 5000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"totalCashInvested = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"cashOnCashReturn = (annualPreTaxCashFlow / totalCashInvested) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"cash-on-cash-return","title":"Cash On Cash Return","description":"Calculate cash-on-cash return and recoup time from down payment and annual cash flow.","category":"finance","icon":"dollar-sign","tags":["cash","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Investment Analysis","label":null,"prefix":null,"suffix":null,"section":"Investment Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchase price = 300000 // 50k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":50000,"max":1000000,"step":5000},"value":300000,"display":"$300,000.00"},{"text":"$down payment = 60000 // 0..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":1000},"value":60000,"display":"$60,000.00"},{"text":"$closing costs = 9000 // 0..50k","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":500},"value":9000,"display":"$9,000.00"},{"text":"$total annual pre tax cash flow = 7200 // 0..50k by 100","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":100},"value":7200,"display":"$7,200.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_cash_invested = down payment + closing costs","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":69000,"display":"$69,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"cash on cash return = (total annual pre tax cash flow / total_cash_invested) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":10.434782608695652,"display":"10.43"},{"text":"$monthly cash flow = total annual pre tax cash flow / 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":600,"display":"$600.00"},{"text":"years to recoup investment = total_cash_invested / total annual pre tax cash flow","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":9.583333333333334,"display":"9.583"}]},{"id":"cat-years-to-human-years","title":"Cat Years To Human Years","description":"Convert a cat's age in years to its equivalent human age.","category":"everyday","icon":"cat","tags":["human","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"actual_cat_age_years = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"first_year_human_equivalent = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"second_year_human_equivalent = 9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"additional_years_multiplier = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"equivalent_human_age = first_year_human_equivalent + second_year_human_equivalent + (actual_cat_age_years - 2) * additional_years_multiplier","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"cell-turnover","title":"Cell Turnover","description":"Total cells in the body and how many are replaced each day or year.","category":"health","icon":"atom","tags":["biology","body","turnover"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"# Person","label":null,"prefix":null,"suffix":null,"section":"Person","hero":false,"slider":null,"value":null,"display":null},{"text":"body weight kg = 70 // kg 1..200","label":null,"prefix":null,"suffix":"kg","section":"Person","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":70,"display":"70"},{"text":"turnover years = 7 // years 1..80","label":null,"prefix":null,"suffix":"years","section":"Person","hidden":false,"hero":false,"slider":{"min":1,"max":80,"step":1},"value":7,"display":"7"},{"text":"# Cell Count (≈ 528 billion per kg)","label":null,"prefix":null,"suffix":null,"section":"Cell Count (≈ 528 billion per kg)","hero":false,"slider":null,"value":null,"display":null},{"text":"_cells_per_kg = 528000000000","label":null,"prefix":null,"suffix":null,"section":"Cell Count (≈ 528 billion per kg)","hidden":true,"hero":false,"slider":null,"value":528000000000,"display":"528,000,000,000"},{"text":"total cells = body weight kg * cells_per_kg // @hero @label(Total cells in body)","label":"Total cells in body","prefix":null,"suffix":null,"section":"Cell Count (≈ 528 billion per kg)","hidden":false,"hero":true,"slider":null,"value":36960000000000,"display":"36,960,000,000,000"},{"text":"# Replacement Rate","label":null,"prefix":null,"suffix":null,"section":"Replacement Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"cells per year = total cells / turnover years // @label(Cells replaced per year)","label":"Cells replaced per year","prefix":null,"suffix":null,"section":"Replacement Rate","hidden":false,"hero":false,"slider":null,"value":5280000000000,"display":"5,280,000,000,000"},{"text":"cells per day = cells per year / 365 // @label(Cells replaced per day)","label":"Cells replaced per day","prefix":null,"suffix":null,"section":"Replacement Rate","hidden":false,"hero":false,"slider":null,"value":14465753424.657534,"display":"14,465,753,424.66"},{"text":"cells per second = round(cells per day / 86400) // @label(Cells replaced per second)","label":"Cells replaced per second","prefix":null,"suffix":null,"section":"Replacement Rate","hidden":false,"hero":false,"slider":null,"value":167428,"display":"167,428"},{"text":"# Lifetime","label":null,"prefix":null,"suffix":null,"section":"Lifetime","hero":false,"slider":null,"value":null,"display":null},{"text":"lifetime years = 80 // years 1..120","label":null,"prefix":null,"suffix":"years","section":"Lifetime","hidden":false,"hero":false,"slider":{"min":1,"max":120,"step":1},"value":80,"display":"80"},{"text":"total replacements = round(lifetime years / turnover years, 1) // @label(Full-body replacements in a lifetime)","label":"Full-body replacements in a lifetime","prefix":null,"suffix":null,"section":"Lifetime","hidden":false,"hero":false,"slider":null,"value":11.4,"display":"11.4"}]},{"id":"centripetal-acceleration-rotation","title":"Centripetal Acceleration Rotation","description":"Calculate centripetal acceleration from rotational radius and velocity.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"radius = 5 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"velocity = 10 // meters per second","label":null,"prefix":null,"suffix":"meters per second","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"centripetal_acceleration = velocity^2 / radius // meters per second squared @hero","label":null,"prefix":null,"suffix":"meters per second squared","section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"chain-drive-speed-ratio","title":"Chain Drive Speed Ratio","description":"Calculate driven RPM and ratio for chain and sprocket.","category":"engineering","icon":"settings","tags":["engineering","mechanical","drive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"driver_sprocket_teeth = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"driven_sprocket_teeth = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"driver_rpm = 1000 // RPM","label":null,"prefix":null,"suffix":"RPM","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"driven_rpm = driver_rpm * (driver_sprocket_teeth / driven_sprocket_teeth) // RPM @hero","label":null,"prefix":null,"suffix":"RPM","section":null,"hidden":false,"hero":true,"slider":null,"value":333.3333333333333,"display":"333.33"},{"text":"speed_ratio = driven_sprocket_teeth / driver_sprocket_teeth","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"}]},{"id":"champagne-bottle-pressure","title":"Champagne Bottle Pressure","description":"Estimate the internal pressure of a champagne bottle at a given temperature.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"temperature_celsius = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"pressure_atmospheres = 5 + 0.2 * (temperature_celsius - 10) // atmospheres @hero","label":null,"prefix":null,"suffix":"atmospheres","section":null,"hidden":false,"hero":true,"slider":null,"value":7,"display":"7"}]},{"id":"charitable-donation-tax-savings","title":"Charitable Donation Tax Savings","description":"Calculate tax savings and net cost of a charitable donation at your tax bracket.","category":"finance","icon":"dollar-sign","tags":["tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.418Z"},"rows":[{"text":"donation_amount = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"tax_rate = 0.35","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.35,"display":"0.35"},{"text":"tax_savings = donation_amount * tax_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"net_cost = donation_amount - tax_savings","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":650,"display":"650"}]},{"id":"charles-law-volume-temperature","title":"Charles Law Volume Temperature","description":"Calculate the final gas volume after a temperature change using Charles's Law.","category":"education","icon":"book-open","tags":["temperature"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"volume_initial = 1.5 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"temperature_initial_celsius = 25 // Celsius","label":null,"prefix":null,"suffix":"Celsius","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"temperature_final_celsius = 100 // Celsius","label":null,"prefix":null,"suffix":"Celsius","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_t1_kelvin = temperature_initial_celsius + 273.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":298.15,"display":"298.15"},{"text":"_t2_kelvin = temperature_final_celsius + 273.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":373.15,"display":"373.15"},{"text":"volume_final = volume_initial * (t2_kelvin / t1_kelvin) // liters @hero","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":1.8773268489015598,"display":"1.877"}]},{"id":"cheese-yield-from-milk","title":"Cheese Yield From Milk","description":"Estimate cheese yield in pounds from milk volume, fat content, and cheese type.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"milk_volume_gallons = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"milk_fat_percent = 3.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.5,"display":"3.5"},{"text":"cheese_type_factor = 0.1 // Hard cheese: 0.1, Soft: 0.2","label":null,"prefix":null,"suffix":"Hard cheese: 0.1, Soft: 0.2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"estimated_cheese_weight_pounds = milk_volume_gallons * 8.6 * cheese_type_factor * (milk_fat_percent / 3.5) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.72,"display":"1.72"}]},{"id":"chemical-balancing-stoichiometry","title":"Chemical Balancing Stoichiometry","description":"Calculate the total mass of reactants from moles and molar masses.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"reactant_1_moles = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"reactant_1_molar_mass = 18.02 // g/mol","label":null,"prefix":null,"suffix":"g/mol","section":null,"hidden":false,"hero":false,"slider":null,"value":18.02,"display":"18.02"},{"text":"reactant_2_moles = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"reactant_2_molar_mass = 32.00 // g/mol","label":null,"prefix":null,"suffix":"g/mol","section":null,"hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"total_mass = (reactant_1_moles * reactant_1_molar_mass) + (reactant_2_moles * reactant_2_molar_mass) // grams @hero","label":null,"prefix":null,"suffix":"grams","section":null,"hidden":false,"hero":true,"slider":null,"value":82.02,"display":"82.02"}]},{"id":"chess-elo-rating-change","title":"Chess Elo Rating Change","description":"Calculate Elo rating change after a chess game from K-factor and outcome.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Ratings","label":null,"prefix":null,"suffix":null,"section":"Ratings","hero":false,"slider":null,"value":null,"display":null},{"text":"your rating = 1500","label":null,"prefix":null,"suffix":null,"section":"Ratings","hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"opponent rating = 1600","label":null,"prefix":null,"suffix":null,"section":"Ratings","hidden":false,"hero":false,"slider":null,"value":1600,"display":"1,600"},{"text":"k factor = 32 // stability factor","label":null,"prefix":null,"suffix":"stability factor","section":"Ratings","hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"# Outcome","label":null,"prefix":null,"suffix":null,"section":"Outcome","hero":false,"slider":null,"value":null,"display":null},{"text":"score = 1 // 1 for win, 0.5 for draw, 0 for loss","label":null,"prefix":null,"suffix":"1 for win, 0.5 for draw, 0 for loss","section":"Outcome","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_expected_score = 1 / (1 + 10 ^ ((opponent rating - your rating) / 400))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":0.35993500019711494,"display":"0.3599"},{"text":"rating change = k factor * (score - expected_score) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":20.48207999369232,"display":"20.48"},{"text":"new rating = your rating + rating change // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":1520.4820799936922,"display":"1,520.48"}]},{"id":"chicken-egg-production-timer","title":"Chicken Egg Production Timer","description":"Estimate total eggs from a flock over a collection period.","category":"productivity","icon":"clock","tags":["timer","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"number_of_hens = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"eggs_per_hen_per_week = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"days_to_collect = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"estimated_total_eggs = number_of_hens * (eggs_per_hen_per_week / 7) * days_to_collect // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":25,"display":"25"}]},{"id":"child-support-estimate","title":"Child Support Estimate","description":"Estimate monthly child support based on parental income.","category":"other","icon":"users","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"nonCustodialMonthlyIncome = 5000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"numberOfChildren = 2 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"supportPercentagePerChild = 17 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":17,"display":"17"},{"text":"monthlySupport = nonCustodialMonthlyIncome * (supportPercentagePerChild / 100) * numberOfChildren // @prefix($) @suffix(/mo) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1700,"display":"1,700"}]},{"id":"churn-rate","title":"Churn Rate","description":"Calculate monthly customer churn rate, retention, and estimated customer half-life.","category":"business","icon":"briefcase","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Customer Retention","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hero":false,"slider":null,"value":null,"display":null},{"text":"customers at start of month = 1200 // 1..100k","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hidden":false,"hero":false,"slider":{"min":1,"max":100000,"step":1000},"value":1200,"display":"1,200"},{"text":"customers lost during month = 60 // 0..10k","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":60,"display":"60"},{"text":"new customers added = 80 // 0..10k","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":80,"display":"80"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly churn rate = (customers lost during month / customers at start of month) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"retention rate = 100 - monthly churn rate // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":95,"display":"95"},{"text":"estimated customer half life = 70 / monthly churn rate // months (Rule of 70 approx)","label":null,"prefix":null,"suffix":"months (Rule of 70 approx)","section":"Result","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"$net change = new customers added - customers lost during month","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":20,"display":"$20.00"}]},{"id":"cinematic-aspect-ratio-letterbox","title":"Cinematic Aspect Ratio Letterbox","description":"Calculate letterbox bar height for displaying a cinematic aspect ratio on a screen.","category":"design","icon":"palette","tags":["aspect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"screen_width = 1920 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":1920,"display":"1,920"},{"text":"screen_height = 1080 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":1080,"display":"1,080"},{"text":"target_aspect_ratio = 2.39 // cinematic wide","label":null,"prefix":null,"suffix":"cinematic wide","section":null,"hidden":false,"hero":false,"slider":null,"value":2.39,"display":"2.39"},{"text":"_content_height = screen_width / target_aspect_ratio","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":803.347280334728,"display":"803.35"},{"text":"letterbox_bar_height = (screen_height - content_height) / 2 // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":138.326359832636,"display":"138.33"}]},{"id":"circle-area","title":"Circle Area","description":"Find the area of a circle from its radius: A = π × r².","category":"formulas","icon":"circle","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Radius","label":null,"prefix":null,"suffix":null,"section":"Radius","hero":false,"slider":null,"value":null,"display":null},{"text":"radius = 5 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Radius","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"# Area","label":null,"prefix":null,"suffix":null,"section":"Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = pi * radius^2","label":null,"prefix":null,"suffix":null,"section":"Area","hidden":false,"hero":true,"slider":null,"value":78.53981633974483,"display":"78.54"}]},{"id":"circle-circumference","title":"Circle Circumference","description":"Find the circumference of a circle from its radius: C = 2 × π × r.","category":"formulas","icon":"circle","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Radius","label":null,"prefix":null,"suffix":null,"section":"Radius","hero":false,"slider":null,"value":null,"display":null},{"text":"radius = 5 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Radius","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"# Circumference and diameter","label":null,"prefix":null,"suffix":null,"section":"Circumference and diameter","hero":false,"slider":null,"value":null,"display":null},{"text":"circumference = 2 * pi * radius // @hero","label":null,"prefix":null,"suffix":null,"section":"Circumference and diameter","hidden":false,"hero":true,"slider":null,"value":31.415926535897928,"display":"31.42"},{"text":"diameter = 2 * radius","label":null,"prefix":null,"suffix":null,"section":"Circumference and diameter","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"}]},{"id":"class-grade","title":"Class Grade","description":"Calculate your weighted class grade from assignments and exams.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Homework","label":null,"prefix":null,"suffix":null,"section":"Homework","hero":false,"slider":null,"value":null,"display":null},{"text":"homework_score = 92 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Homework","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":92,"display":"92"},{"text":"homework_weight = 30 // % 5..50 by 5","label":null,"prefix":null,"suffix":"%","section":"Homework","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":5},"value":30,"display":"30"},{"text":"# Midterm","label":null,"prefix":null,"suffix":null,"section":"Midterm","hero":false,"slider":null,"value":null,"display":null},{"text":"midterm_score = 78 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Midterm","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":78,"display":"78"},{"text":"midterm_weight = 30 // % 5..50 by 5","label":null,"prefix":null,"suffix":"%","section":"Midterm","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":5},"value":30,"display":"30"},{"text":"# Final Exam","label":null,"prefix":null,"suffix":null,"section":"Final Exam","hero":false,"slider":null,"value":null,"display":null},{"text":"final_score = 85 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Final Exam","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":85,"display":"85"},{"text":"final_weight = 40 // % 5..50 by 5","label":null,"prefix":null,"suffix":"%","section":"Final Exam","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":5},"value":40,"display":"40"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"total_weight = homework_weight + midterm_weight + final_weight // %","label":null,"prefix":null,"suffix":"%","section":"Results","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"weighted_average = round((homework_score * homework_weight + midterm_score * midterm_weight + final_score * final_weight) / total_weight * 10) / 10 // %","label":null,"prefix":null,"suffix":"%","section":"Results","hidden":false,"hero":true,"slider":null,"value":85,"display":"85"}]},{"id":"clay-shrinkage-pottery-percent","title":"Clay Shrinkage Pottery Percent","description":"Calculate clay shrinkage percentage between wet and fired pottery dimensions.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"wet_length = 10 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"fired_length = 8.8 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":8.8,"display":"8.8"},{"text":"shrinkage_percentage = ((wet_length - fired_length) / wet_length) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12,"display":"12"}]},{"id":"click-to-solve-logistic","title":"Click-to-solve logistic growth","description":"A logistic curve has three knobs: carrying capacity, midpoint, and steepness.","category":"science","icon":"activity","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Logistic parameters","label":null,"prefix":null,"suffix":null,"section":"Logistic parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"K = 100 // 1..200 — carrying capacity (the eventual plateau)","label":null,"prefix":null,"suffix":"1..200 — carrying capacity (the eventual plateau)","section":"Logistic parameters","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"x_0 = 5 // -5..15 — midpoint (where growth peaks)","label":null,"prefix":null,"suffix":"-5..15 — midpoint (where growth peaks)","section":"Logistic parameters","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"k = 1 // 0.1..3 — steepness","label":null,"prefix":null,"suffix":"0.1..3 — steepness","section":"Logistic parameters","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# The logistic curve. Click any point — the solver will move the","label":null,"prefix":null,"suffix":null,"section":"The logistic curve. Click any point — the solver will move the","hero":false,"slider":null,"value":null,"display":null},{"text":"# midpoint `x_0` to land the curve through your click.","label":null,"prefix":null,"suffix":null,"section":"midpoint `x_0` to land the curve through your click.","hero":false,"slider":null,"value":null,"display":null},{"text":"# Click at (8, 90) to see the midpoint shift right so 90% adoption","label":null,"prefix":null,"suffix":null,"section":"Click at (8, 90) to see the midpoint shift right so 90% adoption","hero":false,"slider":null,"value":null,"display":null},{"text":"# lands at x = 8. Then click (3, 50) to shift it left for \"halfway by 3\".","label":null,"prefix":null,"suffix":null,"section":"lands at x = 8. Then click (3, 50) to shift it left for \"halfway by 3\".","hero":false,"slider":null,"value":null,"display":null},{"text":"# Inspect: when does the curve hit 50% of capacity?","label":null,"prefix":null,"suffix":null,"section":"Inspect: when does the curve hit 50% of capacity?","hero":false,"slider":null,"value":null,"display":null},{"text":"half_x = x_0 // by definition, half-capacity is at the midpoint","label":null,"prefix":null,"suffix":"by definition, half-capacity is at the midpoint","section":"Inspect: when does the curve hit 50% of capacity?","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"click-to-solve-parabola","title":"Click-to-solve a parabola","description":"Click any point on the curve to set a goal. The engine reverse-solves the","category":"math","icon":"trending-up","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Coefficients you can vary","label":null,"prefix":null,"suffix":null,"section":"Coefficients you can vary","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 1 // -5..5 — click on the curve to let the solver set this","label":null,"prefix":null,"suffix":"-5..5 — click on the curve to let the solver set this","section":"Coefficients you can vary","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"b = 0 // -10..10 — linear term","label":null,"prefix":null,"suffix":"-10..10 — linear term","section":"Coefficients you can vary","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"c = 0 // -20..20 — constant","label":null,"prefix":null,"suffix":"-20..20 — constant","section":"Coefficients you can vary","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# The parabola — click anywhere on the curve to fit `a` to that point","label":null,"prefix":null,"suffix":null,"section":"The parabola — click anywhere on the curve to fit `a` to that point","hero":false,"slider":null,"value":null,"display":null},{"text":"# Try clicking at (3, 9). The solver will land `a = 1` (since 1*9 + 0 + 0 = 9).","label":null,"prefix":null,"suffix":null,"section":"Try clicking at (3, 9). The solver will land `a = 1` (since 1*9 + 0 + 0 = 9).","hero":false,"slider":null,"value":null,"display":null},{"text":"# Then drag `b` away from 0 and click again at the same spot — `a` re-solves","label":null,"prefix":null,"suffix":null,"section":"Then drag `b` away from 0 and click again at the same spot — `a` re-solves","hero":false,"slider":null,"value":null,"display":null},{"text":"# to land the new curve through (3, 9).","label":null,"prefix":null,"suffix":null,"section":"to land the new curve through (3, 9).","hero":false,"slider":null,"value":null,"display":null},{"text":"# Inspect the roots once the curve fits","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hero":false,"slider":null,"value":null,"display":null},{"text":"disc = b^2 - 4*a*c","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"root_1 = (-b - sqrt(disc)) / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hidden":false,"hero":false,"slider":null,"value":0,"display":"-0"},{"text":"root_2 = (-b + sqrt(disc)) / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"climb-gradient","title":"Climb Gradient","description":"Calculate climb gradient as percent and degrees from elevation gain and distance.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Terrain Info","label":null,"prefix":null,"suffix":null,"section":"Terrain Info","hero":false,"slider":null,"value":null,"display":null},{"text":"elevation gain = 500 // feet 0..5k","label":null,"prefix":null,"suffix":"feet","section":"Terrain Info","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":50},"value":500,"display":"500"},{"text":"horizontal distance = 5280 // feet 0..50k","label":null,"prefix":null,"suffix":"feet","section":"Terrain Info","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":500},"value":5280,"display":"5,280"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"slope decimal = elevation gain / horizontal distance","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":0.0946969696969697,"display":"0.0947"},{"text":"slope percentage = slope decimal * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":9.469696969696969,"display":"9.47"},{"text":"# Degree conversion","label":null,"prefix":null,"suffix":null,"section":"Degree conversion","hero":false,"slider":null,"value":null,"display":null},{"text":"angle degrees = atan(slope decimal)","label":null,"prefix":null,"suffix":null,"section":"Degree conversion","hidden":false,"hero":false,"slider":null,"value":5.409604944473391,"display":"5.4096"},{"text":"grade category = slope percentage","label":null,"prefix":null,"suffix":null,"section":"Degree conversion","hidden":false,"hero":false,"slider":null,"value":9.469696969696969,"display":"9.47"},{"text":"# Classification","label":null,"prefix":null,"suffix":null,"section":"Classification","hero":false,"slider":null,"value":null,"display":null},{"text":"flat = 3","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"moderate = 6","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"steep = 10","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"extreme = 15","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"}]},{"id":"closing-costs","title":"Closing Costs","description":"Estimate closing costs and total cash due at closing.","category":"real-estate","icon":"file-text","tags":["home"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"# Home Purchase","label":null,"prefix":null,"suffix":null,"section":"Home Purchase","hero":false,"slider":null,"value":null,"display":null},{"text":"$home price = 350000 // 50k..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Home Purchase","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":5000},"value":350000,"display":"$350,000.00"},{"text":"down payment pct = 10 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Home Purchase","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":10,"display":"10"},{"text":"$down payment = home price * down payment pct / 100","label":null,"prefix":"$","suffix":null,"section":"Home Purchase","hidden":false,"hero":false,"slider":null,"value":35000,"display":"$35,000.00"},{"text":"# Closing Cost Breakdown","label":null,"prefix":null,"suffix":null,"section":"Closing Cost Breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"$lender fees = home price * 0.01 // @label(Lender/Origination Fees ~1%)","label":"Lender/Origination Fees ~1%","prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":null,"value":3500,"display":"$3,500.00"},{"text":"$title insurance = 1500 // 500..5k by 100","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":500,"max":5000,"step":100},"value":1500,"display":"$1,500.00"},{"text":"$appraisal fee = 500 // 200..1k by 50","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":200,"max":1000,"step":50},"value":500,"display":"$500.00"},{"text":"$home inspection = 450 // 200..800 by 50","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":200,"max":800,"step":50},"value":450,"display":"$450.00"},{"text":"$escrow and recording = 750 // 200..2k by 50","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":200,"max":2000,"step":50},"value":750,"display":"$750.00"},{"text":"$prepaid taxes and insurance = home price * 0.005 // @label(Prepaid Taxes & Insurance ~0.5%)","label":"Prepaid Taxes & Insurance ~0.5%","prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":null,"value":1750,"display":"$1,750.00"},{"text":"# Totals","label":null,"prefix":null,"suffix":null,"section":"Totals","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated closing costs = lender fees + title insurance + appraisal fee + home inspection + escrow and recording + prepaid taxes and insurance","label":null,"prefix":"$","suffix":null,"section":"Totals","hidden":false,"hero":false,"slider":null,"value":8450,"display":"$8,450.00"},{"text":"closing cost pct = round(estimated closing costs / home price * 100 * 10) / 10 // %","label":null,"prefix":null,"suffix":"%","section":"Totals","hidden":false,"hero":false,"slider":null,"value":2.4,"display":"2.4"},{"text":"$total due at closing = down payment + estimated closing costs","label":null,"prefix":"$","suffix":null,"section":"Totals","hidden":false,"hero":true,"slider":null,"value":43450,"display":"$43,450.00"}]},{"id":"cloud-egress-cost-calculator","title":"Cloud Egress Cost Calculator","description":"Estimate total cost of cloud data egress at a given price per gigabyte.","category":"other","icon":"cloud","tags":["cloud"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"egress_data_terabytes = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"cost_per_gigabyte = 0.09","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.09,"display":"0.09"},{"text":"total_egress_cost_dollars = egress_data_terabytes * 1000 * cost_per_gigabyte // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":450,"display":"450"}]},{"id":"cloud-storage-cost-comparison","title":"Cloud Storage Cost Comparison","description":"Compare monthly cloud storage costs across three providers at a given data size.","category":"health","icon":"cloud","tags":["cloud","storage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"data_size_terabytes = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"cost_per_terabyte_month_provider_a = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"cost_per_terabyte_month_provider_b = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"cost_per_terabyte_month_provider_c = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"monthly_cost_provider_a = data_size_terabytes * cost_per_terabyte_month_provider_a","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"monthly_cost_provider_b = data_size_terabytes * cost_per_terabyte_month_provider_b // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"monthly_cost_provider_c = data_size_terabytes * cost_per_terabyte_month_provider_c","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"}]},{"id":"cloud-weight-estimate","title":"Cloud Weight Estimate","description":"Estimate the total weight of a cumulus cloud from its volume and water density.","category":"everyday","icon":"smile","tags":["cloud"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"cloud_volume_m3 = 1e9 // 1 cubic km","label":null,"prefix":null,"suffix":"1 cubic km","section":null,"hidden":false,"hero":false,"slider":null,"value":1000000000,"display":"1,000,000,000"},{"text":"water_density_g_per_m3 = 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"total_weight_kilograms = (cloud_volume_m3 * water_density_g_per_m3) / 1000 // kilograms @hero","label":null,"prefix":null,"suffix":"kilograms","section":null,"hidden":false,"hero":true,"slider":null,"value":500000,"display":"500,000"}]},{"id":"cmyk-to-rgb-color-converter","title":"Cmyk To Rgb Color Converter","description":"Convert CMYK percentages to RGB color values.","category":"design","icon":"palette","tags":["rgb","color"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.422Z"},"rows":[{"text":"cyan_percent = 100 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"magenta_percent = 0 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"yellow_percent = 0 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"black_percent = 0 // 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1..50","label":null,"prefix":null,"suffix":null,"section":"Footing Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":4,"display":"4"},{"text":"# Volume Calculations","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_volume_per_footing_cubic_inches = length * width * depth","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":6912,"display":"6,912"},{"text":"_total_volume_cubic_inches = volume_per_footing_cubic_inches * number of footings","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":27648,"display":"27,648"},{"text":"_total_volume_cubic_feet = total_volume_cubic_inches / 1728","label":null,"prefix":null,"suffix":null,"section":"Volume 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// %","label":null,"prefix":null,"suffix":"%","section":"Chance Settings","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"total crit chance percent = base crit chance percent + equipment bonus percent + buff bonus percent","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"critical-hit-damage-multiplier","title":"Critical Hit Damage Multiplier","description":"Calculate total damage on a critical hit.","category":"math","icon":"target","tags":["gaming","combat"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Damage Settings","label":null,"prefix":null,"suffix":null,"section":"Damage Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base damage = 150","label":null,"prefix":null,"suffix":null,"section":"Damage Settings","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"crit multiplier = 2.0","label":null,"prefix":null,"suffix":null,"section":"Damage Settings","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"crit damage bonus percent = 50 // %","label":null,"prefix":null,"suffix":"%","section":"Damage Settings","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_crit_multiplier = crit multiplier + (crit damage bonus percent / 100)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"final damage = base damage * 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Fabric","label":null,"prefix":null,"suffix":null,"section":"Fabric","hero":false,"slider":null,"value":null,"display":null},{"text":"fabric count = 14 // stitches per inch","label":null,"prefix":null,"suffix":"stitches per inch","section":"Fabric","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"# Margins","label":null,"prefix":null,"suffix":null,"section":"Margins","hero":false,"slider":null,"value":null,"display":null},{"text":"margin inches = 3 // per side","label":null,"prefix":null,"suffix":"per side","section":"Margins","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_design_width = stitches wide / fabric 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0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Cylinder","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"height = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Cylinder","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"# Volume","label":null,"prefix":null,"suffix":null,"section":"Volume","hero":false,"slider":null,"value":null,"display":null},{"text":"volume = pi * radius^2 * height","label":null,"prefix":null,"suffix":null,"section":"Volume","hidden":false,"hero":true,"slider":null,"value":785.3981633974483,"display":"785.4"}]},{"id":"daily-productivity-score-weighted","title":"Daily Productivity Score Weighted","description":"Calculate a daily productivity score from tasks completed, difficulty, and focus 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Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"damage reduction percent = (armor value / (armor value + constant)) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":28.57142857142857,"display":"28.57"}]},{"id":"data-center-cooling-load","title":"Data Center Cooling Load","description":"Calculate data center cooling load in BTU/hour from IT equipment and heat sources.","category":"other","icon":"calculator","tags":["cooling"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"it_equipment_power_watts = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"other_heat_sources_watts = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"cooling_load_btu_per_hour = (it_equipment_power_watts + other_heat_sources_watts) * 3.412 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":375320,"display":"375,320"}]},{"id":"data-table-overrides","title":"📥 Data Table — Load, Override, Add","description":"A pattern for big data tables: load a shared base (a Google Sheet, a hosted JSON), then layer **your own** edits and rows on top — without ever touching the source. Add rows by tapping a button or editing the table. Everything stays in the URL, so your layer is shareable and undoable.","category":"demo","icon":"database","tags":["demo","data"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-27T22:45:45.148Z"},"rows":[{"text":"# 1 · The base (shared, read-only) @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"1 · The base (shared, read-only)","hero":false,"slider":null,"value":null,"display":null},{"text":"base = [{item: \"Iron plate\", cost: 10}, {item: \"Copper plate\", cost: 12}, {item: \"Steel\", cost: 45}] // @cols(Item, Cost) @label(📦 Base table)","label":"📦 Base table","prefix":null,"suffix":null,"section":"1 · The base (shared, read-only)","hidden":false,"hero":false,"slider":null,"value":[{"item":"Iron plate","cost":10},{"item":"Copper plate","cost":12},{"item":"Steel","cost":45}],"display":null},{"text":"# 2 · Your layer (editable) @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"2 · Your layer (editable)","hero":false,"slider":null,"value":null,"display":null},{"text":"mine = [] // @cols(Item, Cost) @label(✏️ Your additions)","label":"✏️ Your additions","prefix":null,"suffix":null,"section":"2 · Your layer (editable)","hidden":false,"hero":false,"slider":null,"value":[],"display":null},{"text":"add = \"\" // buttons({➕ Plastic: {\"mine+\": {item: \"Plastic\", cost: 20}}, ➕ Battery: {\"mine+\": {item: \"Battery\", cost: 40}}, ➕ Circuit: {\"mine+\": {item: \"Circuit\", cost: 8}}}) @label(One-tap add)","label":"One-tap add","prefix":null,"suffix":null,"section":"2 · Your layer (editable)","hidden":false,"hero":false,"slider":null,"value":"","display":null},{"text":"# 3 · The effective table = combine(base, mine)","label":null,"prefix":null,"suffix":null,"section":"3 · The effective table = combine(base, mine)","hero":false,"slider":null,"value":null,"display":null},{"text":"items = combine(base, mine) // @cols(Item, Cost) @label(🧮 Effective — base + your rows, merged live)","label":"🧮 Effective — base + your rows, merged live","prefix":null,"suffix":null,"section":"3 · The effective table = combine(base, mine)","hidden":false,"hero":false,"slider":null,"value":[{"item":"Iron plate","cost":10},{"item":"Copper plate","cost":12},{"item":"Steel","cost":45}],"display":null},{"text":"# 4 · Rollups @skin(spec-sheet) @density(compact)","label":null,"prefix":null,"suffix":null,"section":"4 · Rollups","hero":false,"slider":null,"value":null,"display":null},{"text":"count = sum(map(items, x => 1)) // @label(📋 Items)","label":"📋 Items","prefix":null,"suffix":null,"section":"4 · Rollups","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"total = sum(map(items, x => x.cost)) // @label(💰 Total) @suffix( /ea)","label":"💰 Total","prefix":null,"suffix":null,"section":"4 · Rollups","hidden":false,"hero":false,"slider":null,"value":67,"display":"67"},{"text":"priciest = last(sort(map(items, x => x.cost))) // @label(⬆️ Priciest) @suffix( /ea)","label":"⬆️ Priciest","prefix":null,"suffix":null,"section":"4 · Rollups","hidden":false,"hero":true,"slider":null,"value":45,"display":"45"}]},{"id":"debt-equity-ratio","title":"Debt Equity Ratio","description":"Calculate debt-to-equity ratio and leverage status from liabilities and equity.","category":"finance","icon":"ratio","tags":["debt","equity","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Balance Sheet","label":null,"prefix":null,"suffix":null,"section":"Balance Sheet","hero":false,"slider":null,"value":null,"display":null},{"text":"$total liabilities = 1500000 // 0..100M","label":null,"prefix":"$","suffix":null,"section":"Balance Sheet","hidden":false,"hero":false,"slider":{"min":0,"max":100000000,"step":1000000},"value":1500000,"display":"$1,500,000.00"},{"text":"$shareholders equity = 1000000 // 1k..100M","label":null,"prefix":"$","suffix":null,"section":"Balance Sheet","hidden":false,"hero":false,"slider":{"min":1000,"max":100000000,"step":1000000},"value":1000000,"display":"$1,000,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"debt to equity ratio = total liabilities / shareholders equity // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":1.5,"display":"1.5"},{"text":"total debt ratio = total liabilities / (total liabilities + shareholders equity)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"leverage status = if(debt to equity ratio > 2, \"High Leverage\", if(debt to equity ratio > 1, \"Moderate\", \"Conservative\"))","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Moderate","display":"Moderate"}]},{"id":"debt-payoff","title":"Debt Payoff","description":"Calculate how long to pay off debt and total interest costs.","category":"finance","icon":"credit-card","tags":["debt","payoff","interest"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Debt Details","label":null,"prefix":null,"suffix":null,"section":"Debt Details","hero":false,"slider":null,"value":null,"display":null},{"text":"total debt = $15000 // 500..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Debt Details","hidden":false,"hero":false,"slider":{"min":500,"max":100000,"step":500},"value":15000,"display":"$15,000.00"},{"text":"annual interest rate = 18 // % 1..30","label":null,"prefix":null,"suffix":"%","section":"Debt Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":18,"display":"18"},{"text":"monthly payment = $400 // 50..5k by 25","label":null,"prefix":"$","suffix":null,"section":"Debt Details","hidden":false,"hero":false,"slider":{"min":50,"max":5000,"step":25},"value":400,"display":"$400.00"},{"text":"# Payoff Timeline","label":null,"prefix":null,"suffix":null,"section":"Payoff Timeline","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly rate = annual interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Payoff Timeline","hidden":false,"hero":false,"slider":null,"value":0.015,"display":"0.015"},{"text":"months to payoff = -ln(1 - (total debt * monthly rate / monthly payment)) / ln(1 + monthly rate)","label":null,"prefix":null,"suffix":null,"section":"Payoff Timeline","hidden":false,"hero":false,"slider":null,"value":55.52421849460205,"display":"55.52"},{"text":"years to payoff = round(months to payoff / 12 * 10) / 10 // @hero","label":null,"prefix":null,"suffix":null,"section":"Payoff Timeline","hidden":false,"hero":true,"slider":null,"value":4.6,"display":"4.6"},{"text":"# Cost Summary","label":null,"prefix":null,"suffix":null,"section":"Cost Summary","hero":false,"slider":null,"value":null,"display":null},{"text":"$total paid = round(monthly payment * months to payoff * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":22209.69,"display":"$22,209.69"},{"text":"$total interest paid = round((total paid - total debt) * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":7209.69,"display":"$7,209.69"},{"text":"interest pct = round((total interest paid / total debt) * 100 * 10) / 10 // % @label(Interest as % of Debt)","label":"Interest as % of Debt","prefix":null,"suffix":"%","section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":48.1,"display":"48.1"}]},{"id":"debt-service-coverage-ratio","title":"Debt Service Coverage Ratio","description":"Measure the ability of a property to cover its mortgage payments.","category":"real-estate","icon":"shield-check","tags":["debt","coverage"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"netOperatingIncome = 60000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":60000,"display":"60,000"},{"text":"annualDebtService = 45000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":45000,"display":"45,000"},{"text":"dscr = netOperatingIncome / annualDebtService // ratio @hero","label":null,"prefix":null,"suffix":"ratio","section":null,"hidden":false,"hero":true,"slider":null,"value":1.3333333333333333,"display":"1.333"}]},{"id":"debt-to-income-ratio","title":"Debt To Income Ratio","description":"Calculate debt-to-income ratio (DTI) from monthly income and debt payments.","category":"finance","icon":"ratio","tags":["debt","income","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Monthly Income and Debt","label":null,"prefix":null,"suffix":null,"section":"Monthly Income and Debt","hero":false,"slider":null,"value":null,"display":null},{"text":"$gross monthly income = 6000 // 1k..50k by 100","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":1000,"max":50000,"step":100},"value":6000,"display":"$6,000.00"},{"text":"$monthly mortgage or rent = 1800 // 0..10k by 50","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":50},"value":1800,"display":"$1,800.00"},{"text":"$monthly car payments = 400 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":400,"display":"$400.00"},{"text":"$monthly credit card minimums = 150 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":150,"display":"$150.00"},{"text":"$other monthly debt payments = 200 // 0..5k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":25},"value":200,"display":"$200.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_monthly_debt = monthly mortgage or rent + monthly car payments + monthly credit card minimums + other monthly debt payments","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2550,"display":"$2,550.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"debt to income ratio = (total_monthly_debt / gross monthly income) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":42.5,"display":"42.5"},{"text":"$remaining monthly income = gross monthly income - total_monthly_debt","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":3450,"display":"$3,450.00"},{"text":"health = if(debt to income ratio < 36, \"Healthy\", if(debt to income ratio < 43, \"Moderate\", \"High\"))","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Moderate","display":"Moderate"}]},{"id":"debuff-resistance-probability","title":"Debuff Resistance Probability","description":"Calculate probability to resist a debuff.","category":"math","icon":"shield-off","tags":["gaming","combat"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Resistance Settings","label":null,"prefix":null,"suffix":null,"section":"Resistance Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"attacker debuff chance percent = 80 // %","label":null,"prefix":null,"suffix":"%","section":"Resistance Settings","hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"defender resistance percent = 30 // %","label":null,"prefix":null,"suffix":"%","section":"Resistance Settings","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"final debuff chance percent = attacker debuff chance percent * (1 - (defender resistance percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":56,"display":"56"}]},{"id":"decision-fatigue-level","title":"Decision Fatigue Level","description":"Estimate decision fatigue from daily decision count and complexity.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"decisions_today = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"avg_decision_complexity = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"fatigue_index = (decisions_today * avg_decision_complexity) / 100 // scale 0-10 @hero","label":null,"prefix":null,"suffix":"scale 0-10","section":null,"hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"deck-board-estimator","title":"Deck Board Estimator","description":"Estimate deck boards and linear feet needed from deck size and board width.","category":"everyday","icon":"home","tags":["deck","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Deck Dimensions","label":null,"prefix":null,"suffix":null,"section":"Deck Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"deck length = 16 // feet 1..100","label":null,"prefix":null,"suffix":"feet","section":"Deck Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":16,"display":"16"},{"text":"deck width = 12 // feet 1..100","label":null,"prefix":null,"suffix":"feet","section":"Deck Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":12,"display":"12"},{"text":"# Board Dimensions","label":null,"prefix":null,"suffix":null,"section":"Board Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"board nominal width = 6 // inches","label":null,"prefix":null,"suffix":"inches","section":"Board Dimensions","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"actual board width = 5.5 // inches","label":null,"prefix":null,"suffix":"inches","section":"Board Dimensions","hidden":false,"hero":false,"slider":null,"value":5.5,"display":"5.5"},{"text":"gap width = 0.125 // inches","label":null,"prefix":null,"suffix":"inches","section":"Board Dimensions","hidden":false,"hero":false,"slider":null,"value":0.125,"display":"0.125"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_effective_board_width_inches = actual board width + gap width","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":5.625,"display":"5.625"},{"text":"_effective_board_width_feet = effective_board_width_inches / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.46875,"display":"0.4688"},{"text":"# Assuming boards run along the length","label":null,"prefix":null,"suffix":null,"section":"Assuming boards run along the length","hero":false,"slider":null,"value":null,"display":null},{"text":"boards needed = roundup(deck width / effective_board_width_feet) // @hero","label":null,"prefix":null,"suffix":null,"section":"Assuming boards run along the length","hidden":false,"hero":true,"slider":null,"value":26,"display":"26"},{"text":"# Total linear feet","label":null,"prefix":null,"suffix":null,"section":"Total linear feet","hero":false,"slider":null,"value":null,"display":null},{"text":"total linear feet = boards needed * deck length","label":null,"prefix":null,"suffix":null,"section":"Total linear feet","hidden":false,"hero":false,"slider":null,"value":416,"display":"416"},{"text":"# With 10% waste","label":null,"prefix":null,"suffix":null,"section":"With 10% waste","hero":false,"slider":null,"value":null,"display":null},{"text":"total linear feet with waste = total linear feet * 1.1","label":null,"prefix":null,"suffix":null,"section":"With 10% waste","hidden":false,"hero":false,"slider":null,"value":457.6,"display":"457.6"}]},{"id":"deck-of-cards-shuffles","title":"Deck Of Cards Shuffles","description":"Show the recommended number of riffle shuffles to randomize a 52-card deck.","category":"everyday","icon":"smile","tags":["deck"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"number_of_cards = 52","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":52,"display":"52"},{"text":"shuffles_for_randomness = 7 // recommended shuffles @hero","label":null,"prefix":null,"suffix":"recommended shuffles","section":null,"hidden":false,"hero":true,"slider":null,"value":7,"display":"7"}]},{"id":"deck-railing-baluster-spacing","title":"Deck Railing Baluster Spacing","description":"Calculate even spacing for deck balusters to meet code.","category":"construction","icon":"fence","tags":["construction","deck","woodworking"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"railing_length_inches = 96 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"baluster_width_inches = 1.5 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"max_spacing_inches = 4 // inches (standard code)","label":null,"prefix":null,"suffix":"inches (standard code)","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"total_balusters = ceil(railing_length_inches / (baluster_width_inches + max_spacing_inches))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"actual_spacing_inches = (railing_length_inches - (total_balusters * baluster_width_inches)) / (total_balusters + 1) // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":3.6315789473684212,"display":"3.632"}]},{"id":"deep-work-uninterrupted-ratio","title":"Deep Work Uninterrupted Ratio","description":"Calculate the percentage of a work day spent in deep, uninterrupted focus.","category":"productivity","icon":"clock","tags":["work"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"total_work_hours = 8 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"deep_work_hours = 3 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"deep_work_ratio_percent = (deep_work_hours / total_work_hours) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":37.5,"display":"37.5"}]},{"id":"definite-integral","title":"Definite Integral — Power Rule","description":"Evaluate ∫ₐᵇ c·xⁿ dx = c·(b^(n+1) − a^(n+1))/(n+1).","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Function: f(x) = c · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"c = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 2 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":2,"display":"2"},{"text":"# Bounds","label":null,"prefix":null,"suffix":null,"section":"Bounds","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 0 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Bounds","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":0,"display":"0"},{"text":"b = 4 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Bounds","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":4,"display":"4"},{"text":"# Definite integral","label":null,"prefix":null,"suffix":null,"section":"Definite integral","hero":false,"slider":null,"value":null,"display":null},{"text":"integral = c * (b^(n + 1) - a^(n + 1)) / (n + 1) // @label(∫ₐᵇ f(x) dx)","label":"∫ₐᵇ f(x) dx","prefix":null,"suffix":null,"section":"Definite integral","hidden":false,"hero":true,"slider":null,"value":64,"display":"64"}]},{"id":"deforestation-rate-per-second","title":"Deforestation Rate Per Second","description":"See how many hectares of forest are lost in real-time.","category":"science","icon":"tree-pine","tags":["science","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"annual_deforestation_hectares = 10000000 // hectares per year","label":null,"prefix":null,"suffix":"hectares per year","section":null,"hidden":false,"hero":false,"slider":null,"value":10000000,"display":"10,000,000"},{"text":"seconds_per_year = 31536000 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":31536000,"display":"31,536,000"},{"text":"hectares_lost_per_second = annual_deforestation_hectares / seconds_per_year // hectares @hero","label":null,"prefix":null,"suffix":"hectares","section":null,"hidden":false,"hero":true,"slider":null,"value":0.31709791983764585,"display":"0.3171"},{"text":"football_fields_per_second = hectares_lost_per_second / 0.7 // approx size of football field","label":null,"prefix":null,"suffix":"approx size of football field","section":null,"hidden":false,"hero":false,"slider":null,"value":0.4529970283394941,"display":"0.453"}]},{"id":"delta-v-orbit-change","title":"Delta V Orbit Change","description":"Calculate the delta-V for an orbit change using the Tsiolkovsky rocket equation.","category":"science","icon":"globe","tags":["orbit"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"specific_impulse_seconds = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"gravity_constant = 9.806","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9.806,"display":"9.806"},{"text":"mass_initial_kilograms = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"mass_final_kilograms = 800","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":800,"display":"800"},{"text":"delta_v_meters_per_second = specific_impulse_seconds * gravity_constant * ln(mass_initial_kilograms / mass_final_kilograms) // m/s @hero","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":true,"slider":null,"value":656.4436992561423,"display":"656.44"}]},{"id":"density-altitude","title":"Density Altitude","description":"Calculate density altitude from pressure altitude, temperature, and ISA deviation.","category":"science","icon":"flask-conical","tags":["altitude","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Altitude and Air","label":null,"prefix":null,"suffix":null,"section":"Altitude and Air","hero":false,"slider":null,"value":null,"display":null},{"text":"pressure altitude = 5000 // feet 0..30k","label":null,"prefix":null,"suffix":"feet","section":"Altitude and Air","hidden":false,"hero":false,"slider":{"min":0,"max":30000,"step":500},"value":5000,"display":"5,000"},{"text":"outside air temperature = 85 // fahrenheit -20..120","label":null,"prefix":null,"suffix":"fahrenheit","section":"Altitude and Air","hidden":false,"hero":false,"slider":{"min":-20,"max":120,"step":1},"value":85,"display":"85"},{"text":"# ISA Temperature at Pressure Altitude","label":null,"prefix":null,"suffix":null,"section":"ISA Temperature at Pressure Altitude","hero":false,"slider":null,"value":null,"display":null},{"text":"isa temperature celsius = 15 - (pressure altitude * 0.00198)","label":null,"prefix":null,"suffix":null,"section":"ISA Temperature at Pressure Altitude","hidden":false,"hero":false,"slider":null,"value":5.1,"display":"5.1"},{"text":"temp celsius = (outside air temperature - 32) * 5 / 9","label":null,"prefix":null,"suffix":null,"section":"ISA Temperature at Pressure Altitude","hidden":false,"hero":false,"slider":null,"value":29.444444444444443,"display":"29.44"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"density altitude = pressure altitude + (120 * (temp celsius - isa temperature celsius)) // feet @hero","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":true,"slider":null,"value":7921.333333333335,"display":"7,921.33"},{"text":"# Performance Impact","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hero":false,"slider":null,"value":null,"display":null},{"text":"isa deviation = temp celsius - isa temperature celsius","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":24.344444444444445,"display":"24.34"},{"text":"takeoff distance factor = 1 + (density altitude / 1000) * 0.1","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":1.7921333333333336,"display":"1.792"},{"text":"engine power loss percent = (density altitude / 1000) * 3 // %","label":null,"prefix":null,"suffix":"%","section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":23.764000000000003,"display":"23.76"},{"text":"density ratio = (518.67 / (459.67 + outside air temperature)) * (1 - 0.0000068756 * pressure altitude)^5.2559","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":0.7923290569713252,"display":"0.7923"}]},{"id":"density","title":"Density","description":"Convert mass and volume into density and per-teaspoon weight.","category":"science","icon":"atom","tags":["mass","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Sample","label":null,"prefix":null,"suffix":null,"section":"Sample","hero":false,"slider":null,"value":null,"display":null},{"text":"mass kg = 6000000000000 // kg 0.001..1e20","label":null,"prefix":null,"suffix":"kg","section":"Sample","hidden":false,"hero":false,"slider":{"min":0.001,"max":100000000000000000000,"step":1000000000000000000},"value":6000000000000,"display":"6,000,000,000,000"},{"text":"volume ml = 5 // mL 0.001..100k","label":null,"prefix":null,"suffix":"mL","section":"Sample","hidden":false,"hero":false,"slider":{"min":0.001,"max":100000,"step":1000},"value":5,"display":"5"},{"text":"# Density","label":null,"prefix":null,"suffix":null,"section":"Density","hero":false,"slider":null,"value":null,"display":null},{"text":"_volume_m3 = volume ml / 1000000 // m³","label":null,"prefix":null,"suffix":"m³","section":"Density","hidden":true,"hero":false,"slider":null,"value":0.000005,"display":"0.000005"},{"text":"density kg per m3 = mass kg / volume_m3 // kg/m³ @label(Density (kg/m³))","label":"Density (kg/m³)","prefix":null,"suffix":"kg/m³","section":"Density","hidden":false,"hero":false,"slider":null,"value":1200000000000000000,"display":"1.2e18"},{"text":"density g per cc = density kg per m3 / 1000 // g/cm³ @label(Density (g/cm³))","label":"Density (g/cm³)","prefix":null,"suffix":"g/cm³","section":"Density","hidden":false,"hero":false,"slider":null,"value":1200000000000000,"display":"1,200,000,000,000,000"},{"text":"# Mass per Teaspoon (5 mL)","label":null,"prefix":null,"suffix":null,"section":"Mass per Teaspoon (5 mL)","hero":false,"slider":null,"value":null,"display":null},{"text":"mass per tsp kg = density kg per m3 * 5 / 1000000 // @label(Mass per teaspoon)","label":"Mass per teaspoon","prefix":null,"suffix":null,"section":"Mass per Teaspoon (5 mL)","hidden":false,"hero":false,"slider":null,"value":6000000000000,"display":"6,000,000,000,000"},{"text":"mass per tsp tons = mass per tsp kg / 1000 // tons @hero @label(Mass per teaspoon (metric tons))","label":"Mass per teaspoon (metric tons)","prefix":null,"suffix":"tons","section":"Mass per Teaspoon (5 mL)","hidden":false,"hero":true,"slider":null,"value":6000000000,"display":"6,000,000,000"},{"text":"# Reference","label":null,"prefix":null,"suffix":null,"section":"Reference","hero":false,"slider":null,"value":null,"display":null},{"text":"_water_density = 1000 // kg/m³","label":null,"prefix":null,"suffix":"kg/m³","section":"Reference","hidden":true,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"times denser than water = round(density kg per m3 / water_density)","label":null,"prefix":null,"suffix":null,"section":"Reference","hidden":false,"hero":false,"slider":null,"value":1200000000000000,"display":"1,200,000,000,000,000"}]},{"id":"depth-of-field","title":"Depth of Field","description":"Calculate near, far, and total depth of field for a given lens, aperture, and distance.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Camera Specs","label":null,"prefix":null,"suffix":null,"section":"Camera 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Constants","label":null,"prefix":null,"suffix":null,"section":"Constants","hero":false,"slider":null,"value":null,"display":null},{"text":"coc = 0.03 / sensor crop factor // mm (Circle of Confusion)","label":null,"prefix":null,"suffix":"mm (Circle of Confusion)","section":"Constants","hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"distance mm = subject distance * 304.8","label":null,"prefix":null,"suffix":null,"section":"Constants","hidden":false,"hero":false,"slider":null,"value":3048,"display":"3,048"},{"text":"# Hyperfocal Distance","label":null,"prefix":null,"suffix":null,"section":"Hyperfocal Distance","hero":false,"slider":null,"value":null,"display":null},{"text":"hyperfocal mm = (focal length^2 / (aperture * coc)) + focal length","label":null,"prefix":null,"suffix":null,"section":"Hyperfocal Distance","hidden":false,"hero":false,"slider":null,"value":29811.904761904763,"display":"29,811.9"},{"text":"hyperfocal feet = hyperfocal mm / 304.8","label":null,"prefix":null,"suffix":null,"section":"Hyperfocal Distance","hidden":false,"hero":false,"slider":null,"value":97.80808648918885,"display":"97.81"},{"text":"# DoF Calculation","label":null,"prefix":null,"suffix":null,"section":"DoF Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"near point mm = (hyperfocal mm * distance mm) / (hyperfocal mm + (distance mm - focal length))","label":null,"prefix":null,"suffix":null,"section":"DoF Calculation","hidden":false,"hero":false,"slider":null,"value":2769.4894689176317,"display":"2,769.49"},{"text":"far point mm = (hyperfocal mm * distance mm) / (hyperfocal mm - (distance mm - focal length))","label":null,"prefix":null,"suffix":null,"section":"DoF Calculation","hidden":false,"hero":false,"slider":null,"value":3388.789753716977,"display":"3,388.79"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"total depth of field = (far point mm - near point mm) / 304.8 // feet @hero","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":true,"slider":null,"value":2.0318250813626806,"display":"2.032"},{"text":"near limit = near point mm / 304.8 // feet","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":false,"slider":null,"value":9.086251538443673,"display":"9.086"},{"text":"far limit = far point mm / 304.8 // feet","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":false,"slider":null,"value":11.118076619806356,"display":"11.12"},{"text":"is infinite = distance mm >= hyperfocal mm","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"dof display = if(is infinite, 9999, total depth of field)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":2.0318250813626806,"display":"2.032"}]},{"id":"derivative-chain-rule","title":"Derivative — Chain Rule","description":"Evaluate (f∘g)'(x) = f'(g(x)) · g'(x).","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Values","label":null,"prefix":null,"suffix":null,"section":"Values","hero":false,"slider":null,"value":null,"display":null},{"text":"fprime_at_g = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"gprime_at_x = 7 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":7,"display":"7"},{"text":"# Chain rule","label":null,"prefix":null,"suffix":null,"section":"Chain rule","hero":false,"slider":null,"value":null,"display":null},{"text":"derivative = fprime_at_g * gprime_at_x // @label((f∘g)'(x))","label":"(f∘g)'(x)","prefix":null,"suffix":null,"section":"Chain rule","hidden":false,"hero":true,"slider":null,"value":28,"display":"28"}]},{"id":"derivative-power-rule","title":"Derivative — Power Rule","description":"Evaluate d/dx [a·xⁿ] = a·n·x^(n−1) at a given point.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Function: f(x) = a · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 4 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":4,"display":"4"},{"text":"x = 2 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":2,"display":"2"},{"text":"# Original and derivative at x","label":null,"prefix":null,"suffix":null,"section":"Original and derivative at x","hero":false,"slider":null,"value":null,"display":null},{"text":"f_x = a * x^n // @label(f(x))","label":"f(x)","prefix":null,"suffix":null,"section":"Original and derivative at x","hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"fprime_x = a * n * x^(n - 1) // @label(f'(x))","label":"f'(x)","prefix":null,"suffix":null,"section":"Original and derivative at x","hidden":false,"hero":true,"slider":null,"value":96,"display":"96"}]},{"id":"derivative-product-rule","title":"Derivative — Product Rule","description":"Evaluate (f·g)' = f'·g + f·g' at a given x using user-supplied f, g, f', g'.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Values at x","label":null,"prefix":null,"suffix":null,"section":"Values at x","hero":false,"slider":null,"value":null,"display":null},{"text":"f = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"g = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"fprime = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"gprime = 6 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":6,"display":"6"},{"text":"# Product rule","label":null,"prefix":null,"suffix":null,"section":"Product rule","hero":false,"slider":null,"value":null,"display":null},{"text":"derivative = fprime * g + f * gprime // @label((fg)')","label":"(fg)","prefix":null,"suffix":null,"section":"Product rule","hidden":false,"hero":true,"slider":null,"value":38,"display":"38"}]},{"id":"differential-gear-ratio-impact","title":"Differential Gear Ratio Impact","description":"Calculate RPM change after differential gear change.","category":"engineering","icon":"settings","tags":["automotive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"# Gearing","label":null,"prefix":null,"suffix":null,"section":"Gearing","hero":false,"slider":null,"value":null,"display":null},{"text":"old gear ratio = 3.42","label":null,"prefix":null,"suffix":null,"section":"Gearing","hidden":false,"hero":false,"slider":null,"value":3.42,"display":"3.42"},{"text":"new gear ratio = 4.10","label":null,"prefix":null,"suffix":null,"section":"Gearing","hidden":false,"hero":false,"slider":null,"value":4.1,"display":"4.1"},{"text":"old rpm = 2500","label":null,"prefix":null,"suffix":null,"section":"Gearing","hidden":false,"hero":false,"slider":null,"value":2500,"display":"2,500"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"new rpm = old rpm * (new gear ratio / old gear ratio)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":2997.0760233918127,"display":"2,997.08"}]},{"id":"disability-insurance-benefit-gap","title":"Disability Insurance Benefit Gap","description":"Calculate the income gap between current pay and disability insurance benefits.","category":"other","icon":"calculator","tags":["insurance","benefit","gap"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.426Z"},"rows":[{"text":"current_monthly_income = 6000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6000,"display":"6,000"},{"text":"insurance_benefit_percentage = 0.60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"monthly_benefit = current_monthly_income * insurance_benefit_percentage","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3600,"display":"3,600"},{"text":"income_gap = current_monthly_income - monthly_benefit","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2400,"display":"2,400"}]},{"id":"discount-tax","title":"Discount & Tax","description":"See the final price after discount and sales tax — with effective savings.","category":"everyday","icon":"tag","tags":["tax","price"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Original Price","label":null,"prefix":null,"suffix":null,"section":"Original Price","hero":false,"slider":null,"value":null,"display":null},{"text":"$original price = 89.99 // 1..10k","label":null,"prefix":"$","suffix":null,"section":"Original Price","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":89.99,"display":"$89.99"},{"text":"discount = 30 // % 0..90","label":null,"prefix":null,"suffix":"%","section":"Original Price","hidden":false,"hero":false,"slider":{"min":0,"max":90,"step":1},"value":30,"display":"30"},{"text":"# After Discount","label":null,"prefix":null,"suffix":null,"section":"After Discount","hero":false,"slider":null,"value":null,"display":null},{"text":"$you save = original_price * discount / 100","label":null,"prefix":"$","suffix":null,"section":"After Discount","hidden":false,"hero":false,"slider":null,"value":26.997,"display":"$27.00"},{"text":"$sale price = original_price - you_save // @hero","label":null,"prefix":"$","suffix":null,"section":"After Discount","hidden":false,"hero":true,"slider":null,"value":62.993,"display":"$62.99"},{"text":"# After Sales Tax","label":null,"prefix":null,"suffix":null,"section":"After Sales Tax","hero":false,"slider":null,"value":null,"display":null},{"text":"sales tax rate = 8.25 // % 0..15 by 0.25","label":null,"prefix":null,"suffix":"%","section":"After Sales Tax","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.25},"value":8.25,"display":"8.25"},{"text":"$tax amount = sale_price * sales_tax_rate / 100","label":null,"prefix":"$","suffix":null,"section":"After Sales Tax","hidden":false,"hero":false,"slider":null,"value":5.1969225,"display":"$5.20"},{"text":"$final price with tax = sale_price + tax_amount","label":null,"prefix":"$","suffix":null,"section":"After Sales Tax","hidden":false,"hero":false,"slider":null,"value":68.1899225,"display":"$68.19"},{"text":"# Effective Discount","label":null,"prefix":null,"suffix":null,"section":"Effective Discount","hero":false,"slider":null,"value":null,"display":null},{"text":"pct of original you pay = round(final_price_with_tax / original_price * 100, 1) // %","label":null,"prefix":null,"suffix":"%","section":"Effective Discount","hidden":false,"hero":false,"slider":null,"value":75.8,"display":"75.8"},{"text":"$true savings = original_price - final_price_with_tax","label":null,"prefix":"$","suffix":null,"section":"Effective Discount","hidden":false,"hero":false,"slider":null,"value":21.8000775,"display":"$21.80"},{"text":"effective discount = round((true_savings / original_price) * 100, 1) // %","label":null,"prefix":null,"suffix":"%","section":"Effective Discount","hidden":false,"hero":false,"slider":null,"value":24.2,"display":"24.2"}]},{"id":"discriminant","title":"Discriminant","description":"Compute the discriminant b² − 4ac of a quadratic.","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Coefficients","label":null,"prefix":null,"suffix":null,"section":"Coefficients","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 1 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Coefficients","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":1,"display":"1"},{"text":"b = -5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Coefficients","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":-5,"display":"-5"},{"text":"c = 6 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Coefficients","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":6,"display":"6"},{"text":"# Discriminant","label":null,"prefix":null,"suffix":null,"section":"Discriminant","hero":false,"slider":null,"value":null,"display":null},{"text":"discriminant = b^2 - 4 * a * c","label":null,"prefix":null,"suffix":null,"section":"Discriminant","hidden":false,"hero":true,"slider":null,"value":1,"display":"1"},{"text":"# >0 → two real roots; =0 → one real root; <0 → two complex roots","label":null,"prefix":null,"suffix":null,"section":">0 → two real roots; =0 → one real root; <0 → two complex roots","hero":false,"slider":null,"value":null,"display":null}]},{"id":"disk-raid-10-capacity","title":"Disk Raid 10 Capacity","description":"Calculate usable capacity for a RAID 10 array from drive count and capacity.","category":"other","icon":"calculator","tags":["disk","raid"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# RAID 10 Parameters","label":null,"prefix":null,"suffix":null,"section":"RAID 10 Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"number of drives = 4 // 4..24 (must be even)","label":null,"prefix":null,"suffix":"4..24 (must be even)","section":"RAID 10 Parameters","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"drive capacity terabytes = 4 // TB","label":null,"prefix":null,"suffix":"TB","section":"RAID 10 Parameters","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"# RAID 10 mirrors then stripes, so half capacity is usable","label":null,"prefix":null,"suffix":null,"section":"RAID 10 mirrors then stripes, so half capacity is usable","hero":false,"slider":null,"value":null,"display":null},{"text":"usable capacity terabytes = (number of drives / 2) * drive capacity terabytes // @hero","label":null,"prefix":null,"suffix":null,"section":"RAID 10 mirrors then stripes, so half capacity is usable","hidden":false,"hero":true,"slider":null,"value":8,"display":"8"},{"text":"mirrored overhead terabytes = usable capacity terabytes // @hero","label":null,"prefix":null,"suffix":null,"section":"RAID 10 mirrors then stripes, so half capacity is 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-1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"y2 = 6 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":6,"display":"6"},{"text":"# Distance","label":null,"prefix":null,"suffix":null,"section":"Distance","hero":false,"slider":null,"value":null,"display":null},{"text":"distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)","label":null,"prefix":null,"suffix":null,"section":"Distance","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"distance-time","title":"Distance, Speed, Time","description":"Travel time and distance for any speed, from walking pace to light-speed.","category":"science","icon":"gauge","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"distance km = 149600000 // km 0.001..1e10 by 1","label":null,"prefix":null,"suffix":"km","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000000000,"step":1},"value":149600000,"display":"149,600,000"},{"text":"speed km per s = 299792.458 // km/s 0.0001..299793","label":null,"prefix":null,"suffix":"km/s","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.0001,"max":299793,"step":5000},"value":299792.458,"display":"299,792.46"},{"text":"# Time","label":null,"prefix":null,"suffix":null,"section":"Time","hero":false,"slider":null,"value":null,"display":null},{"text":"time seconds = distance km / speed km per s // s","label":null,"prefix":null,"suffix":"s","section":"Time","hidden":false,"hero":false,"slider":null,"value":499.01188641643546,"display":"499.01"},{"text":"time minutes = time seconds / 60 // min @hero","label":null,"prefix":null,"suffix":"min","section":"Time","hidden":false,"hero":true,"slider":null,"value":8.316864773607257,"display":"8.317"},{"text":"time hours = time minutes / 60 // hr","label":null,"prefix":null,"suffix":"hr","section":"Time","hidden":false,"hero":false,"slider":null,"value":0.13861441289345428,"display":"0.1386"},{"text":"# Inverse: distance at this speed in a given duration","label":null,"prefix":null,"suffix":null,"section":"Inverse: distance at this speed in a given duration","hero":false,"slider":null,"value":null,"display":null},{"text":"duration sec = 1 // s 0..3.6k","label":null,"prefix":null,"suffix":"s","section":"Inverse: distance at this speed in a given duration","hidden":false,"hero":false,"slider":{"min":0,"max":3600,"step":50},"value":1,"display":"1"},{"text":"distance covered km = speed km per s * duration sec // km","label":null,"prefix":null,"suffix":"km","section":"Inverse: distance at this speed in a given 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6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"distance_km = (2 * earth_radius_km * (eye_height_meters / 1000) + (eye_height_meters / 1000) ** 2) ** 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4.654181226596146,"display":"4.654"}]},{"id":"dive-decompression-penalty","title":"Dive Decompression Penalty","description":"Check whether a scuba dive exceeds the no-decompression limit at a given depth.","category":"other","icon":"calculator","tags":["penalty"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"depth_feet = 80","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"bottom_time_minutes = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"no_deco_limit_minutes = 480 / (depth_feet - 30) // Very rough approximation","label":null,"prefix":null,"suffix":"Very rough approximation","section":null,"hidden":false,"hero":false,"slider":null,"value":9.6,"display":"9.6"},{"text":"deco_penalty_status = bottom_time_minutes > no_deco_limit_minutes ? 1 : 0 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"dividend-payout-ratio","title":"Dividend Payout Ratio","description":"Calculate dividend payout ratio from dividends per share and earnings per share.","category":"finance","icon":"ratio","tags":["dividend","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"dividends_per_share = 2.50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"earnings_per_share = 5.00","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"payout_ratio = dividends_per_share / earnings_per_share","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"dividend-yield","title":"Dividend Yield","description":"Calculate dividend yield from annual dividends per share and stock price.","category":"finance","icon":"dollar-sign","tags":["dividend","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Dividend Data","label":null,"prefix":null,"suffix":null,"section":"Dividend Data","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual_dividends_per_share = 4.50 // dollars 0..100","label":null,"prefix":"$","suffix":"dollars","section":"Dividend Data","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":4.5,"display":"$4.50"},{"text":"$share_price = 120 // dollars 1..5k","label":null,"prefix":"$","suffix":"dollars","section":"Dividend Data","hidden":false,"hero":false,"slider":{"min":1,"max":5000,"step":50},"value":120,"display":"$120.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"dividend_yield = (annual_dividends_per_share / share_price) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":3.75,"display":"3.75"},{"text":"$quarterly_dividend = annual_dividends_per_share / 4","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":1.125,"display":"$1.13"},{"text":"$investment_for_1000_monthly = (1000 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@hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":309.24949471099166,"display":"309.25"}]},{"id":"dog-years-to-human-years-detailed","title":"Dog Years To Human Years Detailed","description":"Convert a dog's age in years to its equivalent human age.","category":"everyday","icon":"dog","tags":["dog","human","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"actual_dog_age_years = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"first_year_human_equivalent = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"second_year_human_equivalent = 9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"additional_years_multiplier = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"equivalent_human_age = first_year_human_equivalent + second_year_human_equivalent + (actual_dog_age_years - 2) * additional_years_multiplier","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":39,"display":"39"}]},{"id":"domain-name-registration-value","title":"Domain Name Registration Value","description":"Calculate the total cost of registering a domain over multiple years with renewal increases.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"annual_registration_fee = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"number_of_years = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"renewal_price_increase_percentage = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"total_registration_cost = annual_registration_fee * ((1 + (renewal_price_increase_percentage / 100)) ** number_of_years - 1) / (renewal_price_increase_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":188.66838803323267,"display":"188.67"}]},{"id":"door-swing-clearance-area","title":"Door Swing Clearance Area","description":"Calculate the floor space swept by a swinging door.","category":"design","icon":"door-open","tags":["design","layout"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"door_width_inches = 32 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"swing_angle_degrees = 90 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":90,"display":"90"},{"text":"clearance_area_square_inches = (3.14159 * (door_width_inches^2)) * (swing_angle_degrees / 360) // sq inches @hero","label":null,"prefix":null,"suffix":"sq inches","section":null,"hidden":false,"hero":true,"slider":null,"value":804.24704,"display":"804.25"},{"text":"clearance_area_square_feet = clearance_area_square_inches / 144 // sq ft","label":null,"prefix":null,"suffix":"sq ft","section":null,"hidden":false,"hero":false,"slider":null,"value":5.585048888888889,"display":"5.585"}]},{"id":"doppler-effect-source-moving","title":"Doppler Effect Source Moving","description":"Calculate observed frequency when a sound source moves toward an observer.","category":"education","icon":"book-open","tags":["effect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"source_frequency = 440 // Hz","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":false,"slider":null,"value":440,"display":"440"},{"text":"speed_of_sound = 343 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":343,"display":"343"},{"text":"source_velocity = 30 // m/s (towards observer)","label":null,"prefix":null,"suffix":"m/s (towards observer)","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"observed_frequency = source_frequency * (speed_of_sound / (speed_of_sound - source_velocity)) // Hz @hero","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":true,"slider":null,"value":482.1725239616613,"display":"482.17"}]},{"id":"doppler-shift-frequency","title":"Doppler Shift Frequency","description":"Calculate observed frequency of a moving sound source.","category":"science","icon":"wind","tags":["science","physics","acoustics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"source_frequency_hz = 1000 // Hz","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"speed_of_sound_m_per_s = 343 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":343,"display":"343"},{"text":"source_velocity_m_per_s = 30 // m/s (moving toward observer)","label":null,"prefix":null,"suffix":"m/s 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level","section":null,"hidden":false,"hero":true,"slider":null,"value":6.666666666666667,"display":"6.667"}]},{"id":"drag-force-advanced","title":"Drag Force Advanced","description":"Calculate aerodynamic drag force from velocity, drag coefficient, and frontal area.","category":"science","icon":"flask-conical","tags":["drag","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Fluid Dynamics","label":null,"prefix":null,"suffix":null,"section":"Fluid Dynamics","hero":false,"slider":null,"value":null,"display":null},{"text":"velocity = 60 // mph 1..200","label":null,"prefix":null,"suffix":"mph","section":"Fluid Dynamics","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":60,"display":"60"},{"text":"drag coefficient = 0.30 // 0.1..1.5","label":null,"prefix":null,"suffix":null,"section":"Fluid Dynamics","hidden":false,"hero":false,"slider":{"min":0.1,"max":1.5,"step":0.02},"value":0.3,"display":"0.3"},{"text":"frontal area = 22 // sq ft 5..50","label":null,"prefix":null,"suffix":"sq ft","section":"Fluid Dynamics","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":22,"display":"22"},{"text":"air density = 1.225 // kg/m3","label":null,"prefix":null,"suffix":"kg/m3","section":"Fluid Dynamics","hidden":false,"hero":false,"slider":null,"value":1.225,"display":"1.225"},{"text":"# Conversions","label":null,"prefix":null,"suffix":null,"section":"Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"velocity mps = velocity * 0.44704","label":null,"prefix":null,"suffix":null,"section":"Conversions","hidden":false,"hero":false,"slider":null,"value":26.8224,"display":"26.82"},{"text":"area m2 = frontal area * 0.092903","label":null,"prefix":null,"suffix":null,"section":"Conversions","hidden":false,"hero":false,"slider":null,"value":2.043866,"display":"2.044"},{"text":"# Formula: Fd = 0.5 * rho * v^2 * Cd * A","label":null,"prefix":null,"suffix":null,"section":"Formula: Fd = 0.5 * rho * v^2 * Cd * A","hero":false,"slider":null,"value":null,"display":null},{"text":"drag force newtons = 0.5 * air density * (velocity mps^2) * drag coefficient * area m2","label":null,"prefix":null,"suffix":null,"section":"Formula: Fd = 0.5 * rho * v^2 * Cd * A","hidden":false,"hero":false,"slider":null,"value":270.19358678841655,"display":"270.19"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"drag force = drag force newtons * 0.224809 // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":"Result","hidden":false,"hero":true,"slider":null,"value":60.741950052317144,"display":"60.74"},{"text":"# Energy Loss","label":null,"prefix":null,"suffix":null,"section":"Energy Loss","hero":false,"slider":null,"value":null,"display":null},{"text":"power required hp = (drag force * velocity * 5280 / 3600) / 550 // hp","label":null,"prefix":null,"suffix":"hp","section":"Energy Loss","hidden":false,"hero":false,"slider":null,"value":9.718712008370742,"display":"9.719"},{"text":"fuel consumption impact = (velocity / 60)^3","label":null,"prefix":null,"suffix":null,"section":"Energy Loss","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"rolling resistance estimate = 0.015 * 3000 // lbs","label":null,"prefix":null,"suffix":"lbs","section":"Energy Loss","hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"total force = drag force + rolling resistance estimate","label":null,"prefix":null,"suffix":null,"section":"Energy Loss","hidden":false,"hero":false,"slider":null,"value":105.74195005231715,"display":"105.74"}]},{"id":"drink-dilution","title":"Drink Dilution","description":"Calculate final strength when mixing concentrates with water or mixer.","category":"cooking","icon":"wine","tags":["abv"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Concentrate","label":null,"prefix":null,"suffix":null,"section":"Concentrate","hero":false,"slider":null,"value":null,"display":null},{"text":"concentrate strength = 40 // % 1..100","label":null,"prefix":null,"suffix":"%","section":"Concentrate","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":40,"display":"40"},{"text":"concentrate volume = 2 // oz 0.25..32 by 0.25","label":null,"prefix":null,"suffix":"oz","section":"Concentrate","hidden":false,"hero":false,"slider":{"min":0.25,"max":32,"step":0.25},"value":2,"display":"2"},{"text":"# Mixer","label":null,"prefix":null,"suffix":null,"section":"Mixer","hero":false,"slider":null,"value":null,"display":null},{"text":"mixer strength = 0 // % 0..50","label":null,"prefix":null,"suffix":"%","section":"Mixer","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":0,"display":"0"},{"text":"mixer volume = 6 // oz 0..64 by 0.5","label":null,"prefix":null,"suffix":"oz","section":"Mixer","hidden":false,"hero":false,"slider":{"min":0,"max":64,"step":0.5},"value":6,"display":"6"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"total volume = concentrate_volume + mixer_volume // oz","label":null,"prefix":null,"suffix":"oz","section":"Result","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"final strength = round((concentrate_strength * concentrate_volume + mixer_strength * mixer_volume) / total_volume, 1) // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":10,"display":"10"},{"text":"# Adjustments","label":null,"prefix":null,"suffix":null,"section":"Adjustments","hero":false,"slider":null,"value":null,"display":null},{"text":"target strength = 5 // % 0.5..50","label":null,"prefix":null,"suffix":"%","section":"Adjustments","hidden":false,"hero":false,"slider":{"min":0.5,"max":50,"step":0.5},"value":5,"display":"5"},{"text":"mixer needed for target = round(concentrate_volume * (concentrate_strength - target_strength) / (target_strength - mixer_strength), 1) // oz","label":null,"prefix":null,"suffix":"oz","section":"Adjustments","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"total volume at target = concentrate_volume + mixer_needed_for_target // oz","label":null,"prefix":null,"suffix":"oz","section":"Adjustments","hidden":false,"hero":false,"slider":null,"value":16,"display":"16"}]},{"id":"drive-shaft-critical-speed","title":"Drive Shaft Critical Speed","description":"Calculate drive shaft critical speed.","category":"engineering","icon":"settings","tags":["automotive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Shaft Specs","label":null,"prefix":null,"suffix":null,"section":"Shaft Specs","hero":false,"slider":null,"value":null,"display":null},{"text":"diameter inches = 3","label":null,"prefix":null,"suffix":null,"section":"Shaft Specs","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"length inches = 50","label":null,"prefix":null,"suffix":null,"section":"Shaft Specs","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"material constant = 4800000","label":null,"prefix":null,"suffix":null,"section":"Shaft Specs","hidden":false,"hero":false,"slider":null,"value":4800000,"display":"4,800,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"critical speed rpm = material constant * (diameter inches / (length inches ^ 2))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":5760,"display":"5,760"}]},{"id":"driveway-sealant-volume","title":"Driveway Sealant Volume","description":"Calculate gallons of sealant needed for your driveway.","category":"construction","icon":"container","tags":["construction","maintenance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"driveway_width_feet = 20 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"driveway_length_feet = 40 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"coverage_sq_ft_per_gallon = 80 // sq ft","label":null,"prefix":null,"suffix":"sq ft","section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"total_gallons_needed = (driveway_width_feet * driveway_length_feet) / coverage_sq_ft_per_gallon // gallons @hero","label":null,"prefix":null,"suffix":"gallons","section":null,"hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"drywall-panel-calculator","title":"Drywall Panel Calculator","description":"Estimate drywall panels, joint compound, and tape rolls needed for an area.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Project Area","label":null,"prefix":null,"suffix":null,"section":"Project Area","hero":false,"slider":null,"value":null,"display":null},{"text":"total area = 800 // square feet 10..5k","label":null,"prefix":null,"suffix":"square feet","section":"Project Area","hidden":false,"hero":false,"slider":{"min":10,"max":5000,"step":50},"value":800,"display":"800"},{"text":"# Panel Size","label":null,"prefix":null,"suffix":null,"section":"Panel Size","hero":false,"slider":null,"value":null,"display":null},{"text":"panel width = 4 // feet","label":null,"prefix":null,"suffix":"feet","section":"Panel Size","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"panel length = 8 // feet 8..12 by 2","label":null,"prefix":null,"suffix":"feet","section":"Panel Size","hidden":false,"hero":false,"slider":{"min":8,"max":12,"step":2},"value":8,"display":"8"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_panel_area = panel width * panel length","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"panels needed = roundup(total area / panel_area) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":25,"display":"25"},{"text":"# Materials","label":null,"prefix":null,"suffix":null,"section":"Materials","hero":false,"slider":null,"value":null,"display":null},{"text":"waste factor percent = 15 // 5..30","label":null,"prefix":null,"suffix":null,"section":"Materials","hidden":false,"hero":false,"slider":{"min":5,"max":30,"step":1},"value":15,"display":"15"},{"text":"total panels with waste = roundup(panels needed * (1 + waste factor percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Materials","hidden":false,"hero":false,"slider":null,"value":29,"display":"29"},{"text":"# Accessories","label":null,"prefix":null,"suffix":null,"section":"Accessories","hero":false,"slider":null,"value":null,"display":null},{"text":"# Rule of thumb: 1 gallon of joint compound per 100 sq ft","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 gallon of joint compound per 100 sq ft","hero":false,"slider":null,"value":null,"display":null},{"text":"joint compound gallons = round(total area / 100, 1)","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 gallon of joint compound per 100 sq ft","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Rule of thumb: 1 roll of tape per 200 sq ft","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 roll of tape per 200 sq ft","hero":false,"slider":null,"value":null,"display":null},{"text":"tape rolls = roundup(total area / 200)","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 roll of tape per 200 sq ft","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"}]},{"id":"dunning-kruger-confidence-gap","title":"Dunning Kruger Confidence Gap","description":"Calculate the gap between actual and perceived competence 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div)","section":"Result","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"}]},{"id":"earth-curvature-hidden-height","title":"Earth Curvature Hidden Height","description":"Calculate how much of a distant object is hidden by Earth's curvature.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Geography","label":null,"prefix":null,"suffix":null,"section":"Geography","hero":false,"slider":null,"value":null,"display":null},{"text":"distance to object = 10 // miles 1..500","label":null,"prefix":null,"suffix":"miles","section":"Geography","hidden":false,"hero":false,"slider":{"min":1,"max":500,"step":1},"value":10,"display":"10"},{"text":"observer height = 6 // feet 1..1k","label":null,"prefix":null,"suffix":"feet","section":"Geography","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":6,"display":"6"},{"text":"# Constants","label":null,"prefix":null,"suffix":null,"section":"Constants","hero":false,"slider":null,"value":null,"display":null},{"text":"earth radius miles = 3959","label":null,"prefix":null,"suffix":null,"section":"Constants","hidden":false,"hero":false,"slider":null,"value":3959,"display":"3,959"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"distance to horizon = sqrt(2 * earth radius miles * (observer height / 5280)) // miles","label":null,"prefix":null,"suffix":"miles","section":"Calculation","hidden":false,"hero":false,"slider":null,"value":2.999621188204816,"display":"3"},{"text":"is visible = distance to object <= distance to horizon","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"# Hidden Height Formula","label":null,"prefix":null,"suffix":null,"section":"Hidden Height 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@hero","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":true,"slider":null,"value":32.6784544740555,"display":"32.68"},{"text":"horizon distance = distance to horizon // miles","label":null,"prefix":null,"suffix":"miles","section":"Result","hidden":false,"hero":false,"slider":null,"value":2.999621188204816,"display":"3"},{"text":"total drop = (distance to object^2) / (2 * earth radius miles) * 5280 // feet","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":false,"slider":null,"value":66.68350593584239,"display":"66.68"}]},{"id":"easing-curves","title":"Easing Curves","description":"Hermite-fit cubics that smoothly interpolate between two values with chosen slopes at the endpoints — the basis for animation easing, monotone interpolation, and CAGD 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(ease-in)","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"__hermiteEval","text":"__hermiteEval"},[["folded",[0,0,1,0]],{"type":"id","value":"x","text":"x","canonicalName":"x"}]],"__hermiteCoeffs":[0,0,1,0],"name":"accelerate"},"display":null},{"text":"# Decelerate — start with slope 2, end flat (ease-out)","label":null,"prefix":null,"suffix":null,"section":"Decelerate — start with slope 2, end flat (ease-out)","hero":false,"slider":null,"value":null,"display":null},{"text":"decelerate = hermite(0, 0, 2, 1, 1, 0)","label":null,"prefix":null,"suffix":null,"section":"Decelerate — start with slope 2, end flat (ease-out)","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"__hermiteEval","text":"__hermiteEval"},[["folded",[0,2,-1,0]],{"type":"id","value":"x","text":"x","canonicalName":"x"}]],"__hermiteCoeffs":[0,2,-1,0],"name":"decelerate"},"display":null},{"text":"# Three curves, one per chart","label":null,"prefix":null,"suffix":null,"section":"Three curves, one per chart","hero":false,"slider":null,"value":null,"display":null},{"text":"# Try a custom fit","label":null,"prefix":null,"suffix":null,"section":"Try a custom fit","hero":false,"slider":null,"value":null,"display":null},{"text":"slope_start = 0 // -3..3 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Try a custom fit","hidden":false,"hero":false,"slider":{"min":-3,"max":3,"step":0.1},"value":0,"display":"0"},{"text":"slope_end = 0 // -3..3 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Try a custom 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100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"shipping_charged = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"item_cost = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"shipping_cost = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"ebay_fee_percentage = 0.1325","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1325,"display":"0.1325"},{"text":"ebay_per_order_fee = 0.30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"total_revenue = selling_price + shipping_charged","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":110,"display":"110"},{"text":"ebay_fee = (total_revenue * ebay_fee_percentage) + ebay_per_order_fee","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14.875,"display":"14.88"},{"text":"total_cost = item_cost + shipping_cost + ebay_fee","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":66.875,"display":"66.88"},{"text":"net_profit = total_revenue - total_cost","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":43.125,"display":"43.13"}]},{"id":"ebitda-calculator","title":"Ebitda Calculator","description":"Calculate EBITDA from net income, interest, taxes, depreciation, and amortization.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Company Financials","label":null,"prefix":null,"suffix":null,"section":"Company Financials","hero":false,"slider":null,"value":null,"display":null},{"text":"$net income = 500000 // 0..10M","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":10000000,"step":100000},"value":500000,"display":"$500,000.00"},{"text":"$interest expense = 50000 // 0..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":5000},"value":50000,"display":"$50,000.00"},{"text":"$income tax expense = 120000 // 0..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":5000},"value":120000,"display":"$120,000.00"},{"text":"$depreciation = 80000 // 0..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":5000},"value":80000,"display":"$80,000.00"},{"text":"$amortization = 20000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":20000,"display":"$20,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$ebitda = net income + interest expense + income tax expense + depreciation + amortization // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":770000,"display":"$770,000.00"},{"text":"$ebit = net income + interest expense + income tax expense","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":670000,"display":"$670,000.00"},{"text":"ebitda margin = (ebitda / (net income * 4)) * 100 // % (assumes revenue is 4x net income for context)","label":null,"prefix":null,"suffix":"% (assumes revenue is 4x net income for context)","section":"Result","hidden":false,"hero":false,"slider":null,"value":38.5,"display":"38.5"}]},{"id":"eco-label-product-premium","title":"Eco Label Product Premium","description":"Compare costs of eco-labeled vs standard products.","category":"finance","icon":"tag","tags":["finance","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"standard_product_price = 10 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"eco_label_premium_percent = 15 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"eco_product_price = standard_product_price * (1 + eco_label_premium_percent / 100) // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11.5,"display":"11.5"},{"text":"annual_extra_cost_if_buying_weekly = (eco_product_price - standard_product_price) * 52 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":78,"display":"78"}]},{"id":"economic-order-quantity","title":"Economic Order Quantity","description":"Find the optimal order size to minimize total inventory costs.","category":"business","icon":"shopping-cart","tags":["order"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"annualDemand = 10000 // units","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"orderCost = 50 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"holdingCostPerUnit = 2.50 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"eoq = sqrt((2 * annualDemand * orderCost) / holdingCostPerUnit) // units @hero","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":true,"slider":null,"value":632.4555320336759,"display":"632.46"}]},{"id":"effective-annual-rate","title":"Effective Annual Rate","description":"Effective annual rate from a nominal rate compounded n times per year: EAR = (1 + r/n)ⁿ − 1.","category":"formulas","icon":"percent","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"nominal_rate = 6 // % 0..50","label":null,"prefix":null,"suffix":"%","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":6,"display":"6"},{"text":"compounding_periods = 12 // per year 1..365","label":null,"prefix":null,"suffix":"per year","section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":365,"step":1},"value":12,"display":"12"},{"text":"# Effective rate","label":null,"prefix":null,"suffix":null,"section":"Effective rate","hero":false,"slider":null,"value":null,"display":null},{"text":"effective_rate = ((1 + nominal_rate / 100 / compounding_periods)^compounding_periods - 1) * 100 // @label(EAR (%))","label":"EAR (%)","prefix":null,"suffix":null,"section":"Effective rate","hidden":false,"hero":true,"slider":null,"value":6.16778118644982,"display":"6.168"}]},{"id":"effective-gross-income","title":"Effective Gross Income","description":"Property income after accounting for vacancy and credit losses.","category":"real-estate","icon":"dollar-sign","tags":["income"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"potentialRentalIncome = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"vacancyAndCreditLoss = 5000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"otherIncome = 3000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"egi = potentialRentalIncome - vacancyAndCreditLoss + otherIncome // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":98000,"display":"98,000"}]},{"id":"eisenhower-matrix-task-priority","title":"Eisenhower Matrix Task Priority","description":"Calculate task priority index from urgency and importance scores.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"urgency_score = 8 // 1..10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":8,"display":"8"},{"text":"importance_score = 9 // 1..10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":9,"display":"9"},{"text":"priority_index = urgency_score * importance_score // max 100 @hero","label":null,"prefix":null,"suffix":"max 100","section":null,"hidden":false,"hero":true,"slider":null,"value":72,"display":"72"},{"text":"_quadrant = if (urgency_score > 5) { if (importance_score > 5) { \"Do First\" } else { \"Delegate\" } } else { if (importance_score > 5) { \"Schedule\" } else { \"Eliminate\" } }","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":"Do First","display":"Do First"}]},{"id":"electric-car-emissions-savings","title":"Electric Car Emissions Savings","description":"Compare EV emissions to gas vehicle emissions.","category":"science","icon":"zap","tags":["eco","ev","emissions"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"annual_km_driven = 15000 // km","label":null,"prefix":null,"suffix":"km","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"gas_car_emissions_per_km = 0.12 // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"electric_car_emissions_per_km = 0.05 // kg CO2 (grid dependent)","label":null,"prefix":null,"suffix":"kg CO2 (grid dependent)","section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"annual_co2_savings_kg = annual_km_driven * (gas_car_emissions_per_km - electric_car_emissions_per_km) // kg CO2 @hero","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":true,"slider":null,"value":1050,"display":"1,050"}]},{"id":"electric-circuit-total-resistance-parallel","title":"Electric Circuit Total Resistance Parallel","description":"Calculate total resistance of three resistors in parallel.","category":"education","icon":"book-open","tags":["electric"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"r1 = 100 // ohms","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"r2 = 200 // ohms","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"r3 = 300 // ohms","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"total_resistance_parallel = 1 / (1/r1 + 1/r2 + 1/r3) // ohms @hero","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":true,"slider":null,"value":54.54545454545455,"display":"54.55"}]},{"id":"electric-field-point-charge","title":"Electric Field Point Charge","description":"Calculate the electric field magnitude at a distance from a point charge.","category":"education","icon":"book-open","tags":["electric","charge"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"charge = 1e-6 // Coulombs","label":null,"prefix":null,"suffix":"Coulombs","section":null,"hidden":false,"hero":false,"slider":null,"value":0.000001,"display":"0.000001"},{"text":"distance = 0.1 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"_k = 8.987e9 // N*m^2/C^2","label":null,"prefix":null,"suffix":"N*m^2/C^2","section":null,"hidden":true,"hero":false,"slider":null,"value":8987000000,"display":"8,987,000,000"},{"text":"electric_field_magnitude = k * charge / distance^2 // Newtons per Coulomb @hero","label":null,"prefix":null,"suffix":"Newtons per Coulomb","section":null,"hidden":false,"hero":true,"slider":null,"value":898699.9999999999,"display":"898,700"}]},{"id":"electric-power-efficiency","title":"Electric Power Efficiency","description":"Calculate electric power efficiency and power loss from input and output watts.","category":"education","icon":"book-open","tags":["electric"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"power_input = 1000 // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"power_output = 850 // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":850,"display":"850"},{"text":"efficiency_percentage = (power_output / power_input) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":85,"display":"85"},{"text":"power_loss = power_input - power_output // Watts @hero","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"}]},{"id":"electrical-wire","title":"Wire Gauge","description":"Calculate minimum wire gauge for an electrical circuit.","category":"engineering","icon":"zap","tags":["electrical"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Circuit Requirements","label":null,"prefix":null,"suffix":null,"section":"Circuit Requirements","hero":false,"slider":null,"value":null,"display":null},{"text":"amps = 20 // 1..200","label":null,"prefix":null,"suffix":null,"section":"Circuit Requirements","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":20,"display":"20"},{"text":"distance ft = 100 // 10..1k","label":null,"prefix":null,"suffix":null,"section":"Circuit Requirements","hidden":false,"hero":false,"slider":{"min":10,"max":1000,"step":1},"value":100,"display":"100"},{"text":"voltage = 120 // V 12..480 by 12","label":null,"prefix":null,"suffix":"V","section":"Circuit Requirements","hidden":false,"hero":false,"slider":{"min":12,"max":480,"step":12},"value":120,"display":"120"},{"text":"# Wire Sizing (copper, NEC)","label":null,"prefix":null,"suffix":null,"section":"Wire Sizing (copper, NEC)","hero":false,"slider":null,"value":null,"display":null},{"text":"max voltage drop pct = 3 // % 1..5 by 0.5","label":null,"prefix":null,"suffix":"%","section":"Wire Sizing (copper, NEC)","hidden":false,"hero":false,"slider":{"min":1,"max":5,"step":0.5},"value":3,"display":"3"},{"text":"_resistivity = 10.4 // ohm-cmil/ft (copper at 75°C)","label":null,"prefix":null,"suffix":"ohm-cmil/ft (copper at 75°C)","section":"Wire Sizing (copper, NEC)","hidden":true,"hero":false,"slider":null,"value":10.4,"display":"10.4"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"total wire length = distance ft * 2 // @label(Round-trip wire length) @suffix(ft)","label":"Round-trip wire length","prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"min wire area cmil = round((2 * resistivity * distance ft * amps) / (voltage * max voltage drop pct / 100)) // @hero @label(Min wire area (circular mils))","label":"Min wire area (circular mils)","prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":11556,"display":"11,556"},{"text":"# Voltage Drop","label":null,"prefix":null,"suffix":null,"section":"Voltage Drop","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage drop = round((2 * resistivity * distance ft * amps) / min wire area cmil * 100) / 100 // V","label":null,"prefix":null,"suffix":"V","section":"Voltage Drop","hidden":false,"hero":false,"slider":null,"value":3.6,"display":"3.6"},{"text":"voltage drop pct = round((voltage drop / voltage) * 100 * 100) / 100 // % @label(Voltage drop %)","label":"Voltage drop %","prefix":null,"suffix":"%","section":"Voltage Drop","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"power loss watts = round(voltage drop * amps * 10) / 10 // W @label(Power lost in wire)","label":"Power lost in wire","prefix":null,"suffix":"W","section":"Voltage Drop","hidden":false,"hero":false,"slider":null,"value":72,"display":"72"}]},{"id":"electricity-bill","title":"Electricity Bill","description":"Estimate your monthly electricity bill from appliance usage.","category":"everyday","icon":"zap","tags":["everyday"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Electricity Rate","label":null,"prefix":null,"suffix":null,"section":"Electricity Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"rate = 0.14 // $/kWh 0.05..0.5 by 0.01","label":null,"prefix":null,"suffix":"$/kWh","section":"Electricity Rate","hidden":false,"hero":false,"slider":{"min":0.05,"max":0.5,"step":0.01},"value":0.14,"display":"0.14"},{"text":"# Major Appliances (watts x hours/day)","label":null,"prefix":null,"suffix":null,"section":"Major Appliances (watts x hours/day)","hero":false,"slider":null,"value":null,"display":null},{"text":"ac watts = 1500 // W 0..5k by 100 @label(A/C or Heating)","label":"A/C or Heating","prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":100},"value":1500,"display":"1,500"},{"text":"ac hours = 6 // hrs/day 0..24","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":24,"step":1},"value":6,"display":"6"},{"text":"fridge watts = 150 // W 0..500 by 10","label":null,"prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":500,"step":10},"value":150,"display":"150"},{"text":"fridge hours = 24 // hrs/day","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"washer dryer watts = 3000 // W 0..5k by 100 @label(Washer + Dryer)","label":"Washer + Dryer","prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":100},"value":3000,"display":"3,000"},{"text":"washer dryer hours = 1 // hrs/day 0..4 by 0.5","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.5},"value":1,"display":"1"},{"text":"computer watts = 200 // W 0..1k @label(Computer / TV)","label":"Computer / TV","prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":200,"display":"200"},{"text":"computer hours = 8 // hrs/day 0..24","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":24,"step":1},"value":8,"display":"8"},{"text":"# Daily Usage","label":null,"prefix":null,"suffix":null,"section":"Daily Usage","hero":false,"slider":null,"value":null,"display":null},{"text":"daily kwh = round((ac watts * ac hours + fridge watts * fridge hours + washer dryer watts * washer dryer hours + computer watts * computer hours) / 1000 * 100) / 100","label":null,"prefix":null,"suffix":null,"section":"Daily Usage","hidden":false,"hero":false,"slider":null,"value":17.2,"display":"17.2"},{"text":"# Monthly Bill","label":null,"prefix":null,"suffix":null,"section":"Monthly Bill","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly kwh = round(daily kwh * 30.44 * 10) / 10 // kWh","label":null,"prefix":null,"suffix":"kWh","section":"Monthly Bill","hidden":false,"hero":false,"slider":null,"value":523.6,"display":"523.6"},{"text":"$monthly cost = round(monthly kwh * rate * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Monthly Bill","hidden":false,"hero":true,"slider":null,"value":73.3,"display":"$73.30"},{"text":"$annual cost = round(monthly cost * 12 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Monthly Bill","hidden":false,"hero":false,"slider":null,"value":879.6,"display":"$879.60"}]},{"id":"ellipse-area","title":"Ellipse Area","description":"Find the area of an ellipse from its two semi-axes: A = π × a × b.","category":"formulas","icon":"circle","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Semi-axes","label":null,"prefix":null,"suffix":null,"section":"Semi-axes","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 6 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Semi-axes","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":6,"display":"6"},{"text":"b = 4 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Semi-axes","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":4,"display":"4"},{"text":"# Area","label":null,"prefix":null,"suffix":null,"section":"Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = pi * a * b","label":null,"prefix":null,"suffix":null,"section":"Area","hidden":false,"hero":true,"slider":null,"value":75.39822368615503,"display":"75.4"}]},{"id":"email-marketing-roi","title":"Email Marketing Roi","description":"Calculate ROI of an email marketing campaign from open, click, and conversion rates.","category":"finance","icon":"dollar-sign","tags":["email","roi","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"total_emails_sent = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"open_rate_percentage = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"click_through_rate_percentage = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"conversion_rate_percentage = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"average_order_value = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"campaign_cost = 200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"total_clicks = total_emails_sent * (open_rate_percentage / 100) * (click_through_rate_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"total_conversions = total_clicks * (conversion_rate_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total_revenue = total_conversions * average_order_value","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"return_on_investment_percentage = ((total_revenue - campaign_cost) / campaign_cost) * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":-50,"display":"-50"}]},{"id":"email-open-rate-impact","title":"Email Open Rate Impact","description":"Calculate total clicks expected from email subscribers, open rate, and CTR.","category":"other","icon":"calculator","tags":["email"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"subscribers = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"open_rate = 0.20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"click_through_rate = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"total_opens = subscribers * open_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"total_clicks = total_opens * click_through_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"email-processing-time-batching","title":"Email Processing Time Batching","description":"Calculate daily and weekly hours spent processing email at a given pace.","category":"productivity","icon":"clock","tags":["email"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"emails_per_day = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"time_per_email_seconds = 120 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"_total_seconds = emails_per_day * time_per_email_seconds","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":6000,"display":"6,000"},{"text":"total_time_minutes = total_seconds / 60 // minutes @hero","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"},{"text":"weekly_email_hours = (total_time_minutes * 5) / 60 // hours @hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":8.333333333333334,"display":"8.333"}]},{"id":"emergency-fund-calculator","title":"Emergency Fund","description":"Calculate how much you need saved for a 3-6 month emergency cushion.","category":"finance","icon":"shield-check","tags":["fund","safety"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Monthly Expenses","label":null,"prefix":null,"suffix":null,"section":"Monthly Expenses","hero":false,"slider":null,"value":null,"display":null},{"text":"rent or mortgage = $1800 // 200..5k","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":200,"max":5000,"step":50},"value":1800,"display":"$1,800.00"},{"text":"groceries = $600 // 100..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":100,"max":2000,"step":25},"value":600,"display":"$600.00"},{"text":"utilities = $200 // 50..1k","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":50,"max":1000,"step":1},"value":200,"display":"$200.00"},{"text":"transportation = $300 // 0..1.5k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":1500,"step":25},"value":300,"display":"$300.00"},{"text":"insurance = $250 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":250,"display":"$250.00"},{"text":"other essentials = $400 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":400,"display":"$400.00"},{"text":"# Essential Monthly 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employee.","category":"business","icon":"users","tags":["salary"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Base Compensation","label":null,"prefix":null,"suffix":null,"section":"Base Compensation","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual salary = 75000 // 30k..300k by 1k","label":null,"prefix":"$","suffix":null,"section":"Base Compensation","hidden":false,"hero":false,"slider":{"min":30000,"max":300000,"step":1000},"value":75000,"display":"$75,000.00"},{"text":"benefits rate = 25 // % 0..50","label":null,"prefix":null,"suffix":"%","section":"Base Compensation","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":25,"display":"25"},{"text":"payroll tax rate = 7.65 // % 0..20","label":null,"prefix":null,"suffix":"%","section":"Base Compensation","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":7.65,"display":"7.65"},{"text":"# Overhead","label":null,"prefix":null,"suffix":null,"section":"Overhead","hero":false,"slider":null,"value":null,"display":null},{"text":"$equipment and software = 3000 // 0..20k by 500","label":null,"prefix":"$","suffix":null,"section":"Overhead","hidden":false,"hero":false,"slider":{"min":0,"max":20000,"step":500},"value":3000,"display":"$3,000.00"},{"text":"$office and facilities = 6000 // 0..30k","label":null,"prefix":"$","suffix":null,"section":"Overhead","hidden":false,"hero":false,"slider":{"min":0,"max":30000,"step":500},"value":6000,"display":"$6,000.00"},{"text":"$training and development = 2000 // 0..10k by 500","label":null,"prefix":"$","suffix":null,"section":"Overhead","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":500},"value":2000,"display":"$2,000.00"},{"text":"# True Cost","label":null,"prefix":null,"suffix":null,"section":"True Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$benefits cost = round(annual salary * benefits rate / 100 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":18750,"display":"$18,750.00"},{"text":"$payroll taxes = round(annual salary * payroll tax rate / 100 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":5737.5,"display":"$5,737.50"},{"text":"$total overhead = equipment and software + office and facilities + training and development","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":11000,"display":"$11,000.00"},{"text":"$total annual cost = round((annual salary + benefits cost + payroll taxes + total overhead) * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":true,"slider":null,"value":110487.5,"display":"$110,487.50"},{"text":"cost multiplier = round(total annual cost / annual salary * 100) / 100 // @label(Cost multiplier over salary)","label":"Cost multiplier over salary","prefix":null,"suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":1.47,"display":"1.47"},{"text":"# Hourly Breakdown","label":null,"prefix":null,"suffix":null,"section":"Hourly Breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"working hours per year = 2080 // 1.5k..2.2k","label":null,"prefix":null,"suffix":null,"section":"Hourly Breakdown","hidden":false,"hero":false,"slider":{"min":1500,"max":2200,"step":1},"value":2080,"display":"2,080"},{"text":"$effective hourly rate = round(total annual cost / working hours per year * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Hourly Breakdown","hidden":false,"hero":false,"slider":null,"value":53.12,"display":"$53.12"}]},{"id":"employee-stock-option-valuation-eso","title":"Employee Stock Option Valuation Eso","description":"Estimate the intrinsic value of an employee stock option (ESO).","category":"finance","icon":"dollar-sign","tags":["stock","valuation","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"stock_price = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"strike_price = 80","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"years_to_expiry = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"volatility = 0.30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"risk_free_rate = 0.04","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"},{"text":"value = stock_price - strike_price","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"endangered-species-population-growth","title":"Endangered Species Growth","description":"Model population recovery using logistic growth.","category":"science","icon":"dog","tags":["science","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"initial_population = 500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"annual_growth_rate_percent = 5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"carrying_capacity = 2000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"years = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"population_after_years = carrying_capacity / (1 + ((carrying_capacity - initial_population) / initial_population) * exp(- (annual_growth_rate_percent / 100) * years)) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":709.3224887848869,"display":"709.32"}]},{"id":"energy-conversion","title":"Gas vs EV Energy","description":"Useful work from a gas tank versus an EV battery after efficiency losses.","category":"everyday","icon":"battery-charging","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Gasoline Side","label":null,"prefix":null,"suffix":null,"section":"Gasoline Side","hero":false,"slider":null,"value":null,"display":null},{"text":"gallons = 8 // 0.1..50 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Gasoline Side","hidden":false,"hero":false,"slider":{"min":0.1,"max":50,"step":0.1},"value":8,"display":"8"},{"text":"_kwh_per_gallon = 33.7 // kWh","label":null,"prefix":null,"suffix":"kWh","section":"Gasoline Side","hidden":true,"hero":false,"slider":null,"value":33.7,"display":"33.7"},{"text":"ice efficiency = 25 // % 5..50","label":null,"prefix":null,"suffix":"%","section":"Gasoline Side","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":25,"display":"25"},{"text":"total gas kwh = gallons * kwh_per_gallon // kWh @label(Gas chemical energy)","label":"Gas chemical energy","prefix":null,"suffix":"kWh","section":"Gasoline Side","hidden":false,"hero":false,"slider":null,"value":269.6,"display":"269.6"},{"text":"useful gas kwh = total gas kwh * ice efficiency / 100 // kWh @label(Useful work from gas)","label":"Useful work from gas","prefix":null,"suffix":"kWh","section":"Gasoline Side","hidden":false,"hero":false,"slider":null,"value":67.4,"display":"67.4"},{"text":"# Electric Side","label":null,"prefix":null,"suffix":null,"section":"Electric Side","hero":false,"slider":null,"value":null,"display":null},{"text":"battery kwh = 75 // kWh 10..200 by 5","label":null,"prefix":null,"suffix":"kWh","section":"Electric Side","hidden":false,"hero":false,"slider":{"min":10,"max":200,"step":5},"value":75,"display":"75"},{"text":"ev efficiency = 85 // % 50..100","label":null,"prefix":null,"suffix":"%","section":"Electric Side","hidden":false,"hero":false,"slider":{"min":50,"max":100,"step":1},"value":85,"display":"85"},{"text":"useful ev kwh = battery kwh * ev efficiency / 100 // kWh @hero @label(Useful work from EV battery)","label":"Useful work from EV battery","prefix":null,"suffix":"kWh","section":"Electric Side","hidden":false,"hero":true,"slider":null,"value":63.75,"display":"63.75"},{"text":"# Comparison","label":null,"prefix":null,"suffix":null,"section":"Comparison","hero":false,"slider":null,"value":null,"display":null},{"text":"ev equivalent gallons = round(useful ev kwh / (kwh_per_gallon * ice efficiency / 100), 1) // gal @label(EV battery in \"useful\" gallons)","label":"EV battery in \"useful\" gallons","prefix":null,"suffix":"gal","section":"Comparison","hidden":false,"hero":false,"slider":null,"value":7.6,"display":"7.6"},{"text":"ratio = round(useful ev kwh / useful gas kwh, 2) // @label(EV useful ÷ Gas useful)","label":"EV useful ÷ Gas useful","prefix":null,"suffix":null,"section":"Comparison","hidden":false,"hero":false,"slider":null,"value":0.95,"display":"0.95"}]},{"id":"energy-cost-bitcoin-mining","title":"Energy Cost Bitcoin Mining","description":"Calculate daily electricity cost to run a Bitcoin mining rig at a given rate.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"miner_power_consumption_watts = 3250","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3250,"display":"3,250"},{"text":"electricity_cost_per_kilowatt_hour = 0.12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"mining_duration_hours = 24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"total_daily_energy_cost = (miner_power_consumption_watts * mining_duration_hours / 1000) * electricity_cost_per_kilowatt_hour","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":9.36,"display":"9.36"}]},{"id":"engine-displacement-bore-stroke","title":"Engine Displacement Bore Stroke","description":"Calculate engine displacement from bore, stroke, and cylinder count.","category":"engineering","icon":"settings","tags":["automotive","engine"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Engine Stats","label":null,"prefix":null,"suffix":null,"section":"Engine Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"bore millimeters = 86","label":null,"prefix":null,"suffix":null,"section":"Engine Stats","hidden":false,"hero":false,"slider":null,"value":86,"display":"86"},{"text":"stroke millimeters = 86","label":null,"prefix":null,"suffix":null,"section":"Engine Stats","hidden":false,"hero":false,"slider":null,"value":86,"display":"86"},{"text":"cylinder count = 4","label":null,"prefix":null,"suffix":null,"section":"Engine Stats","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_bore_centimeters = bore millimeters / 10","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":8.6,"display":"8.6"},{"text":"_stroke_centimeters = stroke millimeters / 10","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":8.6,"display":"8.6"},{"text":"_radius_centimeters = bore_centimeters / 2","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":4.3,"display":"4.3"},{"text":"_displacement_per_cylinder = pi * (radius_centimeters ^ 2) * stroke_centimeters","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":499.55721421792737,"display":"499.56"},{"text":"total displacement cubic centimeters = displacement_per_cylinder * cylinder count","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":1998.2288568717095,"display":"1,998.23"}]},{"id":"environmental-compliance-audit-score","title":"Environmental Audit Score","description":"Measure your facility's environmental compliance performance.","category":"other","icon":"leaf","tags":["compliance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"auditPointsEarned = 85 // points","label":null,"prefix":null,"suffix":"points","section":null,"hidden":false,"hero":false,"slider":null,"value":85,"display":"85"},{"text":"totalPossiblePoints = 100 // points","label":null,"prefix":null,"suffix":"points","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"auditScore = (auditPointsEarned / totalPossiblePoints) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":85,"display":"85"}]},{"id":"escape-room-clue-frequency","title":"Escape Room Clue Frequency","description":"Calculate the clue-frequency threshold in minutes per remaining puzzle.","category":"science","icon":"flask-conical","tags":["escape","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Game Stats","label":null,"prefix":null,"suffix":null,"section":"Game Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"total time minutes = 60","label":null,"prefix":null,"suffix":null,"section":"Game Stats","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"number of puzzles = 12","label":null,"prefix":null,"suffix":null,"section":"Game Stats","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"# Progress","label":null,"prefix":null,"suffix":null,"section":"Progress","hero":false,"slider":null,"value":null,"display":null},{"text":"puzzles solved = 4","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"time elapsed = 25 // minutes","label":null,"prefix":null,"suffix":"minutes","section":"Progress","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_time_per_puzzle_goal = total time minutes / number of puzzles","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"_puzzles_remaining = number of puzzles - puzzles solved","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"_time_remaining = total time minutes - time elapsed","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"clue threshold = time_remaining / puzzles_remaining // minutes per puzzle","label":null,"prefix":null,"suffix":"minutes per puzzle","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":4.375,"display":"4.375"}]},{"id":"escape-velocity-planetary","title":"Escape Velocity Planetary","description":"Calculate the escape velocity from a planet in kilometers per 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0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":11185.72649237147,"display":"11,185.73"},{"text":"escape_velocity_kilometers_per_second = escape_velocity_meters_per_second / 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11.18572649237147,"display":"11.19"}]},{"id":"escape-velocity","title":"Escape Velocity","description":"Calculate planetary escape velocity in meters per second from mass and radius.","category":"science","icon":"globe","tags":["escape"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"planetary_mass_kilograms = 5.97e24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5.97e+24,"display":"5.97e24"},{"text":"planetary_radius_meters = 6371000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371000,"display":"6,371,000"},{"text":"gravitational_constant = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"escape_velocity_meters_per_second = sqrt(2 * gravitational_constant * planetary_mass_kilograms / planetary_radius_meters) // m/s @hero","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":true,"slider":null,"value":11183.853306979057,"display":"11,183.85"}]},{"id":"espresso-brew-ratio","title":"Espresso Brew Ratio","description":"Calculate espresso brew ratio from dose and yield in grams.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"dose_grams = 18","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"yield_grams = 36","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"brew_ratio = yield_grams / dose_grams // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"estate-tax-calculator","title":"Estate Tax Calculator","description":"Estimate federal estate tax owed and the amount passing to heirs.","category":"finance","icon":"dollar-sign","tags":["estate","tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Estate Details","label":null,"prefix":null,"suffix":null,"section":"Estate Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$total estate value = 15000000 // 1M..50M by 100k","label":null,"prefix":"$","suffix":null,"section":"Estate Details","hidden":false,"hero":false,"slider":{"min":1000000,"max":50000000,"step":100000},"value":15000000,"display":"$15,000,000.00"},{"text":"$exemption amount = 13610000 // 2024 limit 0..20000000 by 10000","label":null,"prefix":"$","suffix":"2024 limit","section":"Estate Details","hidden":false,"hero":false,"slider":{"min":0,"max":20000000,"step":10000},"value":13610000,"display":"$13,610,000.00"},{"text":"top tax rate = 40 // % 0..50","label":null,"prefix":null,"suffix":"%","section":"Estate Details","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":40,"display":"40"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_taxable_estate = if(total estate value > exemption amount, total estate value - exemption amount, 0)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":1390000,"display":"$1,390,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated federal estate tax = taxable_estate * (top tax rate / 100) // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":556000,"display":"$556,000.00"},{"text":"$remaining estate to heirs = total estate value - estimated federal estate tax","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":14444000,"display":"$14,444,000.00"},{"text":"effective tax rate = (estimated federal estate tax / total estate value) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":3.7066666666666666,"display":"3.707"}]},{"id":"ethereum-staking-reward-estimate","title":"Ethereum Staking Reward Estimate","description":"Estimate monthly ETH staking rewards from staked amount and APY.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"amount_staked_ethereum = 32","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"annual_percentage_yield = 0.04","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"},{"text":"estimated_annual_staking_reward = amount_staked_ethereum * annual_percentage_yield","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.28,"display":"1.28"},{"text":"estimated_monthly_reward = estimated_annual_staking_reward / 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.10666666666666667,"display":"0.1067"}]},{"id":"etsy-fee-breakdown","title":"Etsy Fee Breakdown","description":"Calculate total Etsy fees on a sale from listing, transaction, and processing fees.","category":"other","icon":"calculator","tags":["fee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"item_price = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"shipping_charged = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"listing_fee = 0.20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"transaction_fee_percentage = 0.065","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.065,"display":"0.065"},{"text":"payment_processing_percentage = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"payment_processing_fixed = 0.25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"total_price = item_price + shipping_charged","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"transaction_fee = total_price * transaction_fee_percentage","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.95,"display":"1.95"},{"text":"processing_fee = (total_price * payment_processing_percentage) + payment_processing_fixed","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.15,"display":"1.15"},{"text":"total_fees = listing_fee + transaction_fee + processing_fee","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3.3,"display":"3.3"}]},{"id":"ev-charging-time-calculator","title":"EV Charging Time Calculator","description":"Calculate EV charging 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1000","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":75000,"display":"75,000"},{"text":"estimated range miles = battery_capacity_watt_hours / efficiency watt hours per mile","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":250,"display":"250"}]},{"id":"event-countdown","title":"Event Countdown","description":"Count down to an event in days, hours, and weekends.","category":"everyday","icon":"calendar","tags":["timer"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Event","label":null,"prefix":null,"suffix":null,"section":"Event","hero":false,"slider":null,"value":null,"display":null},{"text":"days until event = 90 // days 1..1k","label":null,"prefix":null,"suffix":"days","section":"Event","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":90,"display":"90"},{"text":"# Countdown","label":null,"prefix":null,"suffix":null,"section":"Countdown","hero":false,"slider":null,"value":null,"display":null},{"text":"weeks = round(days until event / 7 * 10) / 10","label":null,"prefix":null,"suffix":null,"section":"Countdown","hidden":false,"hero":false,"slider":null,"value":12.9,"display":"12.9"},{"text":"hours = days until event * 24 // @hero","label":null,"prefix":null,"suffix":null,"section":"Countdown","hidden":false,"hero":true,"slider":null,"value":2160,"display":"2,160"},{"text":"minutes = hours * 60","label":null,"prefix":null,"suffix":null,"section":"Countdown","hidden":false,"hero":false,"slider":null,"value":129600,"display":"129,600"},{"text":"seconds = minutes * 60","label":null,"prefix":null,"suffix":null,"section":"Countdown","hidden":false,"hero":false,"slider":null,"value":7776000,"display":"7,776,000"},{"text":"# Planning","label":null,"prefix":null,"suffix":null,"section":"Planning","hero":false,"slider":null,"value":null,"display":null},{"text":"weekends left = floor(days until event / 7)","label":null,"prefix":null,"suffix":null,"section":"Planning","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"months approx = round(days until event / 30.44 * 10) / 10 // @label(Approximately Months)","label":"Approximately Months","prefix":null,"suffix":null,"section":"Planning","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"work days = round(days until event * 5 / 7) // @label(Work Days (approx))","label":"Work Days (approx)","prefix":null,"suffix":null,"section":"Planning","hidden":false,"hero":false,"slider":null,"value":64,"display":"64"}]},{"id":"exam-algebra1","title":"Algebra I Final — Linear & Quadratic Equations","description":"Linear equations, systems, and quadratics worked with the `solve` verb — the engine returns every real 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-5","label":null,"prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":-5,"display":"-5"},{"text":"disc = b^2 - 4a*c // @formula @label(discriminant)","label":"discriminant","prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":49,"display":"49"},{"text":"x_plus = (-b + sqrt(disc)) / (2a) // @accent @formula @label($x_+$)","label":"$x_+$","prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"x_minus = (-b - sqrt(disc)) / (2a) // @accent @formula @label($x_-$)","label":"$x_-$","prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":-2.5,"display":"-2.5"},{"text":"# Problem 7: Vertex of a parabola","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Vertex of a parabola","hero":false,"slider":null,"value":null,"display":null},{"text":"x_vertex = -b / (2a) // @accent @formula @label($x$-vertex)","label":"$x$-vertex","prefix":null,"suffix":null,"section":"Problem 7: Vertex of a parabola","hidden":false,"hero":false,"slider":null,"value":-0.75,"display":"-0.75"},{"text":"y_vertex = a*x_vertex^2 + b*x_vertex + c // @accent @formula @label($y$-vertex)","label":"$y$-vertex","prefix":null,"suffix":null,"section":"Problem 7: Vertex of a parabola","hidden":false,"hero":false,"slider":null,"value":-6.125,"display":"-6.125"},{"text":"# Problem 8: Solve an inequality","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Solve an inequality","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: Exponential — solve for the exponent","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Exponential — solve for the 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evaluation","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["add",["sub",["power",["parenExpr",{"type":"id","value":"x","text":"x","offset":17,"lineBreaks":0,"line":1,"col":18}],{"type":"decimal","value":"2","text":"2","offset":20,"lineBreaks":0,"line":1,"col":21}],["parenMult",[{"type":"decimal","value":"3","text":"3","offset":24,"lineBreaks":0,"line":1,"col":25},[[{"type":"id","value":"x","text":"x","offset":26,"lineBreaks":0,"line":1,"col":27}]]]]],{"type":"decimal","value":"2","text":"2","offset":31,"lineBreaks":0,"line":1,"col":32}],"name":"f"},"display":null},{"text":"# Problem 11: Factor a quadratic (symbolic)","label":null,"prefix":null,"suffix":null,"section":"Problem 11: Factor a quadratic (symbolic)","hero":false,"slider":null,"value":null,"display":null},{"text":"factor x^2 - 5x + 6 // @hero @accent @label(factor x^2 - 5x + 6)","label":"factor x^2 - 5x + 6","prefix":null,"suffix":null,"section":"Problem 11: Factor a quadratic (symbolic)","hidden":false,"hero":true,"slider":null,"value":"(x - 2)*(x - 3)","display":"(x - 2)*(x - 3)"},{"text":"# Problem 12: Expand a binomial (symbolic)","label":null,"prefix":null,"suffix":null,"section":"Problem 12: Expand a binomial (symbolic)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 13: Simplify an expression (symbolic)","label":null,"prefix":null,"suffix":null,"section":"Problem 13: Simplify an expression (symbolic)","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-algebra2","title":"Algebra II Final — Functions, Logs & Complex Numbers","description":"Polynomials, exponentials and logarithms, complex numbers, and sequences — the second-year algebra core, every answer computed.","category":"education","icon":"book-open","tags":["algebra","algebra2","logarithms","complex","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.430Z"},"rows":[{"text":"# Problem 1: Roots of a polynomial","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Roots of a polynomial","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: A quadratic with complex roots","label":null,"prefix":null,"suffix":null,"section":"Problem 2: A quadratic with complex roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Complex arithmetic","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Complex arithmetic","hero":false,"slider":null,"value":null,"display":null},{"text":"(2 + 3i) * (1 - i) // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Complex arithmetic","hidden":false,"hero":true,"slider":null,"value":{"r":5,"i":1},"display":"5 + i"},{"text":"# Problem 4: Magnitude of a complex number","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Magnitude of a complex number","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Laws of logarithms","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Laws of logarithms","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 6: Solve an exponential equation","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Solve an exponential equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Compound-growth (change of base)","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Compound-growth (change of base)","hero":false,"slider":null,"value":null,"display":null},{"text":"t_double = ln(2) / ln(1.05) // @accent @formula @label(years)","label":"years","prefix":null,"suffix":null,"section":"Problem 7: Compound-growth (change of base)","hidden":false,"hero":false,"slider":null,"value":14.20669908289046,"display":"14.21"},{"text":"# Problem 8: Arithmetic sequence — nth term","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Arithmetic sequence — nth term","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 3","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Arithmetic sequence — nth term","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"d = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Arithmetic sequence — nth term","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"n = 20","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Arithmetic sequence — nth term","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"a_n = a1 + (n - 1)*d // @accent @formula @label($a_{20}$)","label":"$a_{20}$","prefix":null,"suffix":null,"section":"Problem 8: Arithmetic sequence — nth term","hidden":false,"hero":false,"slider":null,"value":98,"display":"98"},{"text":"# Problem 9: Geometric series sum","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Geometric series sum","hero":false,"slider":null,"value":null,"display":null},{"text":"g1 = 2","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Geometric series sum","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"r = 3","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Geometric series sum","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"n2 = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Geometric series sum","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"S_n = g1 * (r^n2 - 1) / (r - 1) // @accent @formula @label($S_{10}$)","label":"$S_{10}$","prefix":null,"suffix":null,"section":"Problem 9: Geometric series sum","hidden":false,"hero":false,"slider":null,"value":59048,"display":"59,048"},{"text":"# Problem 10: Binomial coefficient (Pascal's triangle)","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Binomial coefficient (Pascal's 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III Final — Multivariable","description":"Gradients, partial derivatives, and vector magnitudes.","category":"education","icon":"book-open","tags":["calculus","multivariable","gradient","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Gradient of a paraboloid","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Gradient of a paraboloid","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Gradient of a mixed polynomial","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Gradient of a mixed polynomial","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Gradient of a triple product","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Gradient of a triple product","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: Gradient of a product of trig 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9: Magnitude of a 3-D gradient","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Magnitude of a 3-D gradient","hero":false,"slider":null,"value":null,"display":null},{"text":"sqrt(2^2 + 2^2 + 1^2) // @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Magnitude of a 3-D gradient","hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"exam-calc3-vector-calculus","title":"Calculus III — Vector Calculus","description":"Dot & cross products, gradient/divergence/curl, line & surface integrals, the integral theorems, and quaternion rotation — computed live, with real-world units carried through.","category":"education","icon":"book-open","tags":["calculus","vector-calculus","stokes","quaternions","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Dot product","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Dot 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Divergence","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Divergence","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Curl","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Curl","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: Laplacian","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Laplacian","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 10: Work done by a force","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Work done by a force","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 11: Work with units carried through","label":null,"prefix":null,"suffix":null,"section":"Problem 11: Work with units carried through","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 12: Magnitude with units","label":null,"prefix":null,"suffix":null,"section":"Problem 12: Magnitude with 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Problem 23: Quaternions — unit norm and conjugate","label":null,"prefix":null,"suffix":null,"section":"Problem 23: Quaternions — unit norm and conjugate","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 24: Quaternion inverse and non-commutativity","label":null,"prefix":null,"suffix":null,"section":"Problem 24: Quaternion inverse and non-commutativity","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 25: Rotations in 3D — composing two turns","label":null,"prefix":null,"suffix":null,"section":"Problem 25: Rotations in 3D — composing two turns","hero":false,"slider":null,"value":null,"display":null},{"text":"rotate(rotate([1,0,0],[0,0,1],pi/2),[1,0,0],pi/2) // @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 25: Rotations in 3D — composing two turns","hidden":false,"hero":true,"slider":null,"value":[0,0,1],"display":null}]},{"id":"exam-combinatorics","title":"Combinatorics Final — Counting Principles","description":"The art of counting: the multiplication rule, permutations, combinations, and the binomial theorem — each count computed with the engine's `C`, `P`, and factorial.","category":"education","icon":"book-open","tags":["combinatorics","permutations","combinations","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: The multiplication principle","label":null,"prefix":null,"suffix":null,"section":"Problem 1: The multiplication principle","hero":false,"slider":null,"value":null,"display":null},{"text":"n_meals = 4 * 6 * 3 // @accent @formula @label(meals)","label":"meals","prefix":null,"suffix":null,"section":"Problem 1: The multiplication principle","hidden":false,"hero":false,"slider":null,"value":72,"display":"72"},{"text":"# Problem 2: Factorial — arrangements of a set","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Factorial — arrangements of a set","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Permutations — order matters","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Permutations — order matters","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: Combinations — order does not matter","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Combinations — order does not matter","hero":false,"slider":null,"value":null,"display":null},{"text":"C(10, 3) // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Combinations — order does not matter","hidden":false,"hero":true,"slider":null,"value":120,"display":"120"},{"text":"# Problem 5: Permutations and combinations are related","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Permutations and combinations are related","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 6: Combination as a factorial ratio","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Combination as a factorial ratio","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Permutations with repeated letters","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Permutations with repeated letters","hero":false,"slider":null,"value":null,"display":null},{"text":"arrangements = 11! / (4! * 4! * 2!) // @accent @formula @label(arrangements)","label":"arrangements","prefix":null,"suffix":null,"section":"Problem 7: Permutations with repeated letters","hidden":false,"hero":false,"slider":null,"value":34650,"display":"34,650"},{"text":"# Problem 8: The binomial theorem coefficients","label":null,"prefix":null,"suffix":null,"section":"Problem 8: The binomial theorem coefficients","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: Sum of a row of Pascal's triangle","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Sum of a row of Pascal's triangle","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 10: Combinations with repetition (stars and bars)","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Combinations with repetition (stars and bars)","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-diffeq-applications","title":"Differential Equations — Applications","description":"Classic first-order applications: RC/RL circuits, mixing tanks, and Newton's law of cooling. Each model is solved numerically (RK4) and cross-checked against its exact exponential solution. Sourced from MIT 18.03 and Boyce-DiPrima.","category":"education","icon":"activity","tags":["differential-equations","ode","circuits","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: RC circuit charging","label":null,"prefix":null,"suffix":null,"section":"Problem 1: RC circuit charging","hero":false,"slider":null,"value":null,"display":null},{"text":"_tau = 1000 * 0.001","label":null,"prefix":null,"suffix":null,"section":"Problem 1: RC circuit charging","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_exact = 0.001 * 10 * (1 - e^(-2/_tau))","label":null,"prefix":null,"suffix":null,"section":"Problem 1: RC circuit charging","hidden":true,"hero":false,"slider":null,"value":0.008646647167633872,"display":"0.008647"},{"text":"# Problem 2: RC circuit discharging","label":null,"prefix":null,"suffix":null,"section":"Problem 2: RC circuit discharging","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 0.01 * e^(-3/1)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: RC circuit discharging","hidden":true,"hero":false,"slider":null,"value":0.0004978706836786395,"display":"0.0004979"},{"text":"# Problem 3: RL circuit current","label":null,"prefix":null,"suffix":null,"section":"Problem 3: RL circuit current","hero":false,"slider":null,"value":null,"display":null},{"text":"_tau = 2 / 4","label":null,"prefix":null,"suffix":null,"section":"Problem 3: RL circuit current","hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_exact = (12/4) * (1 - e^(-1/_tau))","label":null,"prefix":null,"suffix":null,"section":"Problem 3: RL circuit current","hidden":true,"hero":false,"slider":null,"value":2.593994150290162,"display":"2.594"},{"text":"# Problem 4: Mixing tank filling with salt","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Mixing tank filling with salt","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 200 * (1 - e^(-30/20))","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Mixing tank filling with salt","hidden":true,"hero":false,"slider":null,"value":155.37396797031403,"display":"155.37"},{"text":"# Problem 5: Mixing tank flushed with pure water","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Mixing tank flushed with pure water","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 50 * e^(-40/50)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Mixing tank flushed with pure water","hidden":true,"hero":false,"slider":null,"value":22.466448205861077,"display":"22.47"},{"text":"# Problem 6: Newton's law of cooling","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Newton's law of cooling","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 20 + 70 * e^(-0.1 * 15)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Newton's law of cooling","hidden":true,"hero":false,"slider":null,"value":35.61911121039009,"display":"35.62"},{"text":"# Problem 7: Newton's law of warming","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Newton's law of warming","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 25 - 20 * e^(-0.05 * 20)","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Newton's law of warming","hidden":true,"hero":false,"slider":null,"value":17.642411176571155,"display":"17.64"},{"text":"plot T' = -0.05 * (T - 25), T(0) = 5, T(20) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Newton's law of warming","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-diffeq-first-order","title":"Differential Equations — First Order ODEs","description":"First-order initial-value problems solved numerically (RK4) with Instacalc, cross-checked against exact solutions. Sourced from MIT 18.03 and Paul's Online Notes.","category":"education","icon":"activity","tags":["differential-equations","ode","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Exponential growth","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Exponential growth","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = e^1","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Exponential growth","hidden":true,"hero":false,"slider":null,"value":2.718281828459045,"display":"2.718"},{"text":"# Problem 2: Exponential decay","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Exponential decay","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 3 * e^(-4)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Exponential decay","hidden":true,"hero":false,"slider":null,"value":0.05494691666620255,"display":"0.0549"},{"text":"# Problem 3: Linear relaxation to equilibrium","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Linear relaxation to equilibrium","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 - e^(-2)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Linear relaxation to equilibrium","hidden":true,"hero":false,"slider":null,"value":0.8646647167633873,"display":"0.8647"},{"text":"# Problem 4: Logistic growth","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Logistic growth","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Separable with variable coefficient","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Separable with variable coefficient","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = e^(2)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Separable with variable coefficient","hidden":true,"hero":false,"slider":null,"value":7.3890560989306495,"display":"7.389"},{"text":"# Problem 6: Bistable nonlinear ODE","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Bistable nonlinear ODE","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Nonautonomous linear ODE","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Nonautonomous linear ODE","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 3 - 1 + 2 * e^(-3)","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Nonautonomous linear ODE","hidden":true,"hero":false,"slider":null,"value":2.099574136735728,"display":"2.1"},{"text":"plot y' = x - y, y(0) = 1, y(3) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Nonautonomous linear ODE","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-diffeq-laplace","title":"Differential Equations — Laplace Transforms","description":"Laplace transforms L{f(t)} = F(s) of the standard table functions, computed symbolically by Instacalc. Each entry is a classic exam problem from the Laplace-transform table (MIT 18.03, Paul's Online Notes).","category":"education","icon":"activity","tags":["differential-equations","laplace","transforms","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Unit step / constant","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Unit step / constant","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace 1 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Unit step / constant","hidden":false,"hero":true,"slider":null,"value":"1/s","display":"1/s"},{"text":"# Problem 2: Ramp","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Ramp","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Ramp","hidden":false,"hero":true,"slider":null,"value":"1/s^2","display":"1/s^2"},{"text":"# Problem 3: Power t²","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Power t²","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t^2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Power t²","hidden":false,"hero":true,"slider":null,"value":"2/s^3","display":"2/s^3"},{"text":"# Problem 4: Power t³","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Power t³","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t^3 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Power t³","hidden":false,"hero":true,"slider":null,"value":"6/s^4","display":"6/s^4"},{"text":"# Problem 5: Power t⁴","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Power t⁴","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t^4 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Power t⁴","hidden":false,"hero":true,"slider":null,"value":"24/s^5","display":"24/s^5"},{"text":"# Problem 6: Exponential","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exponential","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace e^t // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exponential","hidden":false,"hero":true,"slider":null,"value":"1/(s-1)","display":"1/(s-1)"},{"text":"# Problem 7: Shifted exponential","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Shifted exponential","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace e^(2*t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Shifted exponential","hidden":false,"hero":true,"slider":null,"value":"1/(s-2)","display":"1/(s-2)"},{"text":"# Problem 8: Sine","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Sine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace sin(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Sine","hidden":false,"hero":true,"slider":null,"value":"1/(s^2+1)","display":"1/(s^2+1)"},{"text":"# Problem 9: Sine with frequency","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Sine with frequency","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace sin(2*t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Sine with frequency","hidden":false,"hero":true,"slider":null,"value":"2/(s^2+4)","display":"2/(s^2+4)"},{"text":"# Problem 10: Cosine","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Cosine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace cos(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Cosine","hidden":false,"hero":true,"slider":null,"value":"s/(s^2+1)","display":"s/(s^2+1)"},{"text":"# Problem 11: Cosine with frequency","label":null,"prefix":null,"suffix":null,"section":"Problem 11: Cosine with frequency","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace cos(3*t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 11: Cosine with frequency","hidden":false,"hero":true,"slider":null,"value":"s/(s^2+9)","display":"s/(s^2+9)"},{"text":"# Problem 12: Hyperbolic sine","label":null,"prefix":null,"suffix":null,"section":"Problem 12: Hyperbolic sine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace sinh(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 12: Hyperbolic sine","hidden":false,"hero":true,"slider":null,"value":"1/(s^2-1)","display":"1/(s^2-1)"},{"text":"# Problem 13: Hyperbolic cosine","label":null,"prefix":null,"suffix":null,"section":"Problem 13: Hyperbolic cosine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace cosh(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 13: Hyperbolic cosine","hidden":false,"hero":true,"slider":null,"value":"s/(s^2-1)","display":"s/(s^2-1)"},{"text":"# Problem 14: Resonance term","label":null,"prefix":null,"suffix":null,"section":"Problem 14: Resonance term","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t*sin(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 14: Resonance term","hidden":false,"hero":true,"slider":null,"value":"2*s/(s^2+1)^2","display":"2*s/(s^2+1)^2"}]},{"id":"exam-diffeq-logistic-growth","title":"Differential Equations — Logistic Growth","description":"The logistic equation dP/dt = rP(1 - P/K) and its variants, solved numerically (RK4) and cross-checked against the closed-form logistic solution. Sourced from Paul's Online Notes and standard population-dynamics finals.","category":"education","icon":"activity","tags":["differential-equations","ode","logistic","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Normalized logistic, late time","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Normalized logistic, late time","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 / (1 + (0.7/0.3) * e^(-5))","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Normalized logistic, late time","hidden":true,"hero":false,"slider":null,"value":0.9845214751227109,"display":"0.9845"},{"text":"# Problem 2: Same logistic, mid-rise","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Same logistic, mid-rise","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 / (1 + (0.7/0.3) * e^(-2))","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Same logistic, mid-rise","hidden":true,"hero":false,"slider":null,"value":0.7600041276283265,"display":"0.76"},{"text":"# Problem 3: Slower growth rate (r = 0.5)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Slower growth rate (r = 0.5)","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 / (1 + (0.9/0.1) * e^(-0.5 * 10))","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Slower growth rate (r = 0.5)","hidden":true,"hero":false,"slider":null,"value":0.9428256185740148,"display":"0.9428"},{"text":"# Problem 4: Carrying capacity K = 100","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carrying capacity K = 100","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 100 / (1 + ((100 - 10)/10) * e^(-0.4 * 10))","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carrying capacity K = 100","hidden":true,"hero":false,"slider":null,"value":85.84864497582139,"display":"85.85"},{"text":"# Problem 5: Starting above capacity","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Starting above capacity","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 50 / (1 + ((50 - 80)/80) * e^(-0.3 * 8))","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Starting above capacity","hidden":true,"hero":false,"slider":null,"value":51.760864896461285,"display":"51.76"},{"text":"# Problem 6: Logistic with harvesting","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Logistic with harvesting","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Extinction below threshold","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Extinction below threshold","hero":false,"slider":null,"value":null,"display":null},{"text":"plot y' = y * (y - 0.2), y(0) = 0.1, y(3) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Extinction below threshold","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-diffeq-second-order","title":"Differential Equations — Second Order ODEs","description":"Second-order linear ODEs (oscillators, damping) solved numerically (RK4) with Instacalc, cross-checked against exact solutions. Provide both y(0) and y'(0). Sourced from MIT 18.03 and Boyce-DiPrima.","category":"education","icon":"activity","tags":["differential-equations","ode","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Simple harmonic oscillator","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Simple harmonic oscillator","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = cos(pi)","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Simple harmonic oscillator","hidden":true,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Problem 2: Faster oscillator (ω = 2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Faster oscillator (ω = 2)","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = cos(2 * pi/2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Faster oscillator (ω = 2)","hidden":true,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Problem 3: Oscillator started with velocity","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Oscillator started with velocity","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = sin(pi/2)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Oscillator started with velocity","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Problem 4: Underdamped oscillator","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Underdamped oscillator","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Critically damped","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Critically damped","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = (1 + 2) * e^(-2)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Critically damped","hidden":true,"hero":false,"slider":null,"value":0.4060058497098381,"display":"0.406"},{"text":"# Problem 6: Overdamped","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Overdamped","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 2 * e^(-2) - e^(-4)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Overdamped","hidden":true,"hero":false,"slider":null,"value":0.25235492758449124,"display":"0.2524"},{"text":"# Problem 7: Exponential-growth ODE","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Exponential-growth ODE","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = e^1","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Exponential-growth ODE","hidden":true,"hero":false,"slider":null,"value":2.718281828459045,"display":"2.718"},{"text":"# Problem 8: Undamped oscillator with constant drive","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Undamped oscillator with constant drive","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 - cos(pi)","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Undamped oscillator with constant drive","hidden":true,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"plot y'' = -y + 1, y(0) = 0, y'(0) = 0, y(pi) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Undamped oscillator with constant drive","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-discrete-math","title":"Discrete Math Final — Logic, Sets, Sums & Recurrence","description":"The CS-math core: counting, finite sums in closed form, set sizes by inclusion–exclusion, and a recurrence — each result computed and cross-checked.","category":"education","icon":"grid","tags":["discrete-math","logic","recurrence","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Sum of the first n integers","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Sum of the first n integers","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 100","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Sum of the first n integers","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"gauss_sum = n*(n + 1) / 2 // @accent @formula @label(sum)","label":"sum","prefix":null,"suffix":null,"section":"Problem 1: Sum of the first n integers","hidden":false,"hero":false,"slider":null,"value":5050,"display":"5,050"},{"text":"# Problem 2: Cross-check the closed form","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Cross-check the closed form","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Sum of squares","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Sum of squares","hero":false,"slider":null,"value":null,"display":null},{"text":"n3 = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Sum of squares","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"sum_squares = n3*(n3 + 1)*(2*n3 + 1) / 6 // @accent @formula @label(formula)","label":"formula","prefix":null,"suffix":null,"section":"Problem 3: Sum of squares","hidden":false,"hero":false,"slider":null,"value":385,"display":"385"},{"text":"# Problem 4: Geometric sum (powers of two)","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Geometric sum (powers of two)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Counting subsets (the power set)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Counting subsets (the power set)","hero":false,"slider":null,"value":null,"display":null},{"text":"2^5 // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Counting subsets (the power set)","hidden":false,"hero":true,"slider":null,"value":32,"display":"32"},{"text":"# Problem 6: Counting subsets of a given size","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Counting subsets of a given size","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Inclusion–exclusion","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hero":false,"slider":null,"value":null,"display":null},{"text":"math_n = 18","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"physics_n = 15","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"both_n = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"at_least_one = math_n + physics_n - both_n // @accent @formula @label(at least one)","label":"at least one","prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"neither = 30 - at_least_one // @accent @formula @label(neither)","label":"neither","prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"# Problem 8: The pigeonhole principle","label":null,"prefix":null,"suffix":null,"section":"Problem 8: The pigeonhole principle","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: A linear recurrence (Fibonacci)","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A linear recurrence (Fibonacci)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 10: Hamming distance (a bit of coding theory)","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Hamming distance (a bit of coding theory)","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-eng-dynamics","title":"Engineering Exam — Dynamics","description":"FE-style exam: kinematics, projectile motion, Newton's second law, work-energy, momentum, and circular motion. Launch angle in degrees — trig defaults to degrees.","category":"engineering","icon":"activity","tags":["engineering","mechanical","dynamics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Uniform acceleration kinematics","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hero":false,"slider":null,"value":null,"display":null},{"text":"acceleration = 3 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"time_s = 8 s","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"final_velocity = acceleration * time_s // @accent @formula @label(Final velocity)","label":"Final velocity","prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"_distance_m = 0.5 * acceleration * time_s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":true,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"_final_velocity_mph = final_velocity * 2.23694","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":true,"hero":false,"slider":null,"value":53.68656,"display":"53.6866"},{"text":"# Problem 2: Projectile motion","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hero":false,"slider":null,"value":null,"display":null},{"text":"launch_speed = 40 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"launch_angle = 35 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"g = 9.81 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"_vx = launch_speed * cos(launch_angle)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":32.766081771559676,"display":"32.7661"},{"text":"_vy = launch_speed * sin(launch_angle)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":22.94305745404184,"display":"22.9431"},{"text":"_time_of_flight = (2 * _vy) / g","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":4.6774836807424744,"display":"4.6775"},{"text":"range_m = _vx * _time_of_flight // @accent @formula @label(Range)","label":"Range","prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":153.26281276834385,"display":"153.2628"},{"text":"_max_height_m = _vy^2 / (2 * g)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":26.828944206904424,"display":"26.8289"},{"text":"# Problem 3: Newton's second law","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hero":false,"slider":null,"value":null,"display":null},{"text":"net_force_n = 120 N","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"mass_kg = 15 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"accel_ms2 = net_force_n / mass_kg in m/s^2 // @accent @formula @label(Acceleration)","label":"Acceleration","prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Problem 4: Work–energy theorem","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hero":false,"slider":null,"value":null,"display":null},{"text":"car_mass = 1200 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"v_initial = 25 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"v_final = 10 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"_kinetic_initial_j = 0.5 * car_mass * v_initial^2","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":true,"hero":false,"slider":null,"value":375000,"display":"375,000"},{"text":"_kinetic_final_j = 0.5 * car_mass * v_final^2","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":true,"hero":false,"slider":null,"value":60000,"display":"60,000"},{"text":"work_done_j = _kinetic_final_j - _kinetic_initial_j // @accent @formula @label(Brake work)","label":"Brake work","prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":-315000,"display":"-315,000"},{"text":"_work_done_kj = work_done_j / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":true,"hero":false,"slider":null,"value":-315,"display":"-315"},{"text":"# Problem 5: Conservation of momentum","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hero":false,"slider":null,"value":null,"display":null},{"text":"truck_mass = 2000 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"truck_v = 15 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"car_mass_p = 1000 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"common_velocity = (truck_mass * truck_v) / (truck_mass + car_mass_p) // @accent @formula @label(Common velocity)","label":"Common velocity","prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":9.999999999999998,"display":"10"},{"text":"# Problem 6: Centripetal acceleration and force","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hero":false,"slider":null,"value":null,"display":null},{"text":"speed_circ = 12 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"radius_m = 30 m","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"mass_circ = 5 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"centripetal_accel = speed_circ^2 / radius_m // @accent @formula @label(Centripetal a)","label":"Centripetal a","prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":4.800000000000002,"display":"4.8"},{"text":"_centripetal_force_n = mass_circ * centripetal_accel","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":true,"hero":false,"slider":null,"value":24.000000000000007,"display":"24"},{"text":"# Problem 7: Free-fall height from impact speed","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Free-fall height from impact speed","hero":false,"slider":null,"value":null,"display":null},{"text":"impact_speed = 20 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Free-fall height from impact speed","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"fall_height_m = impact_speed^2 / (2 * g) // @accent @formula @label(Fall height)","label":"Fall height","prefix":null,"suffix":null,"section":"Problem 7: Free-fall height from impact speed","hidden":false,"hero":true,"slider":null,"value":20.38735983690112,"display":"20.3874"}]},{"id":"exam-eng-ee-circuits","title":"Engineering Exam — DC & AC Circuits","description":"FE-style exam: Ohm's law, power, Kirchhoff, series/parallel, RC time constant, and RLC impedance.","category":"engineering","icon":"zap","tags":["engineering","electrical","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Current and power across a resistor","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage = 12 V","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"resistance = 4 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"current_amps = voltage / resistance // @accent @formula @label(Current)","label":"Current","prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_power_watts = voltage * current_amps","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":true,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"# Problem 2: Three resistors in series","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hero":false,"slider":null,"value":null,"display":null},{"text":"r1 = 220 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":220,"display":"220"},{"text":"r2 = 330 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":330,"display":"330"},{"text":"r3 = 470 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":470,"display":"470"},{"text":"source_v = 9 V","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"r_series = r1 + r2 + r3 // @accent @formula @label(Total R)","label":"Total R","prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":1020,"display":"1,020"},{"text":"_series_current_ma = (source_v / r_series) * 1000 // mA","label":null,"prefix":null,"suffix":"mA","section":"Problem 2: Three resistors in series","hidden":true,"hero":false,"slider":null,"value":8.823529411764707,"display":"8.8235"},{"text":"_v_across_r2 = (source_v / r_series) * r2","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":true,"hero":false,"slider":null,"value":2.9117647058823533,"display":"2.9118"},{"text":"# Problem 3: Two resistors in parallel","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hero":false,"slider":null,"value":null,"display":null},{"text":"ra = 100 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"rb = 150 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"r_parallel = (ra * rb) / (ra + rb) // @accent @formula @label(Parallel R)","label":"Parallel R","prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"# Problem 4: Kirchhoff's current law at a node","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hero":false,"slider":null,"value":null,"display":null},{"text":"i_in_1 = 5 A","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"i_in_2 = 3 A","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"i_out_known = 2.5 A","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"i_out_remaining = i_in_1 + i_in_2 - i_out_known // @accent @formula @label(Branch I)","label":"Branch I","prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":5.5,"display":"5.5"},{"text":"# Problem 5: RC charging circuit","label":null,"prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hero":false,"slider":null,"value":null,"display":null},{"text":"r_ohms = 10000 // ohms (typed ohm*F gives no \"second\" label; kept as note)","label":null,"prefix":null,"suffix":"ohms (typed ohm*F gives no \"second\" label; kept as note)","section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"c_farads = 0.0001 // F (100 uF)","label":null,"prefix":null,"suffix":"F (100 uF)","section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":0.0001,"display":"0.0001"},{"text":"v_step = 5 V","label":null,"prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"tau_seconds = r_ohms * c_farads // @accent @formula @label(Time const)","label":"Time const","prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_v_after_one_tau = v_step * (1 - exp(-1))","label":null,"prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hidden":true,"hero":false,"slider":null,"value":3.1606027941427883,"display":"3.1606"},{"text":"# Problem 6: Series RLC impedance and phase","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Series RLC impedance and phase","hero":false,"slider":null,"value":null,"display":null},{"text":"res_ohms = 100 // ohms","label":null,"prefix":null,"suffix":"ohms","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"inductance_h = 0.1 // H","label":null,"prefix":null,"suffix":"H","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"capacitance_f = 0.00001 // F (10 uF)","label":null,"prefix":null,"suffix":"F (10 uF)","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":0.00001,"display":"0.00001"},{"text":"freq_hz = 60 // Hz","label":null,"prefix":null,"suffix":"Hz","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"_omega = 2 * pi * freq_hz // rad/s","label":null,"prefix":null,"suffix":"rad/s","section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":376.99111843077515,"display":"376.99"},{"text":"_x_l = _omega * inductance_h // inductive reactance","label":null,"prefix":null,"suffix":"inductive reactance","section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":37.69911184307751,"display":"37.7"},{"text":"_x_c = 1 / (_omega * capacitance_f) // capacitive reactance","label":null,"prefix":null,"suffix":"capacitive reactance","section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":265.2582384864923,"display":"265.26"},{"text":"impedance_ohms = sqrt(res_ohms^2 + (_x_l - _x_c)^2) // @accent @formula @label(Impedance)","label":"Impedance","prefix":null,"suffix":null,"section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":248.5621775707513,"display":"248.56"},{"text":"_phase_angle_deg = atan((_x_l - _x_c) / res_ohms)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":-66.27709333961397,"display":"-66.2771"},{"text":"# Problem 7: AC real power with a power factor","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hero":false,"slider":null,"value":null,"display":null},{"text":"v_rms = 120 V","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"i_rms = 5 A","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"power_factor = 0.8","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"real_power_w = v_rms * i_rms * power_factor // @accent @formula @label(Real power)","label":"Real power","prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":true,"slider":null,"value":480,"display":"480"},{"text":"_real_power_kw = real_power_w / 1000 // kW","label":null,"prefix":null,"suffix":"kW","section":"Problem 7: AC real power with a power factor","hidden":true,"hero":false,"slider":null,"value":0.48,"display":"0.48"}]},{"id":"exam-eng-fluids","title":"Engineering Exam — Fluid Mechanics","description":"FE-style exam: continuity, Bernoulli, Reynolds number, hydrostatic pressure, flow rate, and head loss. Heavy on unit conversions (gpm, psi, m/s).","category":"engineering","icon":"wind","tags":["engineering","civil","fluids","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Volumetric flow rate from continuity","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hero":false,"slider":null,"value":null,"display":null},{"text":"diameter_m = 0.1 m","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"velocity_ms = 3 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_area_m2 = pi * (diameter_m / 2)^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":true,"hero":false,"slider":null,"value":0.007853981633974483,"display":"0.007854"},{"text":"flow_rate_m3s = _area_m2 * velocity_ms // @accent @formula @label(Flow rate)","label":"Flow rate","prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":false,"hero":false,"slider":null,"value":0.023561944901923447,"display":"0.0236"},{"text":"_flow_rate_gpm = (flow_rate_m3s) * 15850.3 // convert m^3/s to gpm","label":null,"prefix":null,"suffix":"convert","section":"Problem 1: Volumetric flow rate from continuity","hidden":true,"hero":false,"slider":null,"value":373.4638952789572,"display":"373.4639"},{"text":"# Problem 2: Velocity through a contraction","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Velocity through a contraction","hero":false,"slider":null,"value":null,"display":null},{"text":"diameter2_m = 0.05 m","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Velocity through a contraction","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"_area2_m2 = pi * (diameter2_m / 2)^2 // m^2","label":null,"prefix":null,"suffix":"m^2","section":"Problem 2: Velocity through a contraction","hidden":true,"hero":false,"slider":null,"value":0.001963495408493621,"display":"0.001963"},{"text":"velocity2_ms = flow_rate_m3s / _area2_m2 // @accent @formula @label(New velocity)","label":"New velocity","prefix":null,"suffix":null,"section":"Problem 2: Velocity through a contraction","hidden":false,"hero":false,"slider":null,"value":11.999999999999998,"display":"12"},{"text":"# Problem 3: Pressure drop from Bernoulli","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hero":false,"slider":null,"value":null,"display":null},{"text":"rho = 1000 kg/m^3","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"v_in = 2 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"v_out = 8 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"pressure_drop_pa = 0.5 * rho * (v_out^2 - v_in^2) // @accent @formula @label(Pressure drop)","label":"Pressure drop","prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":30000,"display":"30,000"},{"text":"_pressure_drop_kpa = pressure_drop_pa / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":true,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"_pressure_drop_psi = (pressure_drop_pa) * 0.000145038","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":true,"hero":false,"slider":null,"value":4.35114,"display":"4.3511"},{"text":"# Problem 4: Reynolds number and flow regime","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hero":false,"slider":null,"value":null,"display":null},{"text":"flow_velocity = 2 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"pipe_d = 0.05 m","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"kinematic_visc = 0.000001 m^2/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":0.000001,"display":"0.000001"},{"text":"reynolds_number = (flow_velocity * pipe_d) / kinematic_visc // @accent @formula @label(Reynolds)","label":"Reynolds","prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"# Problem 5: Hydrostatic gauge pressure","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hero":false,"slider":null,"value":null,"display":null},{"text":"depth_m = 12 m","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"water_density = 1000 kg/m^3","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"g = 9.81 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"gauge_pressure_pa = water_density * g * depth_m // @accent @formula @label(Gauge p)","label":"Gauge p","prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":117720,"display":"117,720"},{"text":"_gauge_pressure_kpa = gauge_pressure_pa / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":true,"hero":false,"slider":null,"value":117.72,"display":"117.72"},{"text":"_absolute_pressure_kpa = _gauge_pressure_kpa + 101.325 // add 1 atm","label":null,"prefix":null,"suffix":"add 1 atm","section":"Problem 5: Hydrostatic gauge pressure","hidden":true,"hero":false,"slider":null,"value":219.045,"display":"219.045"},{"text":"# Problem 6: Exit velocity by Torricelli","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exit velocity by Torricelli","hero":false,"slider":null,"value":null,"display":null},{"text":"head_m = 5 m","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exit velocity by Torricelli","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"exit_velocity_ms = sqrt(2 * g * head_m) // @accent @formula @label(Exit speed)","label":"Exit speed","prefix":null,"suffix":null,"section":"Problem 6: Exit velocity by Torricelli","hidden":false,"hero":false,"slider":null,"value":9.904544411531507,"display":"9.9045"},{"text":"# Problem 7: Head loss by Darcy–Weisbach","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hero":false,"slider":null,"value":null,"display":null},{"text":"friction_factor = 0.02","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":0.02,"display":"0.02"},{"text":"pipe_length_m = 100 m","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"pipe_diameter_m = 0.1 m","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"darcy_velocity = 3 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"head_loss_m = friction_factor * (pipe_length_m / pipe_diameter_m) * (darcy_velocity^2 / (2 * g)) // @accent @formula @label(Head loss)","label":"Head loss","prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":true,"slider":null,"value":9.174311926605505,"display":"9.1743"}]},{"id":"exam-eng-mechanics-materials","title":"Engineering Exam — Mechanics of Materials","description":"FE-style exam: axial stress/strain, Young's modulus, thermal stress, beam bending, deflection, and torsion. Stress in MPa with psi conversions.","category":"engineering","icon":"tool","tags":["engineering","mechanical","materials","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Axial normal stress","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Axial normal stress","hero":false,"slider":null,"value":null,"display":null},{"text":"load_n = 25000 N // (25 kN)","label":null,"prefix":null,"suffix":"(25 kN)","section":"Problem 1: Axial normal stress","hidden":false,"hero":false,"slider":null,"value":25000,"display":"25,000"},{"text":"area_mm2 = 200 mm^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Axial normal stress","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"stress_mpa = load_n / area_mm2 in MPa // @accent @formula @label(Stress)","label":"Stress","prefix":null,"suffix":null,"section":"Problem 1: Axial normal stress","hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"_stress_psi = (stress_mpa * 1000000) * 0.000145038 // convert MPa to psi","label":null,"prefix":null,"suffix":"convert","section":"Problem 1: Axial normal stress","hidden":true,"hero":false,"slider":null,"value":18129.75,"display":"18,129.75"},{"text":"# Problem 2: Strain and elongation","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hero":false,"slider":null,"value":null,"display":null},{"text":"length_mm = 1500 mm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"youngs_modulus_mpa = 200000 MPa // (200 GPa)","label":null,"prefix":null,"suffix":"(200 GPa)","section":"Problem 2: Strain and elongation","hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"strain = stress_mpa / youngs_modulus_mpa // @accent @formula @label(Strain)","label":"Strain","prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hidden":false,"hero":false,"slider":null,"value":0.000625,"display":"0.000625"},{"text":"_elongation_mm = strain * length_mm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hidden":true,"hero":false,"slider":null,"value":0.9375,"display":"0.9375"},{"text":"# Problem 3: Thermal stress in a restrained bar","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hero":false,"slider":null,"value":null,"display":null},{"text":"alpha = 0.000012 /kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":0.000012,"display":"0.000012"},{"text":"e_modulus_mpa = 200000 MPa","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"temp_rise = 60 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"thermal_stress_mpa = e_modulus_mpa * alpha * temp_rise // @accent @formula @label(Thermal stress)","label":"Thermal stress","prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":144,"display":"144"},{"text":"# Problem 4: Bending stress in a beam","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Bending stress in a beam","hero":false,"slider":null,"value":null,"display":null},{"text":"moment_nmm = 5000000 // N*mm (5000 N*m)","label":null,"prefix":null,"suffix":"N*mm (5000 N*m)","section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":5000000,"display":"5,000,000"},{"text":"b_mm = 50 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"h_mm = 100 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_moment_of_inertia = (b_mm * h_mm^3) / 12 // mm^4","label":null,"prefix":null,"suffix":"mm^4","section":"Problem 4: Bending stress in a beam","hidden":true,"hero":false,"slider":null,"value":4166666.6666666665,"display":"4,166,666.67"},{"text":"_c_mm = h_mm / 2 // distance to extreme fiber; 50 mm","label":null,"prefix":null,"suffix":"distance to extreme fiber; 50 mm","section":"Problem 4: Bending stress in a beam","hidden":true,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"bending_stress_mpa = (moment_nmm * _c_mm) / _moment_of_inertia // @accent @formula @label(Bending stress)","label":"Bending stress","prefix":null,"suffix":null,"section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":60.00000000000001,"display":"60"},{"text":"# Problem 5: Maximum deflection of a beam","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Maximum deflection of a beam","hero":false,"slider":null,"value":null,"display":null},{"text":"p_load_n = 10000 // N","label":null,"prefix":null,"suffix":"N","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"span_mm = 3000 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"e_beam_mpa = 200000 // MPa","label":null,"prefix":null,"suffix":"MPa","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"inertia_mm4 = 4166667 // mm^4","label":null,"prefix":null,"suffix":"mm^4","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":4166667,"display":"4,166,667"},{"text":"max_deflection_mm = (p_load_n * span_mm^3) / (48 * e_beam_mpa * inertia_mm4) // @accent @formula @label(Deflection)","label":"Deflection","prefix":null,"suffix":null,"section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":6.749999460000043,"display":"6.75"},{"text":"# Problem 6: Torsional shear stress","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Torsional shear stress","hero":false,"slider":null,"value":null,"display":null},{"text":"torque_nmm = 800000 // N*mm (800 N*m)","label":null,"prefix":null,"suffix":"N*mm (800 N*m)","section":"Problem 6: Torsional shear stress","hidden":false,"hero":false,"slider":null,"value":800000,"display":"800,000"},{"text":"shaft_d_mm = 40 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 6: Torsional shear stress","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"max_shear_stress_mpa = (16 * torque_nmm) / (pi * shaft_d_mm^3) // @accent @formula @label(Shear stress)","label":"Shear stress","prefix":null,"suffix":null,"section":"Problem 6: Torsional shear stress","hidden":false,"hero":false,"slider":null,"value":63.66197723675813,"display":"63.66"},{"text":"# Problem 7: Factor of safety","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hero":false,"slider":null,"value":null,"display":null},{"text":"yield_strength_mpa = 250 MPa","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"working_stress_mpa = 125 MPa","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"factor_of_safety = yield_strength_mpa / working_stress_mpa // @accent @formula @label(Safety factor)","label":"Safety factor","prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"exam-eng-statics","title":"Engineering Exam — Statics","description":"FE-style exam: force resolution, resultants, moments, equilibrium, truss joints, and friction. Vectors done component-wise (no cross/dot in engine). Angles in degrees — trig defaults to degrees.","category":"engineering","icon":"move","tags":["engineering","mechanical","statics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Resolving a force into components","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hero":false,"slider":null,"value":null,"display":null},{"text":"force_n = 500 N","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"angle_deg = 35 // degrees from horizontal","label":null,"prefix":null,"suffix":"degrees from horizontal","section":"Problem 1: Resolving a force into components","hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"fx = force_n * cos(angle_deg) // @accent @formula @label(Fx)","label":"Fx","prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hidden":false,"hero":false,"slider":null,"value":409.57602214449594,"display":"409.576"},{"text":"_fy = force_n * sin(angle_deg)","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hidden":true,"hero":false,"slider":null,"value":286.788218175523,"display":"286.7882"},{"text":"# Problem 2: Resultant of two concurrent forces","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hero":false,"slider":null,"value":null,"display":null},{"text":"f1 = 300 N","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"a1 = 20 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"f2 = 400 N","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"a2 = 110 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":110,"display":"110"},{"text":"_sum_x = f1 * cos(a1) + f2 * cos(a2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":true,"hero":false,"slider":null,"value":145.09972890550503,"display":"145.0997"},{"text":"_sum_y = f1 * sin(a1) + f2 * sin(a2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":true,"hero":false,"slider":null,"value":478.48309131206395,"display":"478.4831"},{"text":"resultant_n = sqrt(_sum_x^2 + _sum_y^2) // @accent @formula @label(Resultant)","label":"Resultant","prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":499.99999999999994,"display":"500"},{"text":"_resultant_dir_deg = atan2(_sum_y, _sum_x)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":true,"hero":false,"slider":null,"value":73.13010235415598,"display":"73.1301"},{"text":"# Problem 3: Moment of a force about a point","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hero":false,"slider":null,"value":null,"display":null},{"text":"load_n = 250 N","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"lever_arm_m = 0.4 m","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"moment_nm = load_n * lever_arm_m in N*m // @accent @formula @label(Moment)","label":"Moment","prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"# Problem 4: Beam reactions by equilibrium","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hero":false,"slider":null,"value":null,"display":null},{"text":"beam_len = 6 m","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"point_load = 800 N","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":800,"display":"800"},{"text":"load_pos = 2 m // from A","label":null,"prefix":null,"suffix":"from A","section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"_reaction_b = (point_load * load_pos) / beam_len // moment about A","label":null,"prefix":null,"suffix":"moment about A","section":"Problem 4: Beam reactions by equilibrium","hidden":true,"hero":false,"slider":null,"value":266.66666666666663,"display":"266.6667"},{"text":"reaction_a = point_load - _reaction_b // @accent @formula @label(Reaction A)","label":"Reaction A","prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":533.3333333333334,"display":"533.3333"},{"text":"# Problem 5: Truss joint by method of joints","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Truss joint by method of joints","hero":false,"slider":null,"value":null,"display":null},{"text":"horizontal_member_n = 600 N // (+x)","label":null,"prefix":null,"suffix":"(+x)","section":"Problem 5: Truss joint by method of joints","hidden":false,"hero":false,"slider":null,"value":600,"display":"600"},{"text":"diagonal_angle_deg = 40 // deg from horizontal","label":null,"prefix":null,"suffix":"deg from horizontal","section":"Problem 5: Truss joint by method of joints","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"diagonal_force_n = horizontal_member_n / cos(diagonal_angle_deg) // @accent @formula @label(Diagonal)","label":"Diagonal","prefix":null,"suffix":null,"section":"Problem 5: Truss joint by method of joints","hidden":false,"hero":false,"slider":null,"value":783.2443735993671,"display":"783.2444"},{"text":"_diagonal_vertical_comp = diagonal_force_n * sin(diagonal_angle_deg)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Truss joint by method of joints","hidden":true,"hero":false,"slider":null,"value":503.459778706368,"display":"503.4598"},{"text":"# Problem 6: Block on a frictionless incline","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_kg = 200 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"ramp_deg = 25 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"gravity = 9.81 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"_weight_n = mass_kg * gravity","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":true,"hero":false,"slider":null,"value":1962,"display":"1,962"},{"text":"holding_force_n = _weight_n * sin(ramp_deg) // @accent @formula @label(Hold force)","label":"Hold force","prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":829.1770295352524,"display":"829.177"},{"text":"_normal_force_n = _weight_n * cos(ramp_deg)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":true,"hero":false,"slider":null,"value":1778.1758781659073,"display":"1,778.1759"},{"text":"# Problem 7: Maximum static friction","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hero":false,"slider":null,"value":null,"display":null},{"text":"block_weight_n = 400 N","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"mu_s = 0.35","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hidden":false,"hero":false,"slider":null,"value":0.35,"display":"0.35"},{"text":"max_static_friction_n = mu_s * block_weight_n // @accent @formula @label(Max friction)","label":"Max friction","prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hidden":false,"hero":true,"slider":null,"value":140,"display":"140"}]},{"id":"exam-eng-thermo","title":"Engineering Exam — Thermodynamics & Heat Transfer","description":"FE-style exam: ideal gas law, sensible heat, conduction, Carnot efficiency, thermal expansion, and heat-engine work. Temperature unit conversions throughout.","category":"engineering","icon":"thermometer","tags":["engineering","mechanical","thermodynamics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Ideal gas pressure","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hero":false,"slider":null,"value":null,"display":null},{"text":"moles = 2 mol","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"temp_k = 300 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"volume_m3 = 0.05 m^3","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"r_gas = 8.314 J/(mol*kelvin)","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":8.314,"display":"8.314"},{"text":"pressure_pa = (moles * r_gas * temp_k) / volume_m3 in Pa // @accent @formula @label(Pressure)","label":"Pressure","prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":99768,"display":"99,768"},{"text":"_pressure_kpa = pressure_pa / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":true,"hero":false,"slider":null,"value":99.768,"display":"99.768"},{"text":"_pressure_atm = _pressure_kpa / 101.325","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":true,"hero":false,"slider":null,"value":0.9846336047372316,"display":"0.9846"},{"text":"# Problem 2: Sensible heat to warm water","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_water = 5 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"delta_t = (80 - 20) kelvin // same magnitude as deg C","label":null,"prefix":null,"suffix":"same magnitude as deg C","section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"specific_heat = 4186 J/(kg*kelvin)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":4186,"display":"4,186"},{"text":"heat_energy_j = mass_water * specific_heat * delta_t // @accent @formula @label(Heat)","label":"Heat","prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":1255800,"display":"1,255,800"},{"text":"_heat_energy_kj = heat_energy_j / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":true,"hero":false,"slider":null,"value":1255.8,"display":"1,255.8"},{"text":"# Problem 3: Steady conduction through a wall","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hero":false,"slider":null,"value":null,"display":null},{"text":"wall_area = 10 m^2","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"k_conduct = 0.8 W/(m*kelvin)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"thickness_m = 0.2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"temp_diff_k = 25 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"heat_rate_w = (k_conduct * wall_area * temp_diff_k) / thickness_m // @accent @formula @label(Heat rate)","label":"Heat rate","prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"# Problem 4: Carnot efficiency","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hero":false,"slider":null,"value":null,"display":null},{"text":"t_hot = 500 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"t_cold = 300 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"carnot_efficiency = 1 - (t_cold / t_hot) // @accent @formula @label(Efficiency)","label":"Efficiency","prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"_carnot_efficiency_pct = carnot_efficiency * 100","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":true,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"# Problem 5: Heat-engine work and rejected heat","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hero":false,"slider":null,"value":null,"display":null},{"text":"heat_in_kj = 800 kJ","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":false,"hero":false,"slider":null,"value":800,"display":"800"},{"text":"efficiency = 0.4","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"work_out_kj = heat_in_kj * efficiency // @accent @formula @label(Work out)","label":"Work out","prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":false,"hero":false,"slider":null,"value":320,"display":"320"},{"text":"_heat_rejected_kj = heat_in_kj - work_out_kj","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":true,"hero":false,"slider":null,"value":480,"display":"480"},{"text":"# Problem 6: Linear thermal expansion","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hero":false,"slider":null,"value":null,"display":null},{"text":"rod_length_m = 2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"alpha = 0.000012 /kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":0.000012,"display":"0.000012"},{"text":"temp_rise_k = 150 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"delta_length_m = rod_length_m * alpha * temp_rise_k // @accent @formula @label(Expansion)","label":"Expansion","prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":0.0036,"display":"0.0036"},{"text":"_delta_length_mm = delta_length_m * 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":true,"hero":false,"slider":null,"value":3.6,"display":"3.6"},{"text":"# Problem 7: Temperature unit conversion","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Temperature unit conversion","hero":false,"slider":null,"value":null,"display":null},{"text":"setpoint_c = 72 degF in degC // @accent @label(Setpoint C)","label":"Setpoint C","prefix":null,"suffix":null,"section":"Problem 7: Temperature unit conversion","hidden":false,"hero":true,"slider":null,"value":22.22222222222222,"display":"22.2222"},{"text":"_setpoint_k = 72 degF in K","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Temperature unit conversion","hidden":true,"hero":false,"slider":null,"value":295.3722222222222,"display":"295.3722"}]},{"id":"exam-geometry","title":"Geometry Final — Area, Volume & the Pythagorean Theorem","description":"Plane and solid geometry worked from the governing formula to the number — areas, volumes, the Pythagorean theorem, and coordinate distance.","category":"education","icon":"triangle","tags":["geometry","area","volume","pythagorean","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Area and circumference of a circle","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hero":false,"slider":null,"value":null,"display":null},{"text":"r = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"area_circle = pi * r^2 // @accent @formula @label(area)","label":"area","prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hidden":false,"hero":false,"slider":null,"value":78.53981633974483,"display":"78.54"},{"text":"circumference = 2 * pi * r // @accent @formula @label(circumference)","label":"circumference","prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hidden":false,"hero":false,"slider":null,"value":31.415926535897928,"display":"31.42"},{"text":"# Problem 2: The Pythagorean theorem","label":null,"prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hero":false,"slider":null,"value":null,"display":null},{"text":"leg_a = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"leg_b = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"hypotenuse = hypot(leg_a, leg_b) // @hero @accent @formula @label(hypotenuse)","label":"hypotenuse","prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hidden":false,"hero":true,"slider":null,"value":10,"display":"10"},{"text":"# Problem 3: Area of a triangle (Heron's formula)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hero":false,"slider":null,"value":null,"display":null},{"text":"sa = 7","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"sb = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"sc = 9","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"s = (sa + sb + sc) / 2 // @formula @label(semi-perimeter)","label":"semi-perimeter","prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"area_triangle = sqrt(s*(s - sa)*(s - sb)*(s - sc)) // @accent @formula @label(area)","label":"area","prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":26.832815729997478,"display":"26.83"},{"text":"# Problem 4: Volume of a cylinder","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hero":false,"slider":null,"value":null,"display":null},{"text":"r_cyl = 3","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"h_cyl = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"vol_cylinder = pi * r_cyl^2 * h_cyl // @accent @formula @label(volume)","label":"volume","prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hidden":false,"hero":false,"slider":null,"value":282.74333882308133,"display":"282.74"},{"text":"# Problem 5: Volume and surface area of a sphere","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hero":false,"slider":null,"value":null,"display":null},{"text":"r_sph = 4","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"vol_sphere = (4/3) * pi * r_sph^3 // @accent @formula @label(volume)","label":"volume","prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hidden":false,"hero":false,"slider":null,"value":268.082573106329,"display":"268.08"},{"text":"surf_sphere = 4 * pi * r_sph^2 // @accent @formula @label(surface area)","label":"surface area","prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hidden":false,"hero":false,"slider":null,"value":201.06192982974676,"display":"201.06"},{"text":"# Problem 6: Interior angles of a polygon","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Interior angles of a polygon","hero":false,"slider":null,"value":null,"display":null},{"text":"n_sides = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Interior angles of a polygon","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"interior_angle = (n_sides - 2) * 180 / n_sides // @accent @formula @label(angle °)","label":"angle °","prefix":null,"suffix":null,"section":"Problem 6: Interior angles of a polygon","hidden":false,"hero":false,"slider":null,"value":135,"display":"135"},{"text":"# Problem 7: Coordinate distance and midpoint","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hero":false,"slider":null,"value":null,"display":null},{"text":"dist_pts = hypot(8 - 2, 11 - 3) // @accent @formula @label(distance)","label":"distance","prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"mid_x = (2 + 8) / 2 // @formula @label($x_m$)","label":"$x_m$","prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"mid_y = (3 + 11) / 2 // @formula @label($y_m$)","label":"$y_m$","prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"# Problem 8: A missing side by the Law of Cosines","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hero":false,"slider":null,"value":null,"display":null},{"text":"la = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"lb = 7","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"angle_C = 60","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"c_side = sqrt(la^2 + lb^2 - 2*la*lb*cos(angle_C deg)) // @accent @formula @label(c)","label":"c","prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":6.244997998414912,"display":"6.245"},{"text":"# Problem 9: A missing angle by the Law of Cosines","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A missing angle by the Law of Cosines","hero":false,"slider":null,"value":null,"display":null},{"text":"angle_opposite = acos((3^2 + 4^2 - 6^2) / (2*3*4)) deg // @accent @formula @label(angle °)","label":"angle °","prefix":null,"suffix":null,"section":"Problem 9: A missing angle by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":117.279612736,"display":"117.2796"},{"text":"# Problem 10: Arc length and sector area","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hero":false,"slider":null,"value":null,"display":null},{"text":"r_arc = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"arc_length = (90/360) * 2 * pi * r_arc // @accent @formula @label(arc length)","label":"arc length","prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hidden":false,"hero":false,"slider":null,"value":15.707963267948964,"display":"15.71"},{"text":"sector_area = (90/360) * pi * r_arc^2 // @accent @formula @label(sector area)","label":"sector area","prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hidden":false,"hero":false,"slider":null,"value":78.53981633974483,"display":"78.54"}]},{"id":"exam-linalg-systems","title":"Linear Algebra — Systems","description":"Strang 18.06-style: 2×2 and 3×3 linear systems via determinants and Cramer's rule, every cofactor spelled out by formula.","category":"education","icon":"grid","tags":["linear-algebra","systems","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: A single linear equation","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single linear equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: A quadratic with two roots","label":null,"prefix":null,"suffix":null,"section":"Problem 2: A quadratic with two roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: A 2×2 determinant","label":null,"prefix":null,"suffix":null,"section":"Problem 3: A 2×2 determinant","hero":false,"slider":null,"value":null,"display":null},{"text":"# Matrix entries (row-major) @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hero":false,"slider":null,"value":null,"display":null},{"text":"a11 = 2","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"a12 = 1","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"a21 = 3","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"a22 = 4","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"det_2x2 = a11*a22 - a12*a21 // @accent @formula @label(det)","label":"det","prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"# Problem 4: A 2×2 system by Cramer's rule","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hero":false,"slider":null,"value":null,"display":null},{"text":"b1 = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"b2 = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"_det_main = a11*a22 - a12*a21","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"_det_x = b1*a22 - a12*b2","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":true,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"_det_y = a11*b2 - b1*a21","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"x_sol = _det_x / _det_main // @accent @formula @label(x)","label":"x","prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":2.8,"display":"2.8"},{"text":"y_sol = _det_y / _det_main // @accent @formula @label(y)","label":"y","prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":-0.6,"display":"-0.6"},{"text":"# Problem 5: A 3×3 determinant by cofactor expansion","label":null,"prefix":null,"suffix":null,"section":"Problem 5: A 3×3 determinant by cofactor expansion","hero":false,"slider":null,"value":null,"display":null},{"text":"# Row 1 @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Row 1","hero":false,"slider":null,"value":null,"display":null},{"text":"m11 = 1","label":null,"prefix":null,"suffix":null,"section":"Row 1","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"m12 = 2","label":null,"prefix":null,"suffix":null,"section":"Row 1","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"m13 = 3","label":null,"prefix":null,"suffix":null,"section":"Row 1","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Row 2 @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Row 2","hero":false,"slider":null,"value":null,"display":null},{"text":"m21 = 4","label":null,"prefix":null,"suffix":null,"section":"Row 2","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"m22 = 5","label":null,"prefix":null,"suffix":null,"section":"Row 2","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"m23 = 6","label":null,"prefix":null,"suffix":null,"section":"Row 2","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"# Row 3 @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Row 3","hero":false,"slider":null,"value":null,"display":null},{"text":"m31 = 7","label":null,"prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"m32 = 8","label":null,"prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"m33 = 10","label":null,"prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"det_3x3 = m11*(m22*m33 - m23*m32) - m12*(m21*m33 - m23*m31) + m13*(m21*m32 - m22*m31) // @accent @formula @label(det)","label":"det","prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"# Problem 6: A 3×3 system by Cramer's rule","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hero":false,"slider":null,"value":null,"display":null},{"text":"c1 = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"c2 = 15","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"c3 = 25","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"# Replace column 1 with constants → det_x3","label":null,"prefix":null,"suffix":null,"section":"Replace column 1 with constants → det_x3","hero":false,"slider":null,"value":null,"display":null},{"text":"_det_x3 = c1*(m22*m33 - m23*m32) - m12*(c2*m33 - m23*c3) + m13*(c2*m32 - m22*c3)","label":null,"prefix":null,"suffix":null,"section":"Replace column 1 with constants → det_x3","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"# Replace column 2 with constants → det_y3","label":null,"prefix":null,"suffix":null,"section":"Replace column 2 with constants → det_y3","hero":false,"slider":null,"value":null,"display":null},{"text":"_det_y3 = m11*(c2*m33 - m23*c3) - c1*(m21*m33 - m23*m31) + m13*(m21*c3 - c2*m31)","label":null,"prefix":null,"suffix":null,"section":"Replace column 2 with constants → det_y3","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"# Replace column 3 with constants → det_z3","label":null,"prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hero":false,"slider":null,"value":null,"display":null},{"text":"_det_z3 = m11*(m22*c3 - c2*m32) - m12*(m21*c3 - c2*m31) + c1*(m21*m32 - m22*m31)","label":null,"prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"x3 = _det_x3 / det_3x3 // @accent @formula @label(x)","label":"x","prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"y3 = _det_y3 / det_3x3 // @accent @formula @label(y)","label":"y","prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"z3 = _det_z3 / det_3x3 // @accent @formula @label(z)","label":"z","prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Problem 7: Solve by substitution","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Solve by substitution","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Singular matrix test","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hero":false,"slider":null,"value":null,"display":null},{"text":"s11 = 2","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"s12 = 4","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"s21 = 1","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"s22 = 2","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"det_singular = s11*s22 - s12*s21 // @accent @formula @label($0 \\Rightarrow$ singular)","label":"$0 \\Rightarrow$ singular","prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"exam-linalg-vectors","title":"Linear Algebra — Vectors","description":"MIT 18.06-style: dot product, cross product, magnitude, angle, and projection — every operation spelled out component-wise.","category":"education","icon":"move","tags":["linear-algebra","vectors","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Dot product","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Dot product","hero":false,"slider":null,"value":null,"display":null},{"text":"# Vector a @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Vector a","hero":false,"slider":null,"value":null,"display":null},{"text":"ax = 1","label":null,"prefix":null,"suffix":null,"section":"Vector a","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"ay = 2","label":null,"prefix":null,"suffix":null,"section":"Vector a","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"az = 3","label":null,"prefix":null,"suffix":null,"section":"Vector a","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Vector b @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Vector b","hero":false,"slider":null,"value":null,"display":null},{"text":"bx = 4","label":null,"prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"by = 5","label":null,"prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"bz = 6","label":null,"prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"dot_ab = ax*bx + ay*by + az*bz // @accent @formula @label($\\vec a\\cdot\\vec b$)","label":"$\\vec a\\cdot\\vec b$","prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"# Problem 2: Magnitudes","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Magnitudes","hero":false,"slider":null,"value":null,"display":null},{"text":"mag_a = sqrt(ax^2 + ay^2 + az^2) // @formula @label($\\lvert\\vec a\\rvert$)","label":"$\\lvert\\vec a\\rvert$","prefix":null,"suffix":null,"section":"Problem 2: Magnitudes","hidden":false,"hero":false,"slider":null,"value":3.7416573867739413,"display":"3.742"},{"text":"mag_b = sqrt(bx^2 + by^2 + bz^2) // @accent @formula @label($\\lvert\\vec b\\rvert$)","label":"$\\lvert\\vec b\\rvert$","prefix":null,"suffix":null,"section":"Problem 2: Magnitudes","hidden":false,"hero":false,"slider":null,"value":8.774964387392123,"display":"8.775"},{"text":"# Problem 3: Angle between the vectors","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Angle between the vectors","hero":false,"slider":null,"value":null,"display":null},{"text":"_cos_theta = dot_ab / (mag_a * mag_b)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Angle between the vectors","hidden":true,"hero":false,"slider":null,"value":0.974631846197076,"display":"0.9746"},{"text":"angle_ab_deg = acos(_cos_theta) // @accent @formula @label($\\theta$) degrees","label":"$\\theta$","prefix":null,"suffix":"degrees","section":"Problem 3: Angle between the vectors","hidden":false,"hero":false,"slider":null,"value":12.933154491899192,"display":"12.9332"},{"text":"# Problem 4: Cross product","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Cross product","hero":false,"slider":null,"value":null,"display":null},{"text":"# Components @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Components","hero":false,"slider":null,"value":null,"display":null},{"text":"cross_x = ay*bz - az*by // @formula @label($(\\vec a\\times\\vec b)_x$)","label":"$(\\vec a\\times\\vec b)_x$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"cross_y = az*bx - ax*bz // @formula @label($(\\vec a\\times\\vec b)_y$)","label":"$(\\vec a\\times\\vec b)_y$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"cross_z = ax*by - ay*bx // @formula @label($(\\vec a\\times\\vec b)_z$)","label":"$(\\vec a\\times\\vec b)_z$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"cross_mag = sqrt(cross_x^2 + cross_y^2 + cross_z^2) // @accent @formula @label($\\lvert\\vec a\\times\\vec b\\rvert$)","label":"$\\lvert\\vec a\\times\\vec b\\rvert$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":7.3484692283495345,"display":"7.348"},{"text":"# Problem 5: Right-hand rule check","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Right-hand rule check","hero":false,"slider":null,"value":null,"display":null},{"text":"# Vector u @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Vector u","hero":false,"slider":null,"value":null,"display":null},{"text":"ux = 1","label":null,"prefix":null,"suffix":null,"section":"Vector u","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"uy = 0","label":null,"prefix":null,"suffix":null,"section":"Vector u","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"uz = 0","label":null,"prefix":null,"suffix":null,"section":"Vector u","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# Vector v @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Vector v","hero":false,"slider":null,"value":null,"display":null},{"text":"vx = 0","label":null,"prefix":null,"suffix":null,"section":"Vector v","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"vy = 1","label":null,"prefix":null,"suffix":null,"section":"Vector v","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"vz = 0","label":null,"prefix":null,"suffix":null,"section":"Vector v","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# u × v should be (0,0,1) @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hero":false,"slider":null,"value":null,"display":null},{"text":"uv_x = uy*vz - uz*vy","label":null,"prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"uv_y = uz*vx - ux*vz","label":null,"prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"uv_z = ux*vy - uy*vx // @accent @formula @label($(\\vec u\\times\\vec v)_z$)","label":"$(\\vec u\\times\\vec v)_z$","prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Problem 6: Scalar projection","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Scalar projection","hero":false,"slider":null,"value":null,"display":null},{"text":"scalar_proj = dot_ab / mag_b // @accent @formula @label(comp_b a)","label":"comp_b a","prefix":null,"suffix":null,"section":"Problem 6: Scalar projection","hidden":false,"hero":false,"slider":null,"value":3.646738446708414,"display":"3.647"},{"text":"# Problem 7: Vector projection","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Vector projection","hero":false,"slider":null,"value":null,"display":null},{"text":"_proj_scale = dot_ab / mag_b^2","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Vector projection","hidden":true,"hero":false,"slider":null,"value":0.41558441558441556,"display":"0.4156"},{"text":"# Projection vector @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Projection vector","hero":false,"slider":null,"value":null,"display":null},{"text":"proj_x = _proj_scale * bx","label":null,"prefix":null,"suffix":null,"section":"Projection vector","hidden":false,"hero":false,"slider":null,"value":1.662337662337662,"display":"1.662"},{"text":"proj_y = _proj_scale * by","label":null,"prefix":null,"suffix":null,"section":"Projection vector","hidden":false,"hero":false,"slider":null,"value":2.0779220779220773,"display":"2.078"},{"text":"proj_z = _proj_scale * bz // @accent @formula @label(proj_b a, z)","label":"proj_b a, z","prefix":null,"suffix":null,"section":"Projection vector","hidden":false,"hero":false,"slider":null,"value":2.493506493506493,"display":"2.494"},{"text":"# Problem 8: Orthogonality test","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Orthogonality test","hero":false,"slider":null,"value":null,"display":null},{"text":"is_orthogonal = dot_ab // @accent @formula @label($0 \\Rightarrow$ orthogonal)","label":"$0 \\Rightarrow$ orthogonal","prefix":null,"suffix":null,"section":"Problem 8: Orthogonality test","hidden":false,"hero":true,"slider":null,"value":32,"display":"32"}]},{"id":"exam-number-theory","title":"Number Theory Final — Divisibility, Modular Arithmetic & GCD","description":"The integers up close: divisibility, the GCD/LCM identity, modular arithmetic, Fibonacci, and base conversion — every result computed.","category":"education","icon":"book-open","tags":["number-theory","modular","gcd","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Divisibility by remainder","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Divisibility by remainder","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Greatest common divisor (Euclid)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Greatest common divisor (Euclid)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Least common multiple","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Least common multiple","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: The GCD–LCM identity","label":null,"prefix":null,"suffix":null,"section":"Problem 4: The GCD–LCM identity","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Modular arithmetic — clock math","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Modular arithmetic — clock math","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 6: Modular exponentiation","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Modular exponentiation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: A linear congruence","label":null,"prefix":null,"suffix":null,"section":"Problem 7: A linear congruence","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Fibonacci numbers","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Fibonacci numbers","hero":false,"slider":null,"value":null,"display":null},{"text":"fib(10) // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Fibonacci numbers","hidden":false,"hero":true,"slider":null,"value":55,"display":"55"},{"text":"# Problem 9: The golden ratio from Fibonacci","label":null,"prefix":null,"suffix":null,"section":"Problem 9: The golden ratio from Fibonacci","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 10: Base conversion","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Base conversion","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-physics-em-waves","title":"Physics Final — E&M and Waves","description":"MIT 8.02-style final: Coulomb's law, fields, DC circuits, and wave optics — each from the governing law to the number.","category":"physics","icon":"zap","tags":["physics","electromagnetism","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Coulomb force","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Coulomb force","hero":false,"slider":null,"value":null,"display":null},{"text":"k_e = 8.99e9 // N m^2 / C^2","label":null,"prefix":null,"suffix":"N m^2 / C^2","section":"Problem 1: Coulomb force","hidden":false,"hero":false,"slider":null,"value":8990000000,"display":"8,990,000,000"},{"text":"q1 = 2e-6 // C","label":null,"prefix":null,"suffix":"C","section":"Problem 1: Coulomb force","hidden":false,"hero":false,"slider":null,"value":0.000002,"display":"0.000002"},{"text":"q2 = -3e-6 // C","label":null,"prefix":null,"suffix":"C","section":"Problem 1: Coulomb force","hidden":false,"hero":false,"slider":null,"value":-0.000003,"display":"-0.000003"},{"text":"r1 = 0.05 // m","label":null,"prefix":null,"suffix":"m","section":"Problem 1: Coulomb force","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"coulomb_force = k_e * abs(q1 * q2) / r1^2 // @accent @formula @label(F) N","label":"F","prefix":null,"suffix":"N","section":"Problem 1: Coulomb force","hidden":false,"hero":false,"slider":null,"value":21.575999999999997,"display":"21.58"},{"text":"# Problem 2: Field of a point charge","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Field of a point charge","hero":false,"slider":null,"value":null,"display":null},{"text":"charge_q = 5e-9 // C","label":null,"prefix":null,"suffix":"C","section":"Problem 2: Field of a point charge","hidden":false,"hero":false,"slider":null,"value":5e-9,"display":"5e-9"},{"text":"r2 = 0.1 // m","label":null,"prefix":null,"suffix":"m","section":"Problem 2: Field of a point charge","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"e_field = k_e * charge_q / r2^2 // @accent @formula @label(E) N/C","label":"E","prefix":null,"suffix":"N/C","section":"Problem 2: Field of a point charge","hidden":false,"hero":false,"slider":null,"value":4494.999999999999,"display":"4,495"},{"text":"# Problem 3: Parallel-plate capacitance","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Parallel-plate capacitance","hero":false,"slider":null,"value":null,"display":null},{"text":"eps0 = 8.854e-12 // F/m","label":null,"prefix":null,"suffix":"F/m","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":8.854e-12,"display":"8.854e-12"},{"text":"area = 0.02 // m^2","label":null,"prefix":null,"suffix":"m^2","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":0.02,"display":"0.02"},{"text":"d3 = 0.001 // m","label":null,"prefix":null,"suffix":"m","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":0.001,"display":"0.001"},{"text":"capacitance = eps0 * area / d3 // @accent @formula @label(C) F","label":"C","prefix":null,"suffix":"F","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":1.7708e-10,"display":"1.7708e-10"},{"text":"# Problem 4: Ohm's law — current and power","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage = 12 V","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"resistance = 4 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"_current = voltage / resistance","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"power = voltage * _current // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"# Problem 5: Resistors in parallel","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hero":false,"slider":null,"value":null,"display":null},{"text":"ra = 6 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"rb = 3 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"r_parallel = (ra * rb) / (ra + rb) // @accent @formula @label(R_eq)","label":"R_eq","prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"# Problem 6: RC time constant","label":null,"prefix":null,"suffix":null,"section":"Problem 6: RC time constant","hero":false,"slider":null,"value":null,"display":null},{"text":"r6 = 1000 // ohm","label":null,"prefix":null,"suffix":"ohm","section":"Problem 6: RC time constant","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"c6 = 100e-6 // F","label":null,"prefix":null,"suffix":"F","section":"Problem 6: RC time constant","hidden":false,"hero":false,"slider":null,"value":0.0001,"display":"0.0001"},{"text":"time_constant = r6 * c6 // @accent @formula @label($\\tau$) s","label":"$\\tau$","prefix":null,"suffix":"s","section":"Problem 6: RC time constant","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"# Problem 7: Wavelength of light","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Wavelength of light","hero":false,"slider":null,"value":null,"display":null},{"text":"c_light = 3e8 // m/s","label":null,"prefix":null,"suffix":"m/s","section":"Problem 7: Wavelength of light","hidden":false,"hero":false,"slider":null,"value":300000000,"display":"300,000,000"},{"text":"freq = 5e14 // Hz","label":null,"prefix":null,"suffix":"Hz","section":"Problem 7: Wavelength of light","hidden":false,"hero":false,"slider":null,"value":500000000000000,"display":"500,000,000,000,000"},{"text":"wavelength = c_light / freq // @accent @formula @label($\\lambda$) m","label":"$\\lambda$","prefix":null,"suffix":"m","section":"Problem 7: Wavelength of light","hidden":false,"hero":false,"slider":null,"value":6e-7,"display":"0.0000006"},{"text":"# Problem 8: Snell's law refraction","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hero":false,"slider":null,"value":null,"display":null},{"text":"n_air = 1","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"n_glass = 1.5","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"theta_i_deg = 40","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"_theta_i = theta_i_deg * pi / 180","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":true,"hero":false,"slider":null,"value":0.6981317007977318,"display":"0.6981"},{"text":"_sin_refract = n_air * sin(_theta_i) / n_glass","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":true,"hero":false,"slider":null,"value":0.42852507312435956,"display":"0.4285"},{"text":"theta_refract_deg = asin(_sin_refract) // @accent @formula @label($\\theta_2$) degrees","label":"$\\theta_2$","prefix":null,"suffix":"degrees","section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":25.37399393917941,"display":"25.374"},{"text":"# Problem 9: Double-slit fringe spacing","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hero":false,"slider":null,"value":null,"display":null},{"text":"slit_d = 0.0001 m","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":false,"slider":null,"value":0.0001,"display":"0.0001"},{"text":"screen_L = 2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"lambda9 = 600e-9 m","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":false,"slider":null,"value":6e-7,"display":"0.0000006"},{"text":"fringe_spacing = lambda9 * screen_L / slit_d // @accent @formula @label($\\Delta y$)","label":"$\\Delta y$","prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":true,"slider":null,"value":0.012,"display":"0.012"}]},{"id":"exam-physics-mechanics","title":"Physics Final — Mechanics","description":"MIT 8.01-style final: kinematics, Newton's laws, energy, and momentum — each worked from the governing law to the number.","category":"physics","icon":"activity","tags":["physics","mechanics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Projectile range","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Projectile 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range","hidden":false,"hero":false,"slider":null,"value":35.311943069701876,"display":"35.3119"},{"text":"# Problem 1b: Maximum height","label":null,"prefix":null,"suffix":null,"section":"Problem 1b: Maximum height","hero":false,"slider":null,"value":null,"display":null},{"text":"max_height = (v0 * sin(_angle))^2 / (2*g) // @accent @formula @label(H)","label":"H","prefix":null,"suffix":null,"section":"Problem 1b: Maximum height","hidden":false,"hero":false,"slider":null,"value":5.096839959225279,"display":"5.0968"},{"text":"# Problem 2: Constant acceleration from rest","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Constant acceleration from rest","hero":false,"slider":null,"value":null,"display":null},{"text":"a2 = 3 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Constant acceleration from rest","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"t2 = 8 s","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Constant acceleration from rest","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"_v_final = a2 * t2","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Constant acceleration from rest","hidden":true,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"dist = 0.5 * a2 * t2^2 // @accent @formula @label(distance)","label":"distance","prefix":null,"suffix":null,"section":"Problem 2: Constant acceleration from rest","hidden":false,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"# Problem 3: Block on a frictionless incline","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_block = 5 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"incline_deg = 25","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"_incline = incline_deg * pi / 180","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":true,"hero":false,"slider":null,"value":0.4363323129985824,"display":"0.4363"},{"text":"a_slope = g * sin(_incline) // @accent @formula @label(a)","label":"a","prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":4.145885147676261,"display":"4.1459"},{"text":"# Problem 3b: Normal force","label":null,"prefix":null,"suffix":null,"section":"Problem 3b: Normal force","hero":false,"slider":null,"value":null,"display":null},{"text":"normal_force = mass_block * g * cos(_incline) // @accent @formula @label(N)","label":"N","prefix":null,"suffix":null,"section":"Problem 3b: Normal 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energy","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_car = 1200 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Kinetic energy","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"v5 = 25 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Kinetic energy","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"kinetic_energy = 0.5 * mass_car * v5^2 in J // @accent @formula @label(KE)","label":"KE","prefix":null,"suffix":null,"section":"Problem 5: Kinetic energy","hidden":false,"hero":false,"slider":null,"value":375000,"display":"375,000"},{"text":"# Problem 6: Perfectly inelastic collision","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic collision","hero":false,"slider":null,"value":null,"display":null},{"text":"m6a = 2 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic 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period","hero":false,"slider":null,"value":null,"display":null},{"text":"L7 = 2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Pendulum period","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"period = 2 * pi * sqrt(L7 / g) // @accent @formula @label(T)","label":"T","prefix":null,"suffix":null,"section":"Problem 7: Pendulum period","hidden":false,"hero":false,"slider":null,"value":2.8370067068857745,"display":"2.837"},{"text":"# Problem 8: Work against gravity","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_lift = 10 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"h8 = 3 m","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"work = mass_lift * g * h8 in J // @accent @formula @label(W)","label":"W","prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hidden":false,"hero":true,"slider":null,"value":294.3,"display":"294.3"}]},{"id":"exam-prealgebra","title":"Pre-Algebra Final — Integers, Expressions & Equations","description":"The bridge from arithmetic to algebra: signed numbers, exponents, one-variable equations, and the coordinate plane — each step computed.","category":"education","icon":"book-open","tags":["prealgebra","integers","equations","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Signed-number arithmetic","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Signed-number arithmetic","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Absolute value","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Absolute value","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Exponents and the laws of exponents","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Exponents and the laws of exponents","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: Negative and zero exponents","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Negative and zero exponents","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Evaluating an algebraic expression","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Evaluating an algebraic expression","hero":false,"slider":null,"value":null,"display":null},{"text":"x = 4","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Evaluating an algebraic expression","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"# Problem 6: Solve a one-step equation","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Solve a one-step equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Solve a two-step equation","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Solve a two-step equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Distance between two points","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hero":false,"slider":null,"value":null,"display":null},{"text":"dx = 4 - 1","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"dy = 6 - 2","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"distance = hypot(dx, dy) // @hero @accent @formula @label(distance)","label":"distance","prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"# Problem 9: Slope of a line","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Slope of a line","hero":false,"slider":null,"value":null,"display":null},{"text":"slope = dy / dx // @accent @formula @label(slope)","label":"slope","prefix":null,"suffix":null,"section":"Problem 9: Slope of a line","hidden":false,"hero":false,"slider":null,"value":1.3333333333333333,"display":"1.333"},{"text":"# Problem 10: Mean of a data set","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Mean of a data set","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-probability","title":"Probability Final — Counting, Conditional & Distributions","description":"Classical probability worked end to end: equally-likely outcomes, complements, conditional probability, and the binomial distribution — every number computed.","category":"education","icon":"book-open","tags":["probability","binomial","conditional","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: A single fair die","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hero":false,"slider":null,"value":null,"display":null},{"text":"favorable = 2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"p_gt4 = favorable / total // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hidden":false,"hero":false,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"# Problem 2: Two independent events (AND)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Two independent events (AND)","hero":false,"slider":null,"value":null,"display":null},{"text":"p_two_heads = 0.5 * 0.5 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 2: Two independent events (AND)","hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"# Problem 3: Complement (at least one)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Complement (at least one)","hero":false,"slider":null,"value":null,"display":null},{"text":"p_at_least_one_six = 1 - (5/6)^2 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 3: Complement (at least one)","hidden":false,"hero":false,"slider":null,"value":0.3055555555555555,"display":"0.3056"},{"text":"# Problem 4: Mutually exclusive events (OR)","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Mutually exclusive events (OR)","hero":false,"slider":null,"value":null,"display":null},{"text":"p_king_or_queen = 4/52 + 4/52 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 4: Mutually exclusive events (OR)","hidden":false,"hero":false,"slider":null,"value":0.15384615384615385,"display":"0.1538"},{"text":"# Problem 5: Conditional probability","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conditional probability","hero":false,"slider":null,"value":null,"display":null},{"text":"p_both_red = (5/8) * (4/7) // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 5: Conditional probability","hidden":false,"hero":false,"slider":null,"value":0.3571428571428571,"display":"0.3571"},{"text":"# Problem 6: A binomial probability","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A binomial probability","hero":false,"slider":null,"value":null,"display":null},{"text":"p_exactly_3 = C(10, 3) * 0.5^3 * 0.5^7 // @hero @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 6: A binomial probability","hidden":false,"hero":true,"slider":null,"value":0.1171875,"display":"0.1172"},{"text":"# Problem 7: Binomial — at least k successes","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Binomial — at least k successes","hero":false,"slider":null,"value":null,"display":null},{"text":"p_all_five = 0.8^5 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 7: Binomial — at least k successes","hidden":false,"hero":false,"slider":null,"value":0.3276800000000001,"display":"0.3277"},{"text":"# Problem 8: Expected value","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Expected value","hero":false,"slider":null,"value":null,"display":null},{"text":"expected_value = 10 * 0.2 + 0 * 0.8 - 3 // @accent @formula @label(E net)","label":"E net","prefix":null,"suffix":null,"section":"Problem 8: Expected value","hidden":false,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Problem 9: Odds vs. probability","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Odds vs. probability","hero":false,"slider":null,"value":null,"display":null},{"text":"p_event = 0.75","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Odds vs. probability","hidden":false,"hero":false,"slider":null,"value":0.75,"display":"0.75"},{"text":"odds_in_favor = p_event / (1 - p_event) // @accent @formula @label(odds)","label":"odds","prefix":null,"suffix":null,"section":"Problem 9: Odds vs. probability","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Problem 10: Birthday-style collision","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Birthday-style collision","hero":false,"slider":null,"value":null,"display":null},{"text":"p_distinct = P(365, 5) / 365^5 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 10: Birthday-style collision","hidden":false,"hero":false,"slider":null,"value":0.9728644263002064,"display":"0.9729"}]},{"id":"exam-statistics","title":"Statistics Final — Descriptive & Inferential","description":"Intro statistics worked from raw data: center, spread, z-scores, correlation, and a confidence interval — each computed with the engine's built-in stats functions.","category":"education","icon":"activity","tags":["statistics","data","z-score","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: Measures of center","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Measures of center","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Spread — variance and standard deviation","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Spread — variance and standard deviation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Range","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Range","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: A z-score","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hero":false,"slider":null,"value":null,"display":null},{"text":"mu = 75","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":false,"slider":null,"value":75,"display":"75"},{"text":"sigma = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"score = 91","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":false,"slider":null,"value":91,"display":"91"},{"text":"z_score = (score - mu) / sigma // @hero @accent @formula @label(z)","label":"z","prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"},{"text":"# Problem 5: Converting a z-score back to a value","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Converting a z-score back to a value","hero":false,"slider":null,"value":null,"display":null},{"text":"raw_score = mu + (-1.5) * sigma // @accent @formula @label(score)","label":"score","prefix":null,"suffix":null,"section":"Problem 5: Converting a z-score back to a value","hidden":false,"hero":false,"slider":null,"value":63,"display":"63"},{"text":"# Problem 6: Correlation coefficient","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Correlation coefficient","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: A perfect linear relationship","label":null,"prefix":null,"suffix":null,"section":"Problem 7: A perfect linear relationship","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Standard error of the mean","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hero":false,"slider":null,"value":null,"display":null},{"text":"s_sample = 12","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"n_sample = 36","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"std_error = s_sample / sqrt(n_sample) // @accent @formula @label(SE)","label":"SE","prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"# Problem 9: A 95% confidence interval for the mean","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hero":false,"slider":null,"value":null,"display":null},{"text":"x_bar = 50","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"ci_low = x_bar - 1.96 * std_error // @accent @formula @label(lower)","label":"lower","prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hidden":false,"hero":false,"slider":null,"value":46.08,"display":"46.08"},{"text":"ci_high = x_bar + 1.96 * std_error // @accent @formula @label(upper)","label":"upper","prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hidden":false,"hero":false,"slider":null,"value":53.92,"display":"53.92"},{"text":"# Problem 10: Empirical rule (68–95–99.7)","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hero":false,"slider":null,"value":null,"display":null},{"text":"mu_iq = 100","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"sigma_iq = 15","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"band_low = mu_iq - 2 * sigma_iq // @accent @formula @label(lower)","label":"lower","prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"band_high = mu_iq + 2 * sigma_iq // @accent @formula @label(upper)","label":"upper","prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":130,"display":"130"}]},{"id":"exam-trig-precalc","title":"Trigonometry & Precalculus Final","description":"Right-triangle and unit-circle trig, identities, the laws of sines and cosines, and polar form — every value computed.","category":"education","icon":"triangle","tags":["trigonometry","precalculus","unit-circle","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Problem 1: The basic trig ratios","label":null,"prefix":null,"suffix":null,"section":"Problem 1: The basic trig ratios","hero":false,"slider":null,"value":null,"display":null},{"text":"sin(30 deg) // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 1: The basic trig ratios","hidden":false,"hero":true,"slider":null,"value":0.4999999999997412,"display":"0.5"},{"text":"# Problem 2: Solve a right triangle","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hero":false,"slider":null,"value":null,"display":null},{"text":"h = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"theta = 35","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"opposite = h * sin(theta deg) // @accent @formula @label(opposite)","label":"opposite","prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":5.735764363510335,"display":"5.736"},{"text":"adjacent = h * cos(theta deg) // @accent @formula @label(adjacent)","label":"adjacent","prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":8.191520442890006,"display":"8.192"},{"text":"# Problem 3: Inverse trig — find the angle","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Inverse trig — find the angle","hero":false,"slider":null,"value":null,"display":null},{"text":"ramp_angle = atan(3 / 12) deg // @accent @formula @label(angle °)","label":"angle °","prefix":null,"suffix":null,"section":"Problem 3: Inverse trig — find the angle","hidden":false,"hero":false,"slider":null,"value":14.0362434679,"display":"14.0362"},{"text":"# Problem 4: The Pythagorean identity","label":null,"prefix":null,"suffix":null,"section":"Problem 4: The Pythagorean identity","hero":false,"slider":null,"value":null,"display":null},{"text":"ang = 50","label":null,"prefix":null,"suffix":null,"section":"Problem 4: The Pythagorean identity","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"# Problem 5: Law of Sines","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Law of Sines","hero":false,"slider":null,"value":null,"display":null},{"text":"side_b = 8 * sin(60 deg) / sin(40 deg) // @accent @formula @label(b)","label":"b","prefix":null,"suffix":null,"section":"Problem 5: Law of Sines","hidden":false,"hero":false,"slider":null,"value":10.778370842688613,"display":"10.78"},{"text":"# Problem 6: Law of Cosines","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Law of Cosines","hero":false,"slider":null,"value":null,"display":null},{"text":"side_c = sqrt(5^2 + 7^2 - 2*5*7*cos(60 deg)) // @accent @formula @label(c)","label":"c","prefix":null,"suffix":null,"section":"Problem 6: Law of Cosines","hidden":false,"hero":false,"slider":null,"value":6.244997998414912,"display":"6.245"},{"text":"# Problem 7: Radians and degrees","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Radians and degrees","hero":false,"slider":null,"value":null,"display":null},{"text":"deg_value = (5*pi/6) * 180 / pi // @accent @formula @label(degrees)","label":"degrees","prefix":null,"suffix":null,"section":"Problem 7: Radians and degrees","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"rad_value = 120 * pi / 180 // @accent @formula @label(radians)","label":"radians","prefix":null,"suffix":null,"section":"Problem 7: Radians and degrees","hidden":false,"hero":false,"slider":null,"value":2.0943951023931953,"display":"2.094"},{"text":"# Problem 8: Solve a trig equation (general solution)","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Solve a trig equation (general solution)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: Polar to rectangular (complex form)","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hero":false,"slider":null,"value":null,"display":null},{"text":"r_polar = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"theta_polar = 53.13","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":53.13,"display":"53.13"},{"text":"x_rect = r_polar * cos(theta_polar deg) // @accent @formula @label(x)","label":"x","prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":3.0000071456616615,"display":"3"},{"text":"y_rect = r_polar * sin(theta_polar deg) // @accent @formula @label(y)","label":"y","prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":3.9999946407437807,"display":"4"},{"text":"# Problem 10: Rectangular to polar","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Rectangular to polar","hero":false,"slider":null,"value":null,"display":null},{"text":"r_back = hypot(3, 4) // @accent @formula @label(r)","label":"r","prefix":null,"suffix":null,"section":"Problem 10: Rectangular to polar","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"theta_back = atan2(4, 3) deg // @accent @formula @label(θ °)","label":"θ °","prefix":null,"suffix":null,"section":"Problem 10: Rectangular to polar","hidden":false,"hero":false,"slider":null,"value":53.1301023542,"display":"53.1301"}]},{"id":"exhaust-pipe-sizing","title":"Exhaust Pipe Sizing","description":"Estimate recommended exhaust pipe diameter.","category":"engineering","icon":"settings","tags":["automotive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Engine Power","label":null,"prefix":null,"suffix":null,"section":"Engine Power","hero":false,"slider":null,"value":null,"display":null},{"text":"horsepower = 400","label":null,"prefix":null,"suffix":null,"section":"Engine Power","hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"diameter inches = (horsepower ^ 0.5) * 0.125","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"exoplanet-habitability","title":"Exoplanet Habitability","description":"Calculate the habitable zone boundaries around a star from its luminosity.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"star_luminosity_relative_to_sun = 1.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"inner_boundary_astronomical_units = sqrt(star_luminosity_relative_to_sun / 1.1) // Inner (AU) @hero","label":null,"prefix":null,"suffix":"Inner (AU)","section":null,"hidden":false,"hero":true,"slider":null,"value":0.9534625892455924,"display":"0.9535"},{"text":"outer_boundary_astronomical_units = sqrt(star_luminosity_relative_to_sun / 0.53) // Outer (AU) @hero","label":null,"prefix":null,"suffix":"Outer (AU)","section":null,"hidden":false,"hero":true,"slider":null,"value":1.3736056394868903,"display":"1.374"}]},{"id":"expected-value","title":"Expected Value","description":"E[X] = Σ xᵢ · P(xᵢ) for a discrete distribution (up to 4 outcomes).","category":"formulas","icon":"percent","tags":["probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Outcomes and their probabilities","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 0 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":0,"display":"0"},{"text":"p1 = 0.5 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.5,"display":"0.5"},{"text":"x2 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"p2 = 0.3 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.3,"display":"0.3"},{"text":"x3 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"p3 = 0.15 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.15,"display":"0.15"},{"text":"x4 = 10 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":10,"display":"10"},{"text":"p4 = 0.05 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.05,"display":"0.05"},{"text":"# Expected value","label":null,"prefix":null,"suffix":null,"section":"Expected value","hero":false,"slider":null,"value":null,"display":null},{"text":"expected = x1 * p1 + x2 * p2 + x3 * p3 + x4 * p4 // @label(E[X])","label":"E[X]","prefix":null,"suffix":null,"section":"Expected value","hidden":false,"hero":true,"slider":null,"value":1.55,"display":"1.55"}]},{"id":"expense-ratio-impact-fee","title":"Expense Ratio Impact Fee","description":"Calculate the impact of fund expense ratios on investment value over 30 years.","category":"finance","icon":"ratio","tags":["fee","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"initial_investment = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"annual_return = 0.07","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.07,"display":"0.07"},{"text":"expense_ratio = 0.0075","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.0075,"display":"0.0075"},{"text":"years = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"value_without_fees = initial_investment * (1 + annual_return) ** years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":76122.55042662041,"display":"76,122.55"},{"text":"value_with_fees = initial_investment * (1 + annual_return - expense_ratio) ** years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":61640.78511584826,"display":"61,640.79"},{"text":"fee_impact = value_without_fees - value_with_fees","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":14481.76531077215,"display":"14,481.77"}]},{"id":"experience-gain-multiplier","title":"Experience Gain Multiplier","description":"Calculate total experience gain with bonuses.","category":"math","icon":"trending-up","tags":["gaming","experience"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# EXP Settings","label":null,"prefix":null,"suffix":null,"section":"EXP Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base experience = 500","label":null,"prefix":null,"suffix":null,"section":"EXP Settings","hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"world bonus percent = 50 // %","label":null,"prefix":null,"suffix":"%","section":"EXP Settings","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"item bonus percent = 10 // %","label":null,"prefix":null,"suffix":"%","section":"EXP Settings","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"group bonus percent = 15 // %","label":null,"prefix":null,"suffix":"%","section":"EXP Settings","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_bonus_multiplier = 1 + (world bonus percent / 100) + (item bonus percent / 100) + (group bonus percent / 100)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.75,"display":"1.75"},{"text":"final experience = base experience * total_bonus_multiplier","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":875,"display":"875"}]},{"id":"exponential-decay","title":"Exponential Decay","description":"N(t) = N₀ · e^(−k·t) — continuous exponential decay.","category":"formulas","icon":"trending-up","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Parameters","label":null,"prefix":null,"suffix":null,"section":"Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"initial_amount = 100 // 0..1M","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"decay_constant = 0.1 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.1,"display":"0.1"},{"text":"time = 10 // 0..1k","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Amount remaining at time t","label":null,"prefix":null,"suffix":null,"section":"Amount remaining at time t","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = initial_amount * exp(-decay_constant * time) // @label(N(t))","label":"N(t)","prefix":null,"suffix":null,"section":"Amount remaining at time t","hidden":false,"hero":true,"slider":null,"value":36.787944117144235,"display":"36.79"}]},{"id":"exponential-growth","title":"Exponential Growth","description":"N(t) = N₀ · e^(k·t) — continuous exponential growth.","category":"formulas","icon":"trending-up","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Parameters","label":null,"prefix":null,"suffix":null,"section":"Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"initial_amount = 100 // 0..1M","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"rate = 0.05 // -1..1","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":-1,"max":1,"step":0.02},"value":0.05,"display":"0.05"},{"text":"time = 10 // 0..1k","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Amount at time t","label":null,"prefix":null,"suffix":null,"section":"Amount at time t","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = initial_amount * exp(rate * time) // @label(N(t))","label":"N(t)","prefix":null,"suffix":null,"section":"Amount at time t","hidden":false,"hero":true,"slider":null,"value":164.87212707001282,"display":"164.87"}]},{"id":"exposure-value-compensation","title":"Exposure Value Compensation","description":"Calculate adjusted shutter speed from a base speed and exposure compensation stops.","category":"math","icon":"infinity","tags":["exposure","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"base_shutter_speed_seconds = 0.01 // 1/100","label":null,"prefix":null,"suffix":"1/100","section":null,"hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"ev_compensation = 1 // +1 stop","label":null,"prefix":null,"suffix":"+1 stop","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"adjusted_shutter_speed_seconds = base_shutter_speed_seconds * (2^ev_compensation) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.02,"display":"0.02"}]},{"id":"extrinsic-reward-decay","title":"Extrinsic Reward Decay","description":"Estimate the diminishing effective value of repeated extrinsic rewards.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"number_of_rewards = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"satiation_factor = 0.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"effective_reward_value = 1 / (1 + satiation_factor * number_of_rewards) // relative value @hero","label":null,"prefix":null,"suffix":"relative value","section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"factor-by-grouping","title":"Factor by Grouping Check","description":"Given ax² + bx + c, find the two numbers that multiply to a·c and sum to b.","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Quadratic ax² + bx + c","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 2 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":2,"display":"2"},{"text":"b = 7 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":7,"display":"7"},{"text":"c = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"# Product and sum to find","label":null,"prefix":null,"suffix":null,"section":"Product and sum to find","hero":false,"slider":null,"value":null,"display":null},{"text":"target_product = a * c // @label(a·c)","label":"a·c","prefix":null,"suffix":null,"section":"Product and sum to find","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"target_sum = b // @label(b)","label":"b","prefix":null,"suffix":null,"section":"Product and sum to find","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"# Find m and n where m + n = b and m · n = a · c","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hero":false,"slider":null,"value":null,"display":null},{"text":"discriminant = b^2 - 4 * target_product","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"m = (b + sqrt(abs(discriminant))) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hidden":false,"hero":true,"slider":null,"value":6,"display":"6"},{"text":"n = (b - sqrt(abs(discriminant))) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"factorial-calculator","title":"Factorial Calculator","description":"Calculate the factorial (n!) of a number.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"number = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"result = factorial(number)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":120,"display":"120"}]},{"id":"factorio-recipes-live","title":"Factorio — Live Recipe Data","description":"The same factory math as the main planner, but the recipe table is **loaded from a hosted JSON file** instead of pasted into the calc. Point `import()` at any URL — a file in this repo, GitHub raw, your own API, or a published Google Sheet — and every number below rebalances.","category":"gaming","icon":"database","tags":["factorio","gaming","demo"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-27T00:49:26.633Z"},"rows":[{"text":"base spm = 60 // 30..600 by 30 @hero @suffix( /min) @label(🎯 Science / min)","label":"🎯 Science / min","prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":{"min":30,"max":600,"step":30},"value":60,"display":"60"},{"text":"# Where the data comes from @collapsed","label":null,"prefix":null,"suffix":null,"section":"Where the data comes from","hero":false,"slider":null,"value":null,"display":null},{"text":"recipes = import(\"/gallery/data/factorio-recipes.json\") // @hidden","label":null,"prefix":null,"suffix":null,"section":"Where the data comes from","hidden":true,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"# Loaded catalog @skin(spec-sheet) @density(compact)","label":null,"prefix":null,"suffix":null,"section":"Loaded catalog","hero":false,"slider":null,"value":null,"display":null},{"text":"recipes loaded = sum(map(recipes, r => 1)) // @label(📦 Rows loaded)","label":"📦 Rows loaded","prefix":null,"suffix":null,"section":"Loaded catalog","hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"assembler recipes = sum(map(filter(recipes, r => r.made == \"Assembler\"), r => 1)) // @label(🦾 Assembler recipes)","label":"🦾 Assembler recipes","prefix":null,"suffix":null,"section":"Loaded catalog","hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"furnace recipes = sum(map(filter(recipes, r => r.made == \"Furnace\"), r => 1)) // @label(🔥 Furnace recipes)","label":"🔥 Furnace recipes","prefix":null,"suffix":null,"section":"Loaded catalog","hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"# Factory size at this rate @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"Factory size at this rate","hero":false,"slider":null,"value":null,"display":null},{"text":"_s = base_spm/60 // science packs per second of each colour","label":null,"prefix":null,"suffix":"science packs per second of each colour","section":"Factory size at this rate","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"assemblers = ceil(sum(map(filter(recipes, r => r.made == \"Assembler\"), r => _s*r.mult*r.craft/r.out))) // @hero @label(🦾 Assemblers)","label":"🦾 Assemblers","prefix":null,"suffix":null,"section":"Factory size at this rate","hidden":false,"hero":true,"slider":null,"value":null,"display":null,"loading":true},{"text":"furnaces = ceil(sum(map(filter(recipes, r => r.made == \"Furnace\"), r => _s*r.mult*3.2))) // @hero @label(🔥 Furnaces)","label":"🔥 Furnaces","prefix":null,"suffix":null,"section":"Factory size at this rate","hidden":false,"hero":true,"slider":null,"value":null,"display":null,"loading":true},{"text":"iron ore = round(sum(map(filter(recipes, r => r.item == \"Iron plate\"), r => _s*r.mult*60))) // @label(⛏️ Iron ore) @suffix( /min)","label":"⛏️ Iron ore","prefix":null,"suffix":null,"section":"Factory size at this rate","hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"copper ore = round(sum(map(filter(recipes, r => r.item == \"Copper plate\"), r => _s*r.mult*60))) // @label(⛏️ Copper ore) @suffix( /min)","label":"⛏️ Copper ore","prefix":null,"suffix":null,"section":"Factory size at this rate","hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true}]},{"id":"fair-trade-coffee-premium","title":"Fair Trade Coffee Premium","description":"Calculate the total cost including social and organic premiums.","category":"finance","icon":"coffee","tags":["finance","eco","coffee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"coffee_price_per_lb = 15 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"fair_trade_social_premium_per_lb = 0.20 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"organic_premium_per_lb = 0.30 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"total_fair_trade_organic_price = coffee_price_per_lb + fair_trade_social_premium_per_lb + organic_premium_per_lb // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":15.5,"display":"15.5"},{"text":"percentage_premium = (fair_trade_social_premium_per_lb + organic_premium_per_lb) / coffee_price_per_lb * 100 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":3.333333333333334,"display":"3.333"}]},{"id":"fan-laws-performance-scaling","title":"Fan Laws Performance Scaling","description":"Predict fan performance changes with RPM shifts.","category":"engineering","icon":"fan","tags":["engineering","mechanical","fluids"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"initial_rpm = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"new_rpm = 1500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"initial_cfm = 100 // cubic feet per minute","label":null,"prefix":null,"suffix":"cubic feet per minute","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"new_cfm = initial_cfm * (new_rpm / initial_rpm) // cfm @hero","label":null,"prefix":null,"suffix":"cfm","section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"},{"text":"initial_static_pressure = 1 // in H2O","label":null,"prefix":null,"suffix":"in H2O","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"new_static_pressure = initial_static_pressure * ((new_rpm / initial_rpm)^2) // in H2O","label":null,"prefix":null,"suffix":"in H2O","section":null,"hidden":false,"hero":false,"slider":null,"value":2.25,"display":"2.25"},{"text":"initial_power_watts = 10 // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"new_power_watts = initial_power_watts * ((new_rpm / initial_rpm)^3) // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":33.75,"display":"33.75"}]},{"id":"fantasy-football-expected-points","title":"Fantasy Football Expected Points","description":"Calculate fantasy football points for a player from passing, rushing, and receiving stats.","category":"math","icon":"infinity","tags":["football","points","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Passing","label":null,"prefix":null,"suffix":null,"section":"Passing","hero":false,"slider":null,"value":null,"display":null},{"text":"passing yards = 250","label":null,"prefix":null,"suffix":null,"section":"Passing","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"passing touchdowns = 2","label":null,"prefix":null,"suffix":null,"section":"Passing","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"interceptions = 1","label":null,"prefix":null,"suffix":null,"section":"Passing","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Rushing/Receiving","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hero":false,"slider":null,"value":null,"display":null},{"text":"rushing yards = 40","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"receiving yards = 20","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"receptions = 5 // PPR league","label":null,"prefix":null,"suffix":"PPR league","section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"total touchdowns = 1","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"points = (passing yards * 0.04) + (passing touchdowns * 4) - (interceptions * 2) + (rushing yards * 0.1) + (receiving yards * 0.1) + (receptions * 1) + (total touchdowns * 6)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":33,"display":"33"}]},{"id":"fcpa-compliance-risk-score","title":"FCPA Risk Score","description":"Measure risk levels related to the Foreign Corrupt Practices Act.","category":"other","icon":"globe","tags":["compliance","risk"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"foreignOfficialInteractionFrequency = 8 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"thirdPartyAgentUsage = 6 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"localCorruptionIndex = 5 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"fcpaRisk = (foreignOfficialInteractionFrequency + thirdPartyAgentUsage + localCorruptionIndex) / 3 // scale 1-10 @hero","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":true,"slider":null,"value":6.333333333333333,"display":"6.333"}]},{"id":"fence-calculator","title":"Fence Calculator","description":"Estimate posts, pickets, and material costs for your fence project.","category":"construction","icon":"fence","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Project","label":null,"prefix":null,"suffix":null,"section":"Project","hero":false,"slider":null,"value":null,"display":null},{"text":"total fence length = 150 // ft 10..1k by 5","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":10,"max":1000,"step":5},"value":150,"display":"150"},{"text":"fence height = 6 // ft 3..10","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":3,"max":10,"step":0.1},"value":6,"display":"6"},{"text":"post spacing = 8 // ft 4..12","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":4,"max":12,"step":0.1},"value":8,"display":"8"},{"text":"number of gates = 1 // 0..5","label":null,"prefix":null,"suffix":null,"section":"Project","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.05},"value":1,"display":"1"},{"text":"gate width = 4 // ft 3..16","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":3,"max":16,"step":0.2},"value":4,"display":"4"},{"text":"# Posts","label":null,"prefix":null,"suffix":null,"section":"Posts","hero":false,"slider":null,"value":null,"display":null},{"text":"fence run = total_fence_length - (number_of_gates * gate_width)","label":null,"prefix":null,"suffix":null,"section":"Posts","hidden":false,"hero":false,"slider":null,"value":146,"display":"146"},{"text":"posts needed = roundup(fence_run / post_spacing) + 1 + (number_of_gates * 2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Posts","hidden":false,"hero":true,"slider":null,"value":22,"display":"22"},{"text":"post depth = 2 // ft 1..4 by 0.5","label":null,"prefix":null,"suffix":"ft","section":"Posts","hidden":false,"hero":false,"slider":{"min":1,"max":4,"step":0.5},"value":2,"display":"2"},{"text":"total post length = fence_height + post_depth // ft","label":null,"prefix":null,"suffix":"ft","section":"Posts","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Pickets","label":null,"prefix":null,"suffix":null,"section":"Pickets","hero":false,"slider":null,"value":null,"display":null},{"text":"picket width = 3.5 // in 1..8 by 0.5","label":null,"prefix":null,"suffix":"in","section":"Pickets","hidden":false,"hero":false,"slider":{"min":1,"max":8,"step":0.5},"value":3.5,"display":"3.5"},{"text":"gap between pickets = 0 // in 0..4 by 0.25","label":null,"prefix":null,"suffix":"in","section":"Pickets","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.25},"value":0,"display":"0"},{"text":"pickets per foot = 12 / (picket_width + gap_between_pickets)","label":null,"prefix":null,"suffix":null,"section":"Pickets","hidden":false,"hero":false,"slider":null,"value":3.4285714285714284,"display":"3.429"},{"text":"total pickets = roundup(fence_run * pickets_per_foot)","label":null,"prefix":null,"suffix":null,"section":"Pickets","hidden":false,"hero":false,"slider":null,"value":501,"display":"501"},{"text":"# Cost Estimate","label":null,"prefix":null,"suffix":null,"section":"Cost Estimate","hero":false,"slider":null,"value":null,"display":null},{"text":"$cost per post = 12 // 5..50","label":null,"prefix":"$","suffix":null,"section":"Cost Estimate","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":12,"display":"$12.00"},{"text":"$cost per picket = 2.50 // 0.5..10 by 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@hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"phosphorus_weight = fertilizer_weight_pounds * (phosphorus_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7.5,"display":"7.5"},{"text":"potassium_weight = fertilizer_weight_pounds * (potassium_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"}]},{"id":"fibonacci-nth-term","title":"Fibonacci nth Term","description":"Find the nth Fibonacci number (F₁=1, F₂=1, Fₙ=Fₙ₋₁+Fₙ₋₂).","category":"formulas","icon":"infinity","tags":["number-theory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Index","label":null,"prefix":null,"suffix":null,"section":"Index","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 10 // 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400000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":400000,"display":"400,000"},{"text":"earnings_before_tax = 300000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"degree_of_financial_leverage = operating_income / earnings_before_tax","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.3333333333333333,"display":"1.333"}]},{"id":"fire-calculator","title":"FIRE Calculator","description":"Calculate your Financial Independence, Retire Early number and timeline.","category":"finance","icon":"flame","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"# Current Finances","label":null,"prefix":null,"suffix":null,"section":"Current Finances","hero":false,"slider":null,"value":null,"display":null},{"text":"annual income = $80000 // 20k..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Current Finances","hidden":false,"hero":false,"slider":{"min":20000,"max":500000,"step":1000},"value":80000,"display":"$80,000.00"},{"text":"annual expenses = $45000 // 10k..300k by 1k","label":null,"prefix":"$","suffix":null,"section":"Current Finances","hidden":false,"hero":false,"slider":{"min":10000,"max":300000,"step":1000},"value":45000,"display":"$45,000.00"},{"text":"current savings = $100000 // 0..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Current Finances","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":5000},"value":100000,"display":"$100,000.00"},{"text":"# Assumptions","label":null,"prefix":null,"suffix":null,"section":"Assumptions","hero":false,"slider":null,"value":null,"display":null},{"text":"expected return = 7 // % 1..15","label":null,"prefix":null,"suffix":"%","section":"Assumptions","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.2},"value":7,"display":"7"},{"text":"safe withdrawal rate = 4 // % 2..6","label":null,"prefix":null,"suffix":"%","section":"Assumptions","hidden":false,"hero":false,"slider":{"min":2,"max":6,"step":0.05},"value":4,"display":"4"},{"text":"inflation rate = 2.5 // % 0..10 by 0.5","label":null,"prefix":null,"suffix":"%","section":"Assumptions","hidden":false,"hero":false,"slider":{"min":0,"max":10,"step":0.5},"value":2.5,"display":"2.5"},{"text":"# Analysis","label":null,"prefix":null,"suffix":null,"section":"Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"_savings_rate = ((annual_income - annual_expenses) / annual_income) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Analysis","hidden":true,"hero":false,"slider":null,"value":43.75,"display":"43.75"},{"text":"$_annual_savings = annual_income - annual_expenses","label":null,"prefix":"$","suffix":null,"section":"Analysis","hidden":true,"hero":false,"slider":null,"value":35000,"display":"$35,000.00"},{"text":"_real_return = (expected_return - inflation_rate) / 100","label":null,"prefix":null,"suffix":null,"section":"Analysis","hidden":true,"hero":false,"slider":null,"value":0.045,"display":"0.045"},{"text":"$FIRE number = annual_expenses / (safe_withdrawal_rate / 100) // @hero @label(FIRE Number (25x Expenses))","label":"FIRE Number (25x Expenses)","prefix":"$","suffix":null,"section":"Analysis","hidden":false,"hero":true,"slider":null,"value":1125000,"display":"$1,125,000.00"},{"text":"# Timeline","label":null,"prefix":null,"suffix":null,"section":"Timeline","hero":false,"slider":null,"value":null,"display":null},{"text":"years until FIRE = round(ln((FIRE_number * real_return + annual_savings) / (current_savings * real_return + annual_savings)) / ln(1 + real_return), 1) // 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temperature_difference","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8640,"display":"8,640"}]},{"id":"firewood-cord-volume","title":"Firewood Cord Volume","description":"Calculate how many standard cords a stacked firewood pile contains.","category":"finance","icon":"dollar-sign","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"stack_width = 4 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"stack_height = 4 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"stack_length = 8 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"volume_cubic_feet = stack_width * stack_height * stack_length // cubic feet","label":null,"prefix":null,"suffix":"cubic feet","section":null,"hidden":false,"hero":false,"slider":null,"value":128,"display":"128"},{"text":"cord_volume_cubic_feet = 128 // standard cord is 128 cubic feet","label":null,"prefix":null,"suffix":"standard cord is 128 cubic feet","section":null,"hidden":false,"hero":false,"slider":null,"value":128,"display":"128"},{"text":"number_of_cords = volume_cubic_feet / cord_volume_cubic_feet // cords","label":null,"prefix":null,"suffix":"cords","section":null,"hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"firework-burst-radius","title":"Firework Burst Radius","description":"Estimate firework burst radius in feet from shell diameter in inches.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"shell_diameter_inches = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"burst_radius_feet = shell_diameter_inches * 45 // feet @hero","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":true,"slider":null,"value":180,"display":"180"}]},{"id":"fish-tank-heater-watts","title":"Fish Tank Heater Watts","description":"Calculate required heater wattage for a fish tank from volume and temperature rise.","category":"science","icon":"fish","tags":["heater","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"tank_volume_gallons = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"desired_temperature_increase_fahrenheit = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"watts_per_gallon_per_degree = 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"total_heater_wattage_required = tank_volume_gallons * desired_temperature_increase_fahrenheit * watts_per_gallon_per_degree","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"}]},{"id":"fishing-line-capacity-monofill","title":"Fishing Line Capacity Monofill","description":"Estimate fishing line yardage on a spool when changing line test weight.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"spool_capacity_yards_at_12lb = 200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"target_line_test_lb = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"estimated_capacity_yards = spool_capacity_yards_at_12lb * (12 / target_line_test_lb) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":120,"display":"120"}]},{"id":"flash-guide-number-distance","title":"Flash Guide Number Distance","description":"Calculate maximum flash distance from guide number and aperture f-stop.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.434Z"},"rows":[{"text":"guide_number_feet = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"aperture_f_stop = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"max_flash_distance_feet = guide_number_feet / aperture_f_stop // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12.5,"display":"12.5"}]},{"id":"fleet-utilization-rate","title":"Fleet Utilization Rate","description":"Monitor the percentage of your fleet currently in active service.","category":"business","icon":"truck","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"activeVehicles = 45 // vehicles","label":null,"prefix":null,"suffix":"vehicles","section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"totalVehiclesInFleet = 50 // vehicles","label":null,"prefix":null,"suffix":"vehicles","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"utilizationRatePercent = (activeVehicles / totalVehiclesInFleet) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":90,"display":"90"}]},{"id":"flexible-spending-account-fsa-savings","title":"Flexible Spending Account Fsa Savings","description":"Calculate total FSA tax savings from federal, Social Security, and Medicare withholding.","category":"finance","icon":"dollar-sign","tags":["account","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"annual_contribution = 3050","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3050,"display":"3,050"},{"text":"tax_rate = 0.22","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.22,"display":"0.22"},{"text":"social_security_rate = 0.062","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.062,"display":"0.062"},{"text":"medicare_rate = 0.0145","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.0145,"display":"0.0145"},{"text":"total_tax_savings = annual_contribution * (tax_rate + social_security_rate + medicare_rate)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":904.325,"display":"904.33"}]},{"id":"flight-carbon-footprint","title":"Flight Carbon Footprint","description":"Estimate CO2 emissions for your air 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overtimeThreshold","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"_overtimePay = overtimeHours * (hourlyRate * 1.5)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"totalPay = regularPay + overtimePay // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1100,"display":"1,100"}]},{"id":"fluid-density-buoyancy","title":"Fluid Density Buoyancy","description":"Calculate buoyant force from submerged volume and fluid density.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"volume_submerged = 0.5 // cubic meters","label":null,"prefix":null,"suffix":"cubic 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@hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":67.77281651200002,"display":"67.77"},{"text":"heading_level_2 = base_font_size * scale_factor^2 // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":41.886784000000006,"display":"41.89"},{"text":"heading_level_3 = base_font_size * scale_factor^1 // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":25.888,"display":"25.89"}]},{"id":"font-scale","title":"Font Scale","description":"Generate a modular type scale for consistent typography.","category":"design","icon":"type","tags":["font"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Scale Settings","label":null,"prefix":null,"suffix":null,"section":"Scale 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250","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"touchdowns = 2","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"interceptions = 1","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_a = ((completions / attempts) - 0.3) * 5","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.8333333333333328,"display":"1.833"},{"text":"_b = ((yards / attempts) - 3) * 0.25","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.3333333333333335,"display":"1.333"},{"text":"_c 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1.225","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.225,"display":"1.225"},{"text":"gravity = 9.81","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"time_seconds = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"terminal_velocity = ( (2 * object_mass_kilograms * gravity) / (air_density * projected_area_square_meters * drag_coefficient) ) ** 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40.02040295975572,"display":"40.02"},{"text":"exponent_value = (2 * gravity * time_seconds) / terminal_velocity","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.451249681285038,"display":"2.451"},{"text":"e_val = 2.71828 ** 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dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"business_expenses_annual = 20000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":20000,"display":"20,000"},{"text":"billable_hours_per_week = 20 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"weeks_per_year = 48 // weeks","label":null,"prefix":null,"suffix":"weeks","section":null,"hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"_total_target_revenue = target_annual_income + business_expenses_annual","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":120000,"display":"120,000"},{"text":"_total_billable_hours = billable_hours_per_week * 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Goal","hidden":false,"hero":false,"slider":{"min":30000,"max":300000,"step":1000},"value":80000,"display":"$80,000.00"},{"text":"$annual business expenses = 12000 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Income Goal","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":12000,"display":"$12,000.00"},{"text":"$self employment tax rate = 15.3 // % 0..30 by 0.1","label":null,"prefix":"$","suffix":"%","section":"Income Goal","hidden":false,"hero":false,"slider":{"min":0,"max":30,"step":0.1},"value":15.3,"display":"$15.30"},{"text":"# Availability","label":null,"prefix":null,"suffix":null,"section":"Availability","hero":false,"slider":null,"value":null,"display":null},{"text":"billable hours per week = 25 // 5..50","label":null,"prefix":null,"suffix":null,"section":"Availability","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":25,"display":"25"},{"text":"weeks per year = 48 // 40..52","label":null,"prefix":null,"suffix":null,"section":"Availability","hidden":false,"hero":false,"slider":{"min":40,"max":52,"step":0.2},"value":48,"display":"48"},{"text":"# Required Rate","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_needed = desired annual income + annual business expenses","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hidden":true,"hero":false,"slider":null,"value":92000,"display":"92,000"},{"text":"_tax_adjusted = total_needed / (1 - self employment tax rate / 100)","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hidden":true,"hero":false,"slider":null,"value":108618.65407319953,"display":"108,618.65"},{"text":"total billable hours = billable hours per week * weeks per year","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"$required hourly rate = round(tax_adjusted / total billable hours * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Required Rate","hidden":false,"hero":true,"slider":null,"value":90.52,"display":"$90.52"},{"text":"$required day rate = round(required hourly rate * 8 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Required Rate","hidden":false,"hero":false,"slider":null,"value":724.16,"display":"$724.16"},{"text":"$effective monthly income = round(desired annual income / 12 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Required Rate","hidden":false,"hero":false,"slider":null,"value":6666.67,"display":"$6,666.67"}]},{"id":"freezing-point-depression-colligative","title":"Freezing Point Depression Colligative","description":"Calculate freezing point depression of a solution from molality and solvent 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1728","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":53.333333333333336,"display":"53.33"},{"text":"density = weightInPounds / volumeInCubicFeet // pounds per cubic foot @hero","label":null,"prefix":null,"suffix":"pounds per cubic foot","section":null,"hidden":false,"hero":true,"slider":null,"value":9.375,"display":"9.375"}]},{"id":"frequency","title":"Musical Frequency","description":"Frequency from a reference pitch using 12-tone equal temperament.","category":"science","icon":"music","tags":["acoustics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Reference Note","label":null,"prefix":null,"suffix":null,"section":"Reference Note","hero":false,"slider":null,"value":null,"display":null},{"text":"base frequency = 440 // Hz 20..20k","label":null,"prefix":null,"suffix":"Hz","section":"Reference Note","hidden":false,"hero":false,"slider":{"min":20,"max":20000,"step":200},"value":440,"display":"440"},{"text":"semitones from base = 12 // -48..48","label":null,"prefix":null,"suffix":null,"section":"Reference Note","hidden":false,"hero":false,"slider":{"min":-48,"max":48,"step":1},"value":12,"display":"12"},{"text":"# Equal Temperament","label":null,"prefix":null,"suffix":null,"section":"Equal Temperament","hero":false,"slider":null,"value":null,"display":null},{"text":"frequency = base frequency * 2^(semitones from base / 12) // Hz @hero @label(Frequency) @suffix(Hz)","label":"Frequency","prefix":null,"suffix":"Hz","section":"Equal Temperament","hidden":false,"hero":true,"slider":null,"value":880,"display":"880"},{"text":"# Octave + Cents Breakdown","label":null,"prefix":null,"suffix":null,"section":"Octave + Cents Breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"octaves up = semitones from base / 12 // @label(Octaves from base)","label":"Octaves from base","prefix":null,"suffix":null,"section":"Octave + Cents Breakdown","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"cents from base = semitones from base * 100 // ¢","label":null,"prefix":null,"suffix":"¢","section":"Octave + Cents Breakdown","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"# Period + Wavelength","label":null,"prefix":null,"suffix":null,"section":"Period + Wavelength","hero":false,"slider":null,"value":null,"display":null},{"text":"period ms = 1000 / frequency // ms @label(Period) @suffix(ms)","label":"Period","prefix":null,"suffix":"ms","section":"Period + Wavelength","hidden":false,"hero":false,"slider":null,"value":1.1363636363636365,"display":"1.136"},{"text":"wavelength m = 343 / frequency // m @label(Wavelength in air) @suffix(m)","label":"Wavelength in air","prefix":null,"suffix":"m","section":"Period + Wavelength","hidden":false,"hero":false,"slider":null,"value":0.38977272727272727,"display":"0.3898"}]},{"id":"friction-coefficient","title":"Friction Coefficient","description":"Calculate the coefficient of friction from friction force and normal force.","category":"other","icon":"calculator","tags":["coefficient"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Force Details","label":null,"prefix":null,"suffix":null,"section":"Force Details","hero":false,"slider":null,"value":null,"display":null},{"text":"friction force = 25 // newtons 0..1k","label":null,"prefix":null,"suffix":"newtons","section":"Force Details","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":25,"display":"25"},{"text":"normal force = 100 // newtons 1..2k","label":null,"prefix":null,"suffix":"newtons","section":"Force Details","hidden":false,"hero":false,"slider":{"min":1,"max":2000,"step":20},"value":100,"display":"100"},{"text":"# Formula: mu = Ff / Fn","label":null,"prefix":null,"suffix":null,"section":"Formula: mu = Ff / Fn","hero":false,"slider":null,"value":null,"display":null},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"coefficient of friction = friction force / normal force // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":0.25,"display":"0.25"},{"text":"# Common Values","label":null,"prefix":null,"suffix":null,"section":"Common Values","hero":false,"slider":null,"value":null,"display":null},{"text":"ice on ice = 0.1","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"rubber on concrete = 0.7","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.7,"display":"0.7"},{"text":"wood on wood = 0.4","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"steel on steel = 0.6","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"teflon on steel = 0.04","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"}]},{"id":"frictional-force-coefficient-static","title":"Frictional Force Coefficient Static","description":"Calculate maximum static friction force from normal force and friction coefficient.","category":"education","icon":"book-open","tags":["coefficient"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"normal_force = 100 // Newtons","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"coefficient_of_static_friction = 0.4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"max_static_frictional_force = normal_force * coefficient_of_static_friction // Newtons @hero","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":true,"slider":null,"value":40,"display":"40"}]},{"id":"front-end-load-impact","title":"Front End Load Impact","description":"Calculate future value after a front-end load fee on an initial investment.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"investment_amount = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"front_end_load = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"annual_growth = 0.07","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.07,"display":"0.07"},{"text":"years = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"net_investment = investment_amount * (1 - front_end_load)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9500,"display":"9,500"},{"text":"future_value = net_investment * (1 + annual_growth) ** years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":18687.93789425088,"display":"18,687.94"}]},{"id":"fuel-burn-aviation-gph","title":"Fuel Burn Aviation Gph","description":"Calculate aviation fuel burn rate in gallons per hour from total fuel and time.","category":"other","icon":"flame","tags":["fuel","burn"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"total_fuel_burned_gallons = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"flight_duration_hours = 3.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.5,"display":"3.5"},{"text":"fuel_burn_rate_gallons_per_hour = total_fuel_burned_gallons / flight_duration_hours // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12.857142857142858,"display":"12.86"}]},{"id":"fuel-consumption-l-100km-to-mpg","title":"Fuel Consumption L 100km To MPG","description":"Convert liters per 100km to miles per gallon.","category":"conversion","icon":"settings","tags":["automotive","fuel"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Fuel Consumption","label":null,"prefix":null,"suffix":null,"section":"Fuel Consumption","hero":false,"slider":null,"value":null,"display":null},{"text":"liters per 100km = 10","label":null,"prefix":null,"suffix":null,"section":"Fuel Consumption","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"miles per gallon = 235.215 / liters per 100km","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":23.5215,"display":"23.52"}]},{"id":"fuel-consumption-mpg-to-l-100km","title":"Fuel Consumption MPG To L 100km","description":"Convert miles per gallon to liters per 100km.","category":"conversion","icon":"settings","tags":["automotive","fuel"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Fuel Consumption","label":null,"prefix":null,"suffix":null,"section":"Fuel Consumption","hero":false,"slider":null,"value":null,"display":null},{"text":"miles per gallon = 25","label":null,"prefix":null,"suffix":null,"section":"Fuel Consumption","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"liters per 100km = 235.215 / miles per gallon","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":9.4086,"display":"9.409"}]},{"id":"fuel-cost","title":"Fuel Cost","description":"Calculate fuel costs for trips and estimate your monthly/yearly gas budget.","category":"everyday","icon":"fuel","tags":["fuel","gas"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Your Car","label":null,"prefix":null,"suffix":null,"section":"Your Car","hero":false,"slider":null,"value":null,"display":null},{"text":"tank size = 14 // gallons 5..40","label":null,"prefix":null,"suffix":"gallons","section":"Your Car","hidden":false,"hero":false,"slider":{"min":5,"max":40,"step":1},"value":14,"display":"14"},{"text":"fuel economy = 28 // mpg 5..60","label":null,"prefix":null,"suffix":"mpg","section":"Your Car","hidden":false,"hero":false,"slider":{"min":5,"max":60,"step":1},"value":28,"display":"28"},{"text":"gas price = $3.89 // /gal 1..10","label":null,"prefix":"$","suffix":"gal","section":"Your Car","hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":3.89,"display":"$3.89"},{"text":"# Per Tank","label":null,"prefix":null,"suffix":null,"section":"Per Tank","hero":false,"slider":null,"value":null,"display":null},{"text":"range per tank = tank_size * fuel_economy // miles @hero","label":null,"prefix":null,"suffix":"miles","section":"Per Tank","hidden":false,"hero":true,"slider":null,"value":392,"display":"392"},{"text":"$cost to fill up = tank_size * gas_price","label":null,"prefix":"$","suffix":null,"section":"Per 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30..100","label":null,"prefix":null,"suffix":"mph","section":"Cruise Speed","hidden":false,"hero":false,"slider":{"min":30,"max":100,"step":1},"value":70,"display":"70"},{"text":"# Drag-Dominated Loss (above_peak)","label":null,"prefix":null,"suffix":null,"section":"Drag-Dominated Loss (above_peak)","hero":false,"slider":null,"value":null,"display":null},{"text":"_above_peak = max(cruise speed - peak speed, 0)","label":null,"prefix":null,"suffix":null,"section":"Drag-Dominated Loss (above_peak)","hidden":true,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"_loss_exponent = 1.05","label":null,"prefix":null,"suffix":null,"section":"Drag-Dominated Loss (above_peak)","hidden":true,"hero":false,"slider":null,"value":1.05,"display":"1.05"},{"text":"mpg now = round(peak mpg * (peak speed / max(cruise speed, peak speed))^loss_exponent, 1) // mpg @hero @label(MPG at cruise speed)","label":"MPG at cruise speed","prefix":null,"suffix":"mpg","section":"Drag-Dominated Loss 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speed))^loss_exponent, 1) // mpg @label(MPG at 60 mph)","label":"MPG at 60 mph","prefix":null,"suffix":"mpg","section":"Compare to 60 mph","hidden":false,"hero":false,"slider":null,"value":28.9,"display":"28.9"},{"text":"percent drop 70 vs 60 = round((1 - mpg now / mpg at 60) * 100, 1) // % @label(Drop from 60 → cruise)","label":"Drop from 60 → cruise","prefix":null,"suffix":"%","section":"Compare to 60 mph","hidden":false,"hero":false,"slider":null,"value":14.9,"display":"14.9"},{"text":"# Per 100-Mile Trip","label":null,"prefix":null,"suffix":null,"section":"Per 100-Mile Trip","hero":false,"slider":null,"value":null,"display":null},{"text":"gallons at 60 = round(100 / mpg at 60, 2) // gal @label(Gallons at 60 mph)","label":"Gallons at 60 mph","prefix":null,"suffix":"gal","section":"Per 100-Mile Trip","hidden":false,"hero":false,"slider":null,"value":3.46,"display":"3.46"},{"text":"gallons at cruise = round(100 / mpg now, 2) // gal @label(Gallons at cruise speed)","label":"Gallons at 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way","label":null,"prefix":null,"suffix":null,"section":"Other unaries compose the same way","hero":false,"slider":null,"value":null,"display":null},{"text":"sine_of_square = sin(f) // x → sin(x²) (degrees)","label":null,"prefix":null,"suffix":"x → sin(x²) (degrees)","section":"Other unaries compose the same way","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"sin","text":"sin"},[["callExp",{"type":"id","value":"__composeInner","text":"__composeInner"},[["folded",{"type":"function","params":["x"],"body":["power",["parenExpr",{"type":"id","value":"x","text":"x","offset":17,"lineBreaks":0,"line":1,"col":18}],{"type":"decimal","value":"2","text":"2","offset":20,"lineBreaks":0,"line":1,"col":21}],"name":"f"}],{"type":"id","value":"x","text":"x"}]]]],"_composedFrom":{"outer":"sin","innerName":"f"},"name":"sine_of_square"},"display":null},{"text":"abs_of_line = abs(f) // x → |f(x)|","label":null,"prefix":null,"suffix":"x → |f(x)|","section":"Other unaries compose the same way","hidden":false,"hero":true,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"abs","text":"abs"},[["callExp",{"type":"id","value":"__composeInner","text":"__composeInner"},[["folded",{"type":"function","params":["x"],"body":["power",["parenExpr",{"type":"id","value":"x","text":"x","offset":17,"lineBreaks":0,"line":1,"col":18}],{"type":"decimal","value":"2","text":"2","offset":20,"lineBreaks":0,"line":1,"col":21}],"name":"f"}],{"type":"id","value":"x","text":"x"}]]]],"_composedFrom":{"outer":"abs","innerName":"f"},"name":"abs_of_line"},"display":null}]},{"id":"future-value","title":"Future Value","description":"Future value of a present amount: FV = PV · (1 + r)ⁿ.","category":"formulas","icon":"dollar-sign","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"$present_value = 5000 // 1..10M","label":null,"prefix":"$","suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":10000000,"step":100000},"value":5000,"display":"$5,000.00"},{"text":"growth_rate = 7 // % 0..50 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":0.1},"value":7,"display":"7"},{"text":"$years = 10 // 1..100","label":null,"prefix":"$","suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":10,"display":"$10.00"},{"text":"# Future value","label":null,"prefix":null,"suffix":null,"section":"Future value","hero":false,"slider":null,"value":null,"display":null},{"text":"$future_value = present_value * (1 + growth_rate / 100)^years","label":null,"prefix":"$","suffix":null,"section":"Future value","hidden":false,"hero":true,"slider":null,"value":9835.756786447831,"display":"$9,835.76"}]},{"id":"gacha-multi-pull-probability","title":"Gacha Multi Pull Probability","description":"Calculate the probability of at least one success in multiple gacha pulls.","category":"math","icon":"dice","tags":["gaming","gacha","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Gacha Settings","label":null,"prefix":null,"suffix":null,"section":"Gacha Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"total pulls = 10","label":null,"prefix":null,"suffix":null,"section":"Gacha Settings","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"success rate percent = 0.6 // %","label":null,"prefix":null,"suffix":"%","section":"Gacha Settings","hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_success_rate = success rate percent / 100","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":0.006,"display":"0.006"},{"text":"_failure_rate = 1 - success_rate","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":0.994,"display":"0.994"},{"text":"_probability_of_no_success = failure_rate ^ total pulls","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":0.9415943502102122,"display":"0.9416"},{"text":"at least one success probability = (1 - probability_of_no_success) * 100 // percent","label":null,"prefix":null,"suffix":"percent","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":5.84056497897878,"display":"5.841"}]},{"id":"gacha-pity-counter-probability","title":"Gacha Pity Counter Probability","description":"Calculate the probability of success as you approach a gacha pity limit.","category":"math","icon":"dice","tags":["gaming","gacha","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Pity Settings","label":null,"prefix":null,"suffix":null,"section":"Pity Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"current pulls = 75","label":null,"prefix":null,"suffix":null,"section":"Pity Settings","hidden":false,"hero":false,"slider":null,"value":75,"display":"75"},{"text":"pity threshold = 90","label":null,"prefix":null,"suffix":null,"section":"Pity Settings","hidden":false,"hero":false,"slider":null,"value":90,"display":"90"},{"text":"base success rate percent = 0.6 // %","label":null,"prefix":null,"suffix":"%","section":"Pity Settings","hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_pulls_remaining = pity threshold - current pulls","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"_pity_factor = (current pulls / pity threshold) * 10","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":8.333333333333334,"display":"8.333"},{"text":"adjusted success rate percent = base success rate percent + pity_factor","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":8.933333333333334,"display":"8.933"}]},{"id":"gacha-single-pull-probability","title":"Gacha Single Pull Probability","description":"Calculate the probability of success in a single gacha pull.","category":"math","icon":"dice","tags":["gaming","gacha","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Gacha Settings","label":null,"prefix":null,"suffix":null,"section":"Gacha Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"pulls = 1","label":null,"prefix":null,"suffix":null,"section":"Gacha Settings","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"success rate percent = 0.6 // %","label":null,"prefix":null,"suffix":"%","section":"Gacha Settings","hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_success_rate = success rate percent / 100","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":0.006,"display":"0.006"},{"text":"probability = success_rate * pulls","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":0.006,"display":"0.006"}]},{"id":"galactic-rotation-speed","title":"Galactic Rotation Speed","description":"Calculate galactic rotation velocity from distance from center and enclosed mass.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"distance_from_center_lightyears = 26000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":26000,"display":"26,000"},{"text":"mass_inside_solar_masses = 1e11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000000000,"display":"100,000,000,000"},{"text":"gravitational_constant = 4.302e-3 // pc * (km/s)^2 / M_sun","label":null,"prefix":null,"suffix":"pc * (km/s)^2 / M_sun","section":null,"hidden":false,"hero":false,"slider":null,"value":0.004302,"display":"0.004302"},{"text":"velocity_km_s = sqrt(gravitational_constant * mass_inside_solar_masses / (distance_from_center_lightyears / 3.26)) // km/s @hero","label":null,"prefix":null,"suffix":"km/s","section":null,"hidden":false,"hero":true,"slider":null,"value":232.25085906937252,"display":"232.25"}]},{"id":"game-factorio-bars","title":"Factorio — Magnitude Bars","description":"@bars ranks the rows: a faint bar shows each value vs the section max.","category":"gaming","icon":"cog","tags":["factorio","gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-26T00:18:12.386Z"},"rows":[{"text":"# Settings @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"target rate = 90 // 5..240 by 5 @suffix(/s) @label(Target output)","label":"Target output","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":{"min":5,"max":240,"step":5},"value":90,"display":"90"},{"text":"# Machines @skin(spec-sheet) @density(compact) @bars","label":null,"prefix":null,"suffix":null,"section":"Machines","hero":false,"slider":null,"value":null,"display":null},{"text":"iron plate = ceil(target_rate * 3.2 / 4) // @label(⬜ Iron plate) @suffix( furn)","label":"⬜ Iron plate","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":false,"slider":null,"value":72,"display":"72"},{"text":"copper plate = ceil(target_rate * 3.2 / 4) // @label(🟧 Copper plate) @suffix( furn)","label":"🟧 Copper plate","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":false,"slider":null,"value":72,"display":"72"},{"text":"steel = ceil(target_rate * 16 / 4) // @label(⬛ Steel) @suffix( furn)","label":"⬛ Steel","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"green circuit = ceil(target_rate * 0.5 / 1.25) // @label(🟩 Green circuit) @suffix( asm)","label":"🟩 Green circuit","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"red circuit = ceil(target_rate * 6 / 1.25) // @label(🟥 Red circuit) @suffix( asm)","label":"🟥 Red circuit","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":false,"slider":null,"value":432,"display":"432"},{"text":"blue circuit = ceil(target_rate * 10 / 1.25) // @label(🟦 Blue circuit) @suffix( asm)","label":"🟦 Blue circuit","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":false,"slider":null,"value":720,"display":"720"},{"text":"engine unit = ceil(target_rate * 10 / 1.25) // @label(🛠️ Engine unit) @suffix( asm)","label":"🛠️ Engine unit","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":false,"slider":null,"value":720,"display":"720"},{"text":"inserter = ceil(target_rate * 0.5 / 1.25) // @label(🦿 Inserter) @suffix( asm)","label":"🦿 Inserter","prefix":null,"suffix":null,"section":"Machines","hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"game-factorio-planner","title":"Factorio — Science Factory","description":"Set your target science/min — get the EXACT machine, belt, and power counts for a red + green science factory, raw ore all the way to the finished pack. Flip on 🛡️ Military for a fully oil-free military line, and dial in mining productivity. Edit the recipe table and the whole factory rebalances live.","category":"gaming","icon":"flask","tags":["factorio","gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-28T04:42:15.207Z"},"rows":[{"text":"# Settings @skin(spec-sheet) @density(compact)","label":null,"prefix":null,"suffix":null,"section":"Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"spm = 60 // 30..600 by 30 @suffix( /min) @label(🎯 Science / min)","label":"🎯 Science / min","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":{"min":30,"max":600,"step":30},"value":60,"display":"60"},{"text":"am = {spd: 1.25, pw: 0.375} // radio({A1: {spd: 0.5, pw: 0.075}, A2: {spd: 0.75, pw: 0.15}, A3: {spd: 1.25, pw: 0.375}}) @label(🦾 Assembler)","label":"🦾 Assembler","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":null,"value":{"spd":1.25,"pw":0.375},"display":null},{"text":"fm = {spd: 2, pw: 0.18} // radio({Stone: {spd: 1, pw: 0}, Steel: {spd: 2, pw: 0}, Electric: {spd: 2, pw: 0.18}}) @label(🔥 Furnace)","label":"🔥 Furnace","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":null,"value":{"spd":2,"pw":0.18},"display":null},{"text":"bt = {tp: 30} // radio({Yellow: {tp: 15}, Red: {tp: 30}, Blue: {tp: 45}}) @label(🟨 Belt)","label":"🟨 Belt","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":null,"value":{"tp":30},"display":null},{"text":"mm = {spd: 0, prod: 0} // dropdown({None: {spd: 0, prod: 0}, 🟦 Speed: {spd: 1, prod: 0}, 🟪 Prod: {spd: -0.3, prod: 0.2}, 🔆 Beacons: {spd: 3.7, prod: 0.2}}) @label(✨ Modules)","label":"✨ Modules","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":null,"value":{"spd":0,"prod":0},"display":null},{"text":"military = false // toggle() @label(🛡️ Military science)","label":"🛡️ Military science","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"minprod = 0 // 0..300 by 10 @suffix(%) @label(⛏️ Mining productivity)","label":"⛏️ Mining productivity","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":{"min":0,"max":300,"step":10},"value":0,"display":"0"},{"text":"presets = \"\" // buttons({🌱 Starter: {spm: 30, military: false, minprod: 0}, ⚖️ Balanced: {spm: 180, minprod: 50}, 🏭 Megabase: {spm: 600, minprod: 200, military: true}}) @label(⚡ One-tap presets)","label":"⚡ One-tap presets","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":null,"value":"","display":null},{"text":"# 📊 At a glance @skin(spec-sheet) @density(compact) @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"📊 At a glance","hero":false,"slider":null,"value":null,"display":null},{"text":"build = machines // @label(🏗️ Machines)","label":"🏗️ Machines","prefix":null,"suffix":null,"section":"📊 At a glance","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"draw = power // @label(⚡ Power) @suffix( MW)","label":"⚡ Power","prefix":null,"suffix":null,"section":"📊 At a glance","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"ore in = _ironf + _copperf + _coalf + _stonef // @label(⛏️ Raw ore) @suffix( /min)","label":"⛏️ Raw ore","prefix":null,"suffix":null,"section":"📊 At a glance","hidden":false,"hero":false,"slider":null,"value":600,"display":"600"},{"text":"# 📦 Recipes @tab @skin(spec-sheet) @density(compact)","label":null,"prefix":null,"suffix":null,"section":"📦 Recipes","hero":false,"slider":null,"value":null,"display":null},{"text":"recipes = [{item: \"Red science\", stage: \"Science\", made: \"Assembler\", mult: 1, mil: 0, craft: 5, out: 1, belt: true}, {item: \"Green science\", stage: \"Science\", made: \"Assembler\", mult: 1, mil: 0, craft: 6, out: 1, belt: true}, {item: \"Inserter\", stage: \"Assembly\", made: \"Assembler\", mult: 1, mil: 0, craft: 0.5, out: 1, belt: true}, {item: \"Transport belt\", stage: \"Assembly\", made: \"Assembler\", mult: 1, mil: 0, craft: 0.5, out: 2, belt: true}, {item: \"Iron gear\", stage: \"Assembly\", made: \"Assembler\", mult: 2.5, mil: 0, craft: 0.5, out: 1, belt: true}, {item: \"Green circuit\", stage: \"Assembly\", made: \"Assembler\", mult: 1, mil: 0, craft: 0.5, out: 1, belt: true}, {item: \"Copper cable\", stage: \"Assembly\", made: \"Assembler\", mult: 3, mil: 0, craft: 0.5, out: 2, belt: true}, {item: \"Iron plate\", stage: \"Smelting\", made: \"Furnace\", mult: 7.5, mil: 9.5, craft: 3.2, out: 1, belt: true}, {item: \"Copper plate\", stage: \"Smelting\", made: \"Furnace\", mult: 2.5, mil: 2.5, craft: 3.2, out: 1, belt: true}, {item: \"Military science\", stage: \"Military\", made: \"Assembler\", mult: 0, mil: 1, craft: 10, out: 2, belt: true}, {item: \"Firearm magazine\", stage: \"Military\", made: \"Assembler\", mult: 0, mil: 0.5, craft: 1, out: 1, belt: true}, {item: \"Piercing rounds\", stage: \"Military\", made: \"Assembler\", mult: 0, mil: 0.5, craft: 3, out: 1, belt: true}, {item: \"Grenade\", stage: \"Military\", made: \"Assembler\", mult: 0, mil: 0.5, craft: 8, out: 1, belt: true}, {item: \"Wall\", stage: \"Military\", made: \"Assembler\", mult: 0, mil: 1, craft: 0.5, out: 1, belt: true}, {item: \"Steel plate\", stage: \"Smelting\", made: \"Furnace\", mult: 0, mil: 0.5, craft: 16, out: 1, belt: true}, {item: \"Stone brick\", stage: \"Smelting\", made: \"Furnace\", mult: 0, mil: 5, craft: 3.2, out: 1, belt: true}] // @cols(Item, Stage, Machine, R+G, Mil, Craft s, Out, Belt)","label":null,"prefix":null,"suffix":null,"section":"📦 Recipes","hidden":false,"hero":false,"slider":null,"value":[{"item":"Red science","stage":"Science","made":"Assembler","mult":1,"mil":0,"craft":5,"out":1,"belt":true},{"item":"Green science","stage":"Science","made":"Assembler","mult":1,"mil":0,"craft":6,"out":1,"belt":true},{"item":"Inserter","stage":"Assembly","made":"Assembler","mult":1,"mil":0,"craft":0.5,"out":1,"belt":true},{"item":"Transport belt","stage":"Assembly","made":"Assembler","mult":1,"mil":0,"craft":0.5,"out":2,"belt":true},{"item":"Iron gear","stage":"Assembly","made":"Assembler","mult":2.5,"mil":0,"craft":0.5,"out":1,"belt":true},{"item":"Green circuit","stage":"Assembly","made":"Assembler","mult":1,"mil":0,"craft":0.5,"out":1,"belt":true},{"item":"Copper cable","stage":"Assembly","made":"Assembler","mult":3,"mil":0,"craft":0.5,"out":2,"belt":true},{"item":"Iron plate","stage":"Smelting","made":"Furnace","mult":7.5,"mil":9.5,"craft":3.2,"out":1,"belt":true},{"item":"Copper plate","stage":"Smelting","made":"Furnace","mult":2.5,"mil":2.5,"craft":3.2,"out":1,"belt":true},{"item":"Military science","stage":"Military","made":"Assembler","mult":0,"mil":1,"craft":10,"out":2,"belt":true},{"item":"Firearm magazine","stage":"Military","made":"Assembler","mult":0,"mil":0.5,"craft":1,"out":1,"belt":true},{"item":"Piercing rounds","stage":"Military","made":"Assembler","mult":0,"mil":0.5,"craft":3,"out":1,"belt":true},{"item":"Grenade","stage":"Military","made":"Assembler","mult":0,"mil":0.5,"craft":8,"out":1,"belt":true},{"item":"Wall","stage":"Military","made":"Assembler","mult":0,"mil":1,"craft":0.5,"out":1,"belt":true},{"item":"Steel plate","stage":"Smelting","made":"Furnace","mult":0,"mil":0.5,"craft":16,"out":1,"belt":true},{"item":"Stone brick","stage":"Smelting","made":"Furnace","mult":0,"mil":5,"craft":3.2,"out":1,"belt":true}],"display":null},{"text":"# ⚙️ Engine @hidden","label":null,"prefix":null,"suffix":null,"section":"⚙️ Engine","hero":false,"slider":null,"value":null,"display":null},{"text":"_s = spm/60 // science packs PER SECOND of each colour (red + green, fed 1:1)","label":null,"prefix":null,"suffix":"science packs PER SECOND of each colour (red + green, fed 1:1)","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_mf = (1+mm.spd)*(1+mm.prod) // module factor: (speed multiplier)×(output multiplier). None ⇒ 1, so default counts are unchanged. Speed ⇒ fewer machines; Prod ⇒ slower machines (more) but less ore.","label":null,"prefix":null,"suffix":"module factor: (speed multiplier)×(output multiplier). None ⇒ 1, so default counts are unchanged. Speed ⇒ fewer machines; Prod ⇒ slower machines (more) but less ore.","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_d(r) = r.mult + military*r.mil // effective demand coefficient: red+green demand, plus military demand when 🛡️ is on. Military off ⇒ military=0 ⇒ just r.mult.","label":null,"prefix":null,"suffix":"effective demand coefficient: red+green demand, plus military demand when 🛡️ is on. Military off ⇒ military=0 ⇒ just r.mult.","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":{"type":"function","params":["r"],"body":["add",["parenExpr",{"type":"id","value":"r.mult","text":"r.mult","offset":18,"lineBreaks":0,"line":1,"col":19}],["mul",["parenExpr",{"type":"id","value":"military","text":"military","offset":29,"lineBreaks":0,"line":1,"col":30}],["parenExpr",{"type":"id","value":"r.mil","text":"r.mil","offset":40,"lineBreaks":0,"line":1,"col":41}]]],"name":"_d"},"display":null},{"text":"_mp = 1 + minprod/100 // mining-productivity factor: +X% ore per mining cycle ⇒ raw ore demand divides by this.","label":null,"prefix":null,"suffix":"mining-productivity factor: +X% ore per mining cycle ⇒ raw ore demand divides by this.","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_belts(r) = if(r.belt, ceil(_s*_d(r)/bt.tp), 0) // belts to carry recipe r's output flow","label":null,"prefix":null,"suffix":"belts to carry recipe r's output flow","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":{"type":"function","params":["r"],"body":["callExpWithKeyword",{"type":"if","value":"if","text":"if","offset":21,"lineBreaks":0,"line":1,"col":22},[["parenExpr",{"type":"id","value":"r.belt","text":"r.belt","offset":25,"lineBreaks":0,"line":1,"col":26,"canonicalName":"r.belt"}],["callExp",{"type":"id","value":"ceil","text":"ceil","offset":34,"lineBreaks":0,"line":1,"col":35},[["div",["mul",["parenExpr",{"type":"id","value":"s","text":"s","offset":40,"lineBreaks":0,"line":1,"col":41,"canonicalName":"s"}],["callExp",{"type":"id","value":"d","text":"d","offset":43,"lineBreaks":0,"line":1,"col":44},[["parenExpr",{"type":"id","value":"r","text":"r","offset":46,"lineBreaks":0,"line":1,"col":47,"canonicalName":"r"}]]]],["parenExpr",{"type":"id","value":"bt.tp","text":"bt.tp","offset":51,"lineBreaks":0,"line":1,"col":52,"canonicalName":"bt.tp"}]]]],{"type":"decimal","value":"0","text":"0","offset":60,"lineBreaks":0,"line":1,"col":61}]],"name":"_belts"},"display":null},{"text":"_row(r) = [_mach(r), _belts(r), round(_pw(r))] // table row: [machines, belts, MW]","label":null,"prefix":null,"suffix":"table row:","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":{"type":"function","params":["r"],"body":["arrayLiteral",[["callExp",{"type":"id","value":"mach","text":"mach","offset":20,"lineBreaks":0,"line":1,"col":21},[["parenExpr",{"type":"id","value":"r","text":"r","offset":26,"lineBreaks":0,"line":1,"col":27}]]],["callExp",{"type":"id","value":"belts","text":"belts","offset":31,"lineBreaks":0,"line":1,"col":32},[["parenExpr",{"type":"id","value":"r","text":"r","offset":38,"lineBreaks":0,"line":1,"col":39}]]],["callExp",{"type":"id","value":"round","text":"round","offset":43,"lineBreaks":0,"line":1,"col":44},[["callExp",{"type":"id","value":"pw","text":"pw","offset":49,"lineBreaks":0,"line":1,"col":50},[["parenExpr",{"type":"id","value":"r","text":"r","offset":53,"lineBreaks":0,"line":1,"col":54}]]]]]]],"name":"_row"},"display":null},{"text":"_pwr(x) = sum(map(recipes, r => _pwAt(r, x/60))) // total factory power (MW) as a function of science/min","label":null,"prefix":null,"suffix":"total factory power (MW) as a function of science/min","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"sum","text":"sum","offset":19,"lineBreaks":0,"line":1,"col":20},[["callExp",{"type":"id","value":"map","text":"map","offset":23,"lineBreaks":0,"line":1,"col":24},[["parenExpr",{"type":"id","value":"recipes","text":"recipes","offset":28,"lineBreaks":0,"line":1,"col":29}],["functionDeclaration","",[{"type":"id","value":"r","text":"r","offset":38,"lineBreaks":0,"line":1,"col":39}],["callExp",{"type":"id","value":"pwat","text":"pwat","offset":43,"lineBreaks":0,"line":1,"col":44},[["parenExpr",{"type":"id","value":"r","text":"r","offset":49,"lineBreaks":0,"line":1,"col":50}],["div",["parenExpr",{"type":"id","value":"x","text":"x","offset":54,"lineBreaks":0,"line":1,"col":55}],{"type":"decimal","value":"60","text":"60","offset":57,"lineBreaks":0,"line":1,"col":58}]]]]]]]],"name":"_pwr"},"display":null},{"text":"_oref(name) = round(sum(map(filter(recipes, r => r.item == name), r => _s*_d(r)*60))/((1+mm.prod)*_mp)) // raw input for plate `name` (items/min) — prod modules + mining prod both stretch each ore","label":null,"prefix":null,"suffix":"raw input for plate `name` (items/min) — prod modules + mining prod both stretch each ore","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":{"type":"function","params":["name"],"body":["callExp",{"type":"id","value":"round","text":"round","offset":23,"lineBreaks":0,"line":1,"col":24},[["div",["callExp",{"type":"id","value":"sum","text":"sum","offset":29,"lineBreaks":0,"line":1,"col":30},[["callExp",{"type":"id","value":"map","text":"map","offset":33,"lineBreaks":0,"line":1,"col":34},[["callExp",{"type":"id","value":"filter","text":"filter","offset":37,"lineBreaks":0,"line":1,"col":38},[["parenExpr",{"type":"id","value":"recipes","text":"recipes","offset":45,"lineBreaks":0,"line":1,"col":46,"canonicalName":"recipes"}],["functionDeclaration","",[{"type":"id","value":"r","text":"r","offset":55,"lineBreaks":0,"line":1,"col":56}],["equal",["parenExpr",{"type":"id","value":"r.item","text":"r.item","offset":61,"lineBreaks":0,"line":1,"col":62,"canonicalName":"r.item"}],["parenExpr",{"type":"id","value":"name","text":"name","offset":73,"lineBreaks":0,"line":1,"col":74,"canonicalName":"name"}]]]]],["functionDeclaration","",[{"type":"id","value":"r","text":"r","offset":81,"lineBreaks":0,"line":1,"col":82}],["mul",["mul",["parenExpr",{"type":"id","value":"s","text":"s","offset":87,"lineBreaks":0,"line":1,"col":88,"canonicalName":"s"}],["callExp",{"type":"id","value":"d","text":"d","offset":90,"lineBreaks":0,"line":1,"col":91},[["parenExpr",{"type":"id","value":"r","text":"r","offset":93,"lineBreaks":0,"line":1,"col":94,"canonicalName":"r"}]]]],{"type":"decimal","value":"60","text":"60","offset":97,"lineBreaks":0,"line":1,"col":98}]]]]]],["parenExpr",["mul",["parenExpr",["add",{"type":"decimal","value":"1","text":"1","offset":104,"lineBreaks":0,"line":1,"col":105},["parenExpr",{"type":"id","value":"mm.prod","text":"mm.prod","offset":107,"lineBreaks":0,"line":1,"col":108,"canonicalName":"mm.prod"}]]],["parenExpr",{"type":"id","value":"mp","text":"mp","offset":118,"lineBreaks":0,"line":1,"col":119,"canonicalName":"mp"}]]]]]],"name":"_oref"},"display":null},{"text":"_ironf = _oref(\"Iron plate\") // iron ore (items/min)","label":null,"prefix":null,"suffix":"iron ore (items/min)","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":450,"display":"450"},{"text":"_copperf = _oref(\"Copper plate\") // copper ore (items/min)","label":null,"prefix":null,"suffix":"copper ore (items/min)","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"_coalf = round(_s*military*2.5*60/_mp) // coal (items/min) — only military science consumes it (grenades), scaled by mining prod","label":null,"prefix":null,"suffix":"coal (items/min) — only military science consumes it (grenades), scaled by mining prod","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"_stonef = round(_s*military*10*60/_mp) // stone (items/min) — walls + stone brick, scaled by mining prod","label":null,"prefix":null,"suffix":"stone (items/min) — walls + stone brick, scaled by mining prod","section":"⚙️ Engine","hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# 🧪 Science @tab @skin(spec-sheet) @layout(table) @density(dense) @cols(Pack, Machines, Belts, MW)","label":null,"prefix":null,"suffix":null,"section":"🧪 Science","hero":false,"slider":null,"value":null,"display":null},{"text":"red science = _row(recipes[0]) // @label(🔴 Automation)","label":"🔴 Automation","prefix":null,"suffix":null,"section":"🧪 Science","hidden":false,"hero":false,"slider":null,"value":[4,1,2],"display":null},{"text":"green science = _row(recipes[1]) // @label(🟢 Logistic)","label":"🟢 Logistic","prefix":null,"suffix":null,"section":"🧪 Science","hidden":false,"hero":false,"slider":null,"value":[5,1,2],"display":null},{"text":"# 🔧 Assembly @tab @skin(spec-sheet) @layout(table) @density(dense) @cols(Item, Machines, Belts, MW)","label":null,"prefix":null,"suffix":null,"section":"🔧 Assembly","hero":false,"slider":null,"value":null,"display":null},{"text":"inserter = _row(recipes[2]) // @label(🦿 Inserter)","label":"🦿 Inserter","prefix":null,"suffix":null,"section":"🔧 Assembly","hidden":false,"hero":false,"slider":null,"value":[1,1,0],"display":null},{"text":"transport belt = _row(recipes[3]) // @label(🟨 Transport belt)","label":"🟨 Transport belt","prefix":null,"suffix":null,"section":"🔧 Assembly","hidden":false,"hero":false,"slider":null,"value":[1,1,0],"display":null},{"text":"gear wheel = _row(recipes[4]) // @label(⚙️ Iron gear)","label":"⚙️ Iron gear","prefix":null,"suffix":null,"section":"🔧 Assembly","hidden":false,"hero":false,"slider":null,"value":[1,1,0],"display":null},{"text":"green circuit = _row(recipes[5]) // @label(🟩 Green circuit)","label":"🟩 Green circuit","prefix":null,"suffix":null,"section":"🔧 Assembly","hidden":false,"hero":false,"slider":null,"value":[1,1,0],"display":null},{"text":"copper cable = _row(recipes[6]) // @label(🟫 Copper cable)","label":"🟫 Copper cable","prefix":null,"suffix":null,"section":"🔧 Assembly","hidden":false,"hero":false,"slider":null,"value":[1,1,0],"display":null},{"text":"# 🏭 Smelting @tab @skin(spec-sheet) @layout(table) @density(dense) @cols(Plate, Furnaces, Belts, MW)","label":null,"prefix":null,"suffix":null,"section":"🏭 Smelting","hero":false,"slider":null,"value":null,"display":null},{"text":"iron plate = _row(recipes[7]) // @label(⬜ Iron plate)","label":"⬜ Iron plate","prefix":null,"suffix":null,"section":"🏭 Smelting","hidden":false,"hero":false,"slider":null,"value":[12,1,2],"display":null},{"text":"copper plate = _row(recipes[8]) // @label(🟧 Copper plate)","label":"🟧 Copper plate","prefix":null,"suffix":null,"section":"🏭 Smelting","hidden":false,"hero":false,"slider":null,"value":[4,1,1],"display":null},{"text":"steel plate = _row(recipes[14]) // @label(◻️ Steel plate)","label":"◻️ Steel plate","prefix":null,"suffix":null,"section":"🏭 Smelting","hidden":false,"hero":false,"slider":null,"value":[0,0,0],"display":null},{"text":"stone brick = _row(recipes[15]) // @label(🧱 Stone brick)","label":"🧱 Stone brick","prefix":null,"suffix":null,"section":"🏭 Smelting","hidden":false,"hero":false,"slider":null,"value":[0,0,0],"display":null},{"text":"# 🛡️ Military @tab @skin(spec-sheet) @layout(table) @density(dense) @cols(Item, Machines, Belts, MW)","label":null,"prefix":null,"suffix":null,"section":"🛡️ Military","hero":false,"slider":null,"value":null,"display":null},{"text":"military science = _row(recipes[9]) // @label(⚪ Military science)","label":"⚪ Military science","prefix":null,"suffix":null,"section":"🛡️ Military","hidden":false,"hero":false,"slider":null,"value":[0,0,0],"display":null},{"text":"firearm magazine = _row(recipes[10]) // @label(🔫 Firearm magazine)","label":"🔫 Firearm magazine","prefix":null,"suffix":null,"section":"🛡️ Military","hidden":false,"hero":false,"slider":null,"value":[0,0,0],"display":null},{"text":"piercing rounds = _row(recipes[11]) // @label(🟡 Piercing rounds)","label":"🟡 Piercing rounds","prefix":null,"suffix":null,"section":"🛡️ Military","hidden":false,"hero":false,"slider":null,"value":[0,0,0],"display":null},{"text":"grenade = _row(recipes[12]) // @label(💣 Grenade)","label":"💣 Grenade","prefix":null,"suffix":null,"section":"🛡️ Military","hidden":false,"hero":false,"slider":null,"value":[0,0,0],"display":null},{"text":"wall = _row(recipes[13]) // @label(🧱 Wall)","label":"🧱 Wall","prefix":null,"suffix":null,"section":"🛡️ Military","hidden":false,"hero":false,"slider":null,"value":[0,0,0],"display":null},{"text":"# 📊 Summary @tab @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"📊 Summary","hero":false,"slider":null,"value":null,"display":null},{"text":"_sci = round(sum(map(filter(recipes, r => r.stage == \"Science\"), r => _pw(r)))) // science-stage power (MW)","label":null,"prefix":null,"suffix":"science-stage power (MW)","section":"📊 Summary","hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_asmb = round(sum(map(filter(recipes, r => r.stage == \"Assembly\"), r => _pw(r)))) // intermediate-assembly power (MW)","label":null,"prefix":null,"suffix":"intermediate-assembly power (MW)","section":"📊 Summary","hidden":true,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"_smelt = round(sum(map(filter(recipes, r => r.stage == \"Smelting\"), r => _pw(r)))) // smelting power (MW)","label":null,"prefix":null,"suffix":"smelting power (MW)","section":"📊 Summary","hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_mil = round(sum(map(filter(recipes, r => r.stage == \"Military\"), r => _pw(r)))) // military-line power (MW)","label":null,"prefix":null,"suffix":"military-line power (MW)","section":"📊 Summary","hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"machines = sum(map(recipes, r => _mach(r))) // @label(🏗️ Total machines)","label":"🏗️ Total machines","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"power = _sci + _asmb + _smelt + _mil // @label(⚡ Total power) @suffix( MW)","label":"⚡ Total power","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"where power goes = bars([_sci, _asmb, _smelt, _mil], [\"Science\", \"Assembly\", \"Smelting\", \"Military\"])","label":null,"prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"iron ore = _ironf // @label(⛏️ Iron ore) @suffix( /min)","label":"⛏️ Iron ore","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":450,"display":"450"},{"text":"copper ore = _copperf // @label(⛏️ Copper ore) @suffix( /min)","label":"⛏️ Copper ore","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"coal = _coalf // @label(⛏️ Coal) @suffix( /min) @note(military only)","label":"⛏️ Coal","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"stone = _stonef // @label(⛏️ Stone) @suffix( /min) @note(military only)","label":"⛏️ Stone","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"iron drills = ceil(_ironf/30) // @label(⛏️ Iron drills) @note(electric drill = 0.5 ore/s)","label":"⛏️ Iron drills","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"copper drills = ceil(_copperf/30) // @label(⛏️ Copper drills)","label":"⛏️ Copper drills","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"iron belts = round(_ironf/(60*bt.tp), 2) // @label(🟨 Iron ore belts) @note(at your belt tier)","label":"🟨 Iron ore belts","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"copper belts = round(_copperf/(60*bt.tp), 2) // @label(🟨 Copper ore belts)","label":"🟨 Copper ore belts","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":0.08,"display":"0.08"},{"text":"solar = ceil(power*24) // @label(☀️ Solar panels) @hero","label":"☀️ Solar panels","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":true,"slider":null,"value":192,"display":"192"},{"text":"accumulators = ceil(power*21) // @label(🔋 Accumulators) @note(to run the base through the night)","label":"🔋 Accumulators","prefix":null,"suffix":null,"section":"📊 Summary","hidden":false,"hero":false,"slider":null,"value":168,"display":"168"},{"text":"# 📈 Scaling @tab @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"📈 Scaling","hero":false,"slider":null,"value":null,"display":null},{"text":"power curve = plot(_pwr, 0, 600, 10, {ylabel: \"Power (MW)\", xlabel: \"Science / min\"})","label":null,"prefix":null,"suffix":null,"section":"📈 Scaling","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# 🔀 Flow @tab @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"🔀 Flow","hero":false,"slider":null,"value":null,"display":null},{"text":"material flow = sankey([{source: \"⛏️ Iron ore\", target: \"⬜ Iron plate\", value: _ironf}, {source: \"⛏️ Copper ore\", target: \"🟧 Copper plate\", value: _copperf}, {source: \"⬜ Iron plate\", target: \"🧪 Science\", value: _ironf}, {source: \"🟧 Copper plate\", target: \"🧪 Science\", value: _copperf}])","label":null,"prefix":null,"suffix":null,"section":"🔀 Flow","hidden":false,"hero":false,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# 🎯 Goal @tab @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"🎯 Goal","hero":false,"slider":null,"value":null,"display":null},{"text":"budget = 40 // 10..100 by 5 @suffix( MW) @label(⚡ Power budget)","label":"⚡ Power budget","prefix":null,"suffix":null,"section":"🎯 Goal","hidden":false,"hero":false,"slider":{"min":10,"max":100,"step":5},"value":40,"display":"40"},{"text":"power_fit = _psm(spm) // @label(≈ Power at this rate) @suffix( MW)","label":"≈ Power at this rate","prefix":null,"suffix":null,"section":"🎯 Goal","hidden":false,"hero":false,"slider":null,"value":7.154999999999999,"display":"7.155"}]},{"id":"game-factorio-ratios","title":"Factorio Production Ratios","description":"How many assemblers hit your target rate — and whether one belt can carry it.","category":"gaming","icon":"cog","tags":["gaming","factorio"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-25T21:02:51.171Z"},"rows":[{"text":"# Recipe (in-game values)","label":null,"prefix":null,"suffix":null,"section":"Recipe (in-game values)","hero":false,"slider":null,"value":null,"display":null},{"text":"recipe time = 0.5 // 0.1..30 by 0.1 @suffix(s) @note(displayed craft time @ speed 1)","label":null,"prefix":null,"suffix":null,"section":"Recipe (in-game values)","hidden":false,"hero":false,"slider":{"min":0.1,"max":30,"step":0.1},"value":0.5,"display":"0.5"},{"text":"output per craft = 1 // 1..10 @note(items made per cycle)","label":null,"prefix":null,"suffix":null,"section":"Recipe (in-game values)","hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":1,"display":"1"},{"text":"target rate = 30 // 1..200 by 5 @suffix(/s) @note(what you want to produce)","label":null,"prefix":null,"suffix":null,"section":"Recipe (in-game values)","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":5},"value":30,"display":"30"},{"text":"# Machine","label":null,"prefix":null,"suffix":null,"section":"Machine","hero":false,"slider":null,"value":null,"display":null},{"text":"crafting speed = 1.25 // dropdown({Assembler 1 (0.5): 0.5, Assembler 2 (0.75): 0.75, Assembler 3 (1.25): 1.25, Chemical plant (1.0): 1, Electric furnace (2.0): 2})","label":null,"prefix":null,"suffix":null,"section":"Machine","hidden":false,"hero":false,"slider":null,"value":1.25,"display":"1.25"},{"text":"speed modules = 0 // 0..8 @note(+50% speed each)","label":null,"prefix":null,"suffix":null,"section":"Machine","hidden":false,"hero":false,"slider":{"min":0,"max":8,"step":0.1},"value":0,"display":"0"},{"text":"_eff_speed = crafting_speed * (1 + speed_modules * 0.5) // @hidden","label":null,"prefix":null,"suffix":null,"section":"Machine","hidden":true,"hero":false,"slider":null,"value":1.25,"display":"1.25"},{"text":"# Per-machine output","label":null,"prefix":null,"suffix":null,"section":"Per-machine output","hero":false,"slider":null,"value":null,"display":null},{"text":"output per machine = output_per_craft * _eff_speed / recipe_time // @label(Output / machine) @suffix(/s)","label":"Output / machine","prefix":null,"suffix":null,"section":"Per-machine output","hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"machines needed = ceil(target_rate / output_per_machine) // @hero @label(Assemblers needed) @suffix(machines)","label":"Assemblers needed","prefix":null,"suffix":null,"section":"Per-machine output","hidden":false,"hero":true,"slider":null,"value":12,"display":"12"},{"text":"actual rate = machines_needed * output_per_machine // @label(Actual rate) @suffix(/s)","label":"Actual rate","prefix":null,"suffix":null,"section":"Per-machine output","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# Belt check","label":null,"prefix":null,"suffix":null,"section":"Belt check","hero":false,"slider":null,"value":null,"display":null},{"text":"belt throughput = 15 // dropdown({Yellow (15/s): 15, Red (30/s): 30, Blue (45/s): 45, Green (60/s): 60})","label":null,"prefix":null,"suffix":null,"section":"Belt check","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"belts required = ceil(actual_rate / belt_throughput) // @hero @label(Belts to carry it) @suffix(belts)","label":"Belts to carry it","prefix":null,"suffix":null,"section":"Belt check","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"},{"text":"belt utilization = 100 * actual_rate / (belts_required * belt_throughput) // @label(Belt utilization) @suffix(%)","label":"Belt utilization","prefix":null,"suffix":null,"section":"Belt check","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"}]},{"id":"game-factorio-table","title":"Factorio — Production Table","description":"One row per item, every metric in columns. The dense table — scroll → on mobile.","category":"gaming","icon":"cog","tags":["factorio","gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-26T02:03:04.381Z"},"rows":[{"text":"# Settings @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"rate = 90 // 30..240 by 30 @suffix(/s) @label(Target rate)","label":"Target rate","prefix":null,"suffix":null,"section":"Settings","hidden":false,"hero":false,"slider":{"min":30,"max":240,"step":30},"value":90,"display":"90"},{"text":"_mach(t) = rate*t -> 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0..200","label":null,"prefix":null,"suffix":"%","section":"Tune","hidden":false,"hero":false,"slider":{"min":0,"max":200,"step":1},"value":46.6,"display":"46.6"},{"text":"crit rate = 70 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Tune","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":70,"display":"70"},{"text":"crit dmg = 180 // % 0..400","label":null,"prefix":null,"suffix":"%","section":"Tune","hidden":false,"hero":false,"slider":{"min":0,"max":400,"step":1},"value":180,"display":"180"},{"text":"talent = 250 // % 50..400","label":null,"prefix":null,"suffix":"%","section":"Tune","hidden":false,"hero":false,"slider":{"min":50,"max":400,"step":1},"value":250,"display":"250"},{"text":"# Enemy @layout(form) @density(dense) @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"Enemy","hero":false,"slider":null,"value":null,"display":null},{"text":"character level = 90 // 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flat_atk // @hidden","label":null,"prefix":null,"suffix":null,"section":"Enemy","hidden":true,"hero":false,"slider":null,"value":1751,"display":"1,751"},{"text":"_base = _atk * (talent/100) * (1 + dmg_bonus/100) // @hidden","label":null,"prefix":null,"suffix":null,"section":"Enemy","hidden":true,"hero":false,"slider":null,"value":6417.415,"display":"6,417.42"},{"text":"_crit = 1 + (crit_rate/100) * (crit_dmg/100) // @hidden","label":null,"prefix":null,"suffix":null,"section":"Enemy","hidden":true,"hero":false,"slider":null,"value":2.26,"display":"2.26"},{"text":"_def = (character_level + 100) / ((character_level + 100) + (enemy_level + 100) * (1 - def_shred/100)) // @hidden","label":null,"prefix":null,"suffix":null,"section":"Enemy","hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_res = enemy_res < 0 ? 1 - (enemy_res/100)/2 : 1 - enemy_res/100 // @hidden","label":null,"prefix":null,"suffix":null,"section":"Enemy","hidden":true,"hero":false,"slider":null,"value":0.9,"display":"0.9"},{"text":"# Output @density(dense) @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"Output","hero":false,"slider":null,"value":null,"display":null},{"text":"average damage = _base * _crit * _def * _res * reaction // @hero @label(Average) @suffix()","label":"Average","prefix":null,"suffix":null,"section":"Output","hidden":false,"hero":true,"slider":null,"value":6526.511055,"display":"6,526.51"},{"text":"on crit = _base * (1 + crit_dmg/100) * _def * _res * reaction // @label(On crit) @suffix()","label":"On crit","prefix":null,"suffix":null,"section":"Output","hidden":false,"hero":false,"slider":null,"value":8085.9429,"display":"8,085.94"},{"text":"non crit = _base * _def * _res * reaction // @label(Non-crit) @suffix()","label":"Non-crit","prefix":null,"suffix":null,"section":"Output","hidden":false,"hero":false,"slider":null,"value":2887.83675,"display":"2,887.84"}]},{"id":"game-osrs-maxhit","title":"OSRS Melee Max Hit","description":"Effective strength → base max hit, the exact integer-floor formula from the wiki.","category":"gaming","icon":"sword","tags":["gaming","osrs","runescape"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-25T21:02:51.175Z"},"rows":[{"text":"# Levels & boosts","label":null,"prefix":null,"suffix":null,"section":"Levels & boosts","hero":false,"slider":null,"value":null,"display":null},{"text":"strength level = 99 // 1..99","label":null,"prefix":null,"suffix":null,"section":"Levels & boosts","hidden":false,"hero":false,"slider":{"min":1,"max":99,"step":1},"value":99,"display":"99"},{"text":"potion bonus = 19 // 0..28 @note(Super str = +19, flat add)","label":null,"prefix":null,"suffix":null,"section":"Levels & boosts","hidden":false,"hero":false,"slider":{"min":0,"max":28,"step":1},"value":19,"display":"19"},{"text":"_boosted = strength_level + potion_bonus // @hidden","label":null,"prefix":null,"suffix":null,"section":"Levels & boosts","hidden":true,"hero":false,"slider":null,"value":118,"display":"118"},{"text":"prayer = 1.23 // dropdown({None (1x): 1, Burst of Strength (1.05x): 1.05, Superhuman (1.1x): 1.1, Ultimate (1.15x): 1.15, Piety (1.23x): 1.23})","label":null,"prefix":null,"suffix":null,"section":"Levels & boosts","hidden":false,"hero":false,"slider":null,"value":1.23,"display":"1.23"},{"text":"attack style = 3 // dropdown({Aggressive (+3): 3, Controlled (+1): 1, Accurate/Defensive (+0): 0})","label":null,"prefix":null,"suffix":null,"section":"Levels & boosts","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Gear","label":null,"prefix":null,"suffix":null,"section":"Gear","hero":false,"slider":null,"value":null,"display":null},{"text":"strength bonus = 138 // 0..200 @note(Equipment tab: Melee Strength)","label":null,"prefix":null,"suffix":null,"section":"Gear","hidden":false,"hero":false,"slider":{"min":0,"max":200,"step":1},"value":138,"display":"138"},{"text":"# Calculation (each step floors)","label":null,"prefix":null,"suffix":null,"section":"Calculation (each step floors)","hero":false,"slider":null,"value":null,"display":null},{"text":"effective strength = floor(floor(_boosted * prayer) + attack_style + 8) // @label(Effective Strength)","label":"Effective Strength","prefix":null,"suffix":null,"section":"Calculation (each step floors)","hidden":false,"hero":false,"slider":null,"value":156,"display":"156"},{"text":"max hit = floor(0.5 + effective_strength * (strength_bonus + 64) / 640) // @hero @label(Max hit) @suffix(dmg)","label":"Max hit","prefix":null,"suffix":null,"section":"Calculation (each step floors)","hidden":false,"hero":true,"slider":null,"value":49,"display":"49"},{"text":"# Special-multiplier example","label":null,"prefix":null,"suffix":null,"section":"Special-multiplier example","hero":false,"slider":null,"value":null,"display":null},{"text":"gear multiplier = 1 // dropdown({None (1x): 1, Salve amulet (e) (1.2x): 1.2, Slayer helm (i) (1.1667x): 1.1667, Void melee (1.1x): 1.1)})","label":null,"prefix":null,"suffix":"})","section":"Special-multiplier example","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"max hit with set bonus = floor(max_hit * gear_multiplier) // @hero @label(With set bonus) @suffix(dmg)","label":"With set bonus","prefix":null,"suffix":null,"section":"Special-multiplier example","hidden":false,"hero":true,"slider":null,"value":49,"display":"49"}]},{"id":"game-poe-dps","title":"Path of Exile DPS","description":"The classic \"increased vs more\" distinction — additive vs multiplicative — drives every PoE build.","category":"gaming","icon":"zap","tags":["gaming","poe"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-25T21:02:51.175Z"},"rows":[{"text":"# Base hit","label":null,"prefix":null,"suffix":null,"section":"Base hit","hero":false,"slider":null,"value":null,"display":null},{"text":"average hit = 450 // 50..3000 by 10 @note(weapon + added damage)","label":null,"prefix":null,"suffix":null,"section":"Base hit","hidden":false,"hero":false,"slider":{"min":50,"max":3000,"step":10},"value":450,"display":"450"},{"text":"attack speed = 1.6 // 0.5..8 by 0.05 @suffix(/s)","label":null,"prefix":null,"suffix":null,"section":"Base hit","hidden":false,"hero":false,"slider":{"min":0.5,"max":8,"step":0.05},"value":1.6,"display":"1.6"},{"text":"hits per attack = 1 // 1..10 @note(projectiles / strikes)","label":null,"prefix":null,"suffix":null,"section":"Base hit","hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":1,"display":"1"},{"text":"# Crit","label":null,"prefix":null,"suffix":null,"section":"Crit","hero":false,"slider":null,"value":null,"display":null},{"text":"crit chance = 40 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Crit","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":40,"display":"40"},{"text":"crit multiplier = 250 // % 100..600","label":null,"prefix":null,"suffix":"%","section":"Crit","hidden":false,"hero":false,"slider":{"min":100,"max":600,"step":1},"value":250,"display":"250"},{"text":"_crit_avg = (1 - crit_chance/100) + (crit_chance/100) * (crit_multiplier/100) // @hidden","label":null,"prefix":null,"suffix":null,"section":"Crit","hidden":true,"hero":false,"slider":null,"value":1.6,"display":"1.6"},{"text":"# Accuracy","label":null,"prefix":null,"suffix":null,"section":"Accuracy","hero":false,"slider":null,"value":null,"display":null},{"text":"hit chance = 92 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Accuracy","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":92,"display":"92"},{"text":"# Scaling — the heart of PoE","label":null,"prefix":null,"suffix":null,"section":"Scaling — the heart of PoE","hero":false,"slider":null,"value":null,"display":null},{"text":"increased damage = 220 // % 0..600 @note(ALL increases add together)","label":null,"prefix":null,"suffix":"%","section":"Scaling — the heart of PoE","hidden":false,"hero":false,"slider":{"min":0,"max":600,"step":1},"value":220,"display":"220"},{"text":"more multiplier a = 39 // % 0..150 @note(each 'more' is separate)","label":null,"prefix":null,"suffix":"%","section":"Scaling — the heart of PoE","hidden":false,"hero":false,"slider":{"min":0,"max":150,"step":1},"value":39,"display":"39"},{"text":"more multiplier b = 25 // % 0..150","label":null,"prefix":null,"suffix":"%","section":"Scaling — the heart of PoE","hidden":false,"hero":false,"slider":{"min":0,"max":150,"step":1},"value":25,"display":"25"},{"text":"_inc = 1 + increased_damage/100 // @hidden","label":null,"prefix":null,"suffix":null,"section":"Scaling — the heart of PoE","hidden":true,"hero":false,"slider":null,"value":3.2,"display":"3.2"},{"text":"_more = (1 + more_multiplier_a/100) * (1 + more_multiplier_b/100) // @hidden","label":null,"prefix":null,"suffix":null,"section":"Scaling — the heart of PoE","hidden":true,"hero":false,"slider":null,"value":1.7375,"display":"1.738"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"damage per hit = average_hit * _inc * _more * _crit_avg * (hit_chance/100) // @label(Damage per hit)","label":"Damage per hit","prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":3682.944,"display":"3,682.94"},{"text":"dps = damage_per_hit * attack_speed * hits_per_attack // @hero @label(DPS) @suffix(/s)","label":"DPS","prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":5892.7104,"display":"5,892.71"},{"text":"# Why \"more\" wins","label":null,"prefix":null,"suffix":null,"section":"Why \"more\" wins","hero":false,"slider":null,"value":null,"display":null},{"text":"_inc_only = 1 + (increased_damage + more_multiplier_a + more_multiplier_b)/100 // @hidden","label":null,"prefix":null,"suffix":null,"section":"Why \"more\" wins","hidden":true,"hero":false,"slider":null,"value":3.84,"display":"3.84"},{"text":"if these were all 'increased' = average_hit * _inc_only * _crit_avg * (hit_chance/100) * attack_speed * hits_per_attack // @label(Same %, all additive) @suffix(/s)","label":"Same %, all additive","prefix":null,"suffix":null,"section":"Why \"more\" wins","hidden":false,"hero":false,"slider":null,"value":4069.7856,"display":"4,069.79"}]},{"id":"game-pokemon-damage","title":"Pokémon Damage Calculator","description":"Gen-9 single-target damage. STAB, type effectiveness, and crit fold into a min–max damage roll.","category":"gaming","icon":"swords","tags":["gaming","pokemon"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-25T21:02:51.175Z"},"rows":[{"text":"# Attacker & move","label":null,"prefix":null,"suffix":null,"section":"Attacker & move","hero":false,"slider":null,"value":null,"display":null},{"text":"level = 50 // 1..100","label":null,"prefix":null,"suffix":null,"section":"Attacker & move","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":50,"display":"50"},{"text":"base power = 90 // 10..250 by 5 @note(Flamethrower = 90)","label":null,"prefix":null,"suffix":null,"section":"Attacker & move","hidden":false,"hero":false,"slider":{"min":10,"max":250,"step":5},"value":90,"display":"90"},{"text":"attack = 152 // 1..650 @note(your Atk or Sp.Atk)","label":null,"prefix":null,"suffix":null,"section":"Attacker & move","hidden":false,"hero":false,"slider":{"min":1,"max":650,"step":1},"value":152,"display":"152"},{"text":"defense = 120 // 1..650 @note(foe Def or Sp.Def)","label":null,"prefix":null,"suffix":null,"section":"Attacker & move","hidden":false,"hero":false,"slider":{"min":1,"max":650,"step":1},"value":120,"display":"120"},{"text":"# Modifiers","label":null,"prefix":null,"suffix":null,"section":"Modifiers","hero":false,"slider":null,"value":null,"display":null},{"text":"stab = 1.5 // dropdown({Matches type (1.5x): 1.5, No STAB (1x): 1})","label":null,"prefix":null,"suffix":null,"section":"Modifiers","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"type effectiveness = 2 // dropdown({Immune (0x): 0, Quarter (0.25x): 0.25, Half (0.5x): 0.5, Neutral (1x): 1, Super (2x): 2, Double super (4x): 4})","label":null,"prefix":null,"suffix":null,"section":"Modifiers","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"critical hit = false // @label(Critical hit) toggle()","label":"Critical hit","prefix":null,"suffix":null,"section":"Modifiers","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"_crit = critical_hit ? 1.5 : 1 // @hidden","label":null,"prefix":null,"suffix":null,"section":"Modifiers","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Damage","label":null,"prefix":null,"suffix":null,"section":"Damage","hero":false,"slider":null,"value":null,"display":null},{"text":"_lvl = floor(2 * level / 5) + 2 // @hidden","label":null,"prefix":null,"suffix":null,"section":"Damage","hidden":true,"hero":false,"slider":null,"value":22,"display":"22"},{"text":"_base = floor(_lvl * base_power * attack / defense / 50) + 2 // @hidden","label":null,"prefix":null,"suffix":null,"section":"Damage","hidden":true,"hero":false,"slider":null,"value":52,"display":"52"},{"text":"_modifier = stab * type_effectiveness * _crit // @hidden","label":null,"prefix":null,"suffix":null,"section":"Damage","hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"min damage = floor(_base * _modifier * 0.85) // @hero @label(Min damage) @suffix(HP)","label":"Min damage","prefix":null,"suffix":null,"section":"Damage","hidden":false,"hero":true,"slider":null,"value":132,"display":"132"},{"text":"max damage = floor(_base * _modifier) // @hero @label(Max damage) @suffix(HP)","label":"Max damage","prefix":null,"suffix":null,"section":"Damage","hidden":false,"hero":true,"slider":null,"value":156,"display":"156"}]},{"id":"game-rpg-loadout","title":"RPG — Damage Loadout","description":"Equip gear from dropdowns, toggle buffs, watch your DPS update. Each item is a stat bundle.","category":"gaming","icon":"swords","tags":["rpg","gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-26T02:59:22.909Z"},"rows":[{"text":"# ⚔️ Loadout @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"⚔️ Loadout","hero":false,"slider":null,"value":null,"display":null},{"text":"weapon = {atk: 50, crit: 8, spd: 1.4} // dropdown({Iron Sword: {atk: 50, crit: 8, spd: 1.4}, Steel Greatsword: {atk: 95, crit: 5, spd: 0.9}, Twin Daggers: {atk: 34, crit: 22, spd: 2.6}}) @label(🗡️ Weapon)","label":"🗡️ Weapon","prefix":null,"suffix":null,"section":"⚔️ Loadout","hidden":false,"hero":false,"slider":null,"value":{"atk":50,"crit":8,"spd":1.4},"display":null},{"text":"ring = {atk: 0, crit: 12} // dropdown({None: {atk: 0, crit: 0}, Ring of Power: {atk: 18, crit: 0}, Ring of Fortune: {atk: 0, crit: 12}}) @label(💍 Ring)","label":"💍 Ring","prefix":null,"suffix":null,"section":"⚔️ Loadout","hidden":false,"hero":false,"slider":null,"value":{"atk":0,"crit":12},"display":null},{"text":"berserk = false // toggle() @label(🔥 Berserk (+50% atk, −15% crit))","label":"🔥 Berserk (+50% atk, −15% crit)","prefix":null,"suffix":null,"section":"⚔️ Loadout","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"sharpen = false // toggle() @label(🪙 Whetstone (+10 atk))","label":"🪙 Whetstone (+10 atk)","prefix":null,"suffix":null,"section":"⚔️ Loadout","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"# 📊 Damage @skin(spec-sheet)","label":null,"prefix":null,"suffix":null,"section":"📊 Damage","hero":false,"slider":null,"value":null,"display":null},{"text":"_atk = (weapon.atk + ring.atk + sharpen*10) * (1 + berserk*0.5) // total attack after gear + buffs","label":null,"prefix":null,"suffix":"total attack after gear + buffs","section":"📊 Damage","hidden":true,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"_crit = weapon.crit + ring.crit - berserk*15 // crit chance after gear + berserk penalty","label":null,"prefix":null,"suffix":"crit chance after gear + berserk penalty","section":"📊 Damage","hidden":true,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"attack = _atk -> round // @label(⚔️ Attack power)","label":"⚔️ Attack power","prefix":null,"suffix":null,"section":"📊 Damage","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"crit chance = _crit // @label(🎯 Crit chance) @suffix(%)","label":"🎯 Crit chance","prefix":null,"suffix":null,"section":"📊 Damage","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"hits per sec = weapon.spd // @label(⚡ Attack speed) @suffix(/s)","label":"⚡ Attack speed","prefix":null,"suffix":null,"section":"📊 Damage","hidden":false,"hero":false,"slider":null,"value":1.4,"display":"1.4"},{"text":"dps = _atk * (1 + _crit/100) * weapon.spd -> round // @label(💥 Effective DPS) @hero","label":"💥 Effective DPS","prefix":null,"suffix":null,"section":"📊 Damage","hidden":false,"hero":true,"slider":null,"value":84,"display":"84"}]},{"id":"garden-path-paver-count","title":"Garden Path Paver Count","description":"Calculate pavers needed for a path, including joint width.","category":"construction","icon":"layout","tags":["construction","garden"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"path_length_meters = 15 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"path_width_meters = 0.9 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.9,"display":"0.9"},{"text":"paver_length_cm = 30 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"paver_width_cm = 30 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"joint_width_mm = 5 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"effective_paver_length_m = (paver_length_cm + joint_width_mm / 10) / 100 // m","label":null,"prefix":null,"suffix":"m","section":null,"hidden":false,"hero":false,"slider":null,"value":0.305,"display":"0.305"},{"text":"effective_paver_width_m = (paver_width_cm + joint_width_mm / 10) / 100 // m","label":null,"prefix":null,"suffix":"m","section":null,"hidden":false,"hero":false,"slider":null,"value":0.305,"display":"0.305"},{"text":"total_pavers_needed = ceil((path_length_meters / effective_paver_length_m) * (path_width_meters / effective_paver_width_m)) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":146,"display":"146"}]},{"id":"gas-cost","title":"Gas Cost","description":"Calculate fuel cost for a road trip.","category":"everyday","icon":"fuel","tags":["gas","fuel"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Trip Details","label":null,"prefix":null,"suffix":null,"section":"Trip Details","hero":false,"slider":null,"value":null,"display":null},{"text":"trip distance = 350 // miles 10..5k by 10","label":null,"prefix":null,"suffix":"miles","section":"Trip Details","hidden":false,"hero":false,"slider":{"min":10,"max":5000,"step":10},"value":350,"display":"350"},{"text":"fuel economy = 28 // mpg 10..60","label":null,"prefix":null,"suffix":"mpg","section":"Trip Details","hidden":false,"hero":false,"slider":{"min":10,"max":60,"step":1},"value":28,"display":"28"},{"text":"gas price = $3.89 // /gal 1..8","label":null,"prefix":"$","suffix":"gal","section":"Trip Details","hidden":false,"hero":false,"slider":{"min":1,"max":8,"step":0.1},"value":3.89,"display":"$3.89"},{"text":"# Fuel Needed","label":null,"prefix":null,"suffix":null,"section":"Fuel Needed","hero":false,"slider":null,"value":null,"display":null},{"text":"gallons needed = round(trip distance / fuel economy * 10) / 10","label":null,"prefix":null,"suffix":null,"section":"Fuel Needed","hidden":false,"hero":false,"slider":null,"value":12.5,"display":"12.5"},{"text":"$total gas cost = round(gallons needed * gas price * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Fuel Needed","hidden":false,"hero":true,"slider":null,"value":48.63,"display":"$48.63"},{"text":"$cost per mile = round(gas price / fuel economy * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Fuel Needed","hidden":false,"hero":false,"slider":null,"value":0.14,"display":"$0.14"},{"text":"# Round Trip","label":null,"prefix":null,"suffix":null,"section":"Round Trip","hero":false,"slider":null,"value":null,"display":null},{"text":"roundtrip_distance = trip distance * 2 // miles","label":null,"prefix":null,"suffix":"miles","section":"Round Trip","hidden":false,"hero":false,"slider":null,"value":700,"display":"700"},{"text":"roundtrip_gallons = round(roundtrip_distance / fuel economy * 10) / 10","label":null,"prefix":null,"suffix":null,"section":"Round Trip","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"$roundtrip_cost = round(roundtrip_gallons * gas price * 100) / 100 // @label(Round Trip Gas Cost)","label":"Round Trip Gas Cost","prefix":"$","suffix":null,"section":"Round Trip","hidden":false,"hero":false,"slider":null,"value":97.25,"display":"$97.25"}]},{"id":"gas-pressure-altitude-correction","title":"Gas Pressure Altitude Correction","description":"Calculate atmospheric pressure at altitude using the barometric formula.","category":"education","icon":"book-open","tags":["gas","altitude"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"pressure_sea_level = 1013.25 // hPa","label":null,"prefix":null,"suffix":"hPa","section":null,"hidden":false,"hero":false,"slider":null,"value":1013.25,"display":"1,013.25"},{"text":"altitude = 1000 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"_scale_height = 8500 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":true,"hero":false,"slider":null,"value":8500,"display":"8,500"},{"text":"pressure_at_altitude = pressure_sea_level * exp(-altitude / scale_height) // hPa @hero","label":null,"prefix":null,"suffix":"hPa","section":null,"hidden":false,"hero":true,"slider":null,"value":900.7891447943624,"display":"900.79"}]},{"id":"gay-lussacs-law-pressure-temperature","title":"Gay Lussacs Law Pressure Temperature","description":"Calculate final gas pressure after a temperature change at constant volume.","category":"education","icon":"book-open","tags":["temperature"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"pressure_initial = 100 // kPa","label":null,"prefix":null,"suffix":"kPa","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"temperature_initial_celsius = 20 // Celsius","label":null,"prefix":null,"suffix":"Celsius","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"temperature_final_celsius = 80 // Celsius","label":null,"prefix":null,"suffix":"Celsius","section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"_t1_kelvin = temperature_initial_celsius + 273.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":293.15,"display":"293.15"},{"text":"_t2_kelvin = temperature_final_celsius + 273.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":353.15,"display":"353.15"},{"text":"pressure_final = pressure_initial * (t2_kelvin / t1_kelvin) // kPa @hero","label":null,"prefix":null,"suffix":"kPa","section":null,"hidden":false,"hero":true,"slider":null,"value":120.46733754050827,"display":"120.47"}]},{"id":"gcd-greatest-common-divisor","title":"GCD (Greatest Common Divisor)","description":"Find the greatest common divisor of two 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@label(GCD)","label":"GCD","prefix":null,"suffix":null,"section":"GCD","hidden":false,"hero":true,"slider":null,"value":6,"display":"6"}]},{"id":"gdpr-data-breach-fine-estimator","title":"GDPR Fine Estimator","description":"Estimate hypothetical GDPR fines based on company revenue.","category":"other","icon":"shield-alert","tags":["breach"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"annualRevenue = 100000000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000000,"display":"100,000,000"},{"text":"severityFactor = 2 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"estimatedFine = annualRevenue * (severityFactor / 100) // @prefix($) 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1500","label":null,"prefix":null,"suffix":null,"section":"Game Result","hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"opponent rd = 30","label":null,"prefix":null,"suffix":null,"section":"Game Result","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"outcome = 1 // win","label":null,"prefix":null,"suffix":"win","section":"Game Result","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Simplified Step","label":null,"prefix":null,"suffix":null,"section":"Simplified Step","hero":false,"slider":null,"value":null,"display":null},{"text":"_g = 1 / sqrt(1 + 3 * (opponent rd / pi)^2)","label":null,"prefix":null,"suffix":null,"section":"Simplified Step","hidden":true,"hero":false,"slider":null,"value":0.0603497778616256,"display":"0.0603"},{"text":"_e = 1 / (1 + exp(-g * (rating - opponent rating)))","label":null,"prefix":null,"suffix":null,"section":"Simplified 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10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"glide_ratio = distance_traveled_feet / altitude_lost_feet // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"global-time-zone-offset","title":"Global Time Zone Offset","description":"Convert UTC time to local time using a timezone offset.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"current_hour_utc = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"offset_hours = -5 // EST","label":null,"prefix":null,"suffix":"EST","section":null,"hidden":false,"hero":false,"slider":null,"value":-5,"display":"-5"},{"text":"local_hour = mod(current_hour_utc + 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100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"average_daily_yield_quarts = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"total_yield_gallons = (number_of_goats * average_daily_yield_quarts * days_in_lactation) / 4 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"}]},{"id":"gold-gain-multiplier","title":"Gold Gain Multiplier","description":"Calculate total gold gain with bonuses.","category":"math","icon":"dollar-sign","tags":["gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Gold Settings","label":null,"prefix":null,"suffix":null,"section":"Gold Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base gold = 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width into main content and sidebar using the golden ratio.","category":"design","icon":"palette","tags":["layout"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"total_width = 1200 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"phi = 1.618","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.618,"display":"1.618"},{"text":"main_content_width = total_width / phi // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":741.6563658838072,"display":"741.66"},{"text":"sidebar_width = total_width - main_content_width // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":458.3436341161928,"display":"458.34"}]},{"id":"golden-ratio","title":"Golden Ratio","description":"Compute φ, Fibonacci ratios, and compare against the rule of thirds.","category":"design","icon":"function","tags":["math","design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# The Number","label":null,"prefix":null,"suffix":null,"section":"The Number","hero":false,"slider":null,"value":null,"display":null},{"text":"phi = (1 + sqrt(5)) / 2 // @hero @label(φ = (1+√5)/2)","label":"φ = (1+√5)/2","prefix":null,"suffix":null,"section":"The Number","hidden":false,"hero":true,"slider":null,"value":1.618033988749895,"display":"1.618"},{"text":"one over phi = 1 / phi // @label(1/φ (≈ 0.618))","label":"1/φ (≈ 0.618)","prefix":null,"suffix":null,"section":"The Number","hidden":false,"hero":false,"slider":null,"value":0.6180339887498948,"display":"0.618"},{"text":"phi squared = phi^2 // @label(φ² (≈ 2.618))","label":"φ² (≈ 2.618)","prefix":null,"suffix":null,"section":"The Number","hidden":false,"hero":false,"slider":null,"value":2.618033988749895,"display":"2.618"},{"text":"# Fibonacci Approximation","label":null,"prefix":null,"suffix":null,"section":"Fibonacci Approximation","hero":false,"slider":null,"value":null,"display":null},{"text":"fib n minus 1 = 89 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":89,"display":"89"},{"text":"fib n = 144 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":144,"display":"144"},{"text":"ratio = fib n / fib n minus 1 // @label(Fib ratio (144/89))","label":"Fib ratio (144/89)","prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":null,"value":1.6179775280898876,"display":"1.618"},{"text":"error from phi = round((ratio - phi) * 1000000) / 1000000 // @label(Error vs φ)","label":"Error vs φ","prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":null,"value":-0.000056,"display":"-0.000056"},{"text":"# Rule of Thirds vs Golden Section","label":null,"prefix":null,"suffix":null,"section":"Rule of Thirds vs Golden Section","hero":false,"slider":null,"value":null,"display":null},{"text":"thirds split = 1 / 3 // @label(Rule of thirds (1/3 ≈ 0.333))","label":"Rule of thirds (1/3 ≈ 0.333)","prefix":null,"suffix":null,"section":"Rule of Thirds vs Golden Section","hidden":false,"hero":false,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"golden split = 1 / phi^2 // @label(Golden section (1/φ² ≈ 0.382))","label":"Golden section (1/φ² ≈ 0.382)","prefix":null,"suffix":null,"section":"Rule of Thirds vs Golden Section","hidden":false,"hero":false,"slider":null,"value":0.38196601125010515,"display":"0.382"},{"text":"percent difference = round(abs(thirds split - golden split) / golden split * 100, 1) // % @label(Rule-of-thirds error vs golden section)","label":"Rule-of-thirds error vs golden section","prefix":null,"suffix":"%","section":"Rule of Thirds vs Golden Section","hidden":false,"hero":false,"slider":null,"value":12.7,"display":"12.7"}]},{"id":"golf-handicap-differential","title":"Golf Handicap Differential","description":"Calculate golf handicap differential for a round.","category":"health","icon":"activity","tags":["sports"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Round Settings","label":null,"prefix":null,"suffix":null,"section":"Round Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"score = 85","label":null,"prefix":null,"suffix":null,"section":"Round Settings","hidden":false,"hero":false,"slider":null,"value":85,"display":"85"},{"text":"course rating = 72.0","label":null,"prefix":null,"suffix":null,"section":"Round Settings","hidden":false,"hero":false,"slider":null,"value":72,"display":"72"},{"text":"slope rating = 113","label":null,"prefix":null,"suffix":null,"section":"Round Settings","hidden":false,"hero":false,"slider":null,"value":113,"display":"113"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"handicap differential = (score - course rating) * (113 / slope rating)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":13,"display":"13"}]},{"id":"golf-handicap-index-simple","title":"Golf Handicap Index Simple","description":"Calculate a golf score differential from your score, course rating, and 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(113 / course slope)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":13.8,"display":"13.8"},{"text":"# Note: Real handicap uses average of best 8 of 20 differentials","label":null,"prefix":null,"suffix":null,"section":"Note: Real handicap uses average of best 8 of 20 differentials","hero":false,"slider":null,"value":null,"display":null}]},{"id":"gpa-calculator","title":"GPA Calculator","description":"Calculate your GPA from individual course grades and credits.","category":"education","icon":"graduation-cap","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.438Z"},"rows":[{"text":"# Course 1","label":null,"prefix":null,"suffix":null,"section":"Course 1","hero":false,"slider":null,"value":null,"display":null},{"text":"course1_credits = 3 // 1..6","label":null,"prefix":null,"suffix":null,"section":"Course 1","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":3,"display":"3"},{"text":"course1_grade = 3.7 // 0..4 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Course 1","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.1},"value":3.7,"display":"3.7"},{"text":"# Course 2","label":null,"prefix":null,"suffix":null,"section":"Course 2","hero":false,"slider":null,"value":null,"display":null},{"text":"course2_credits = 4 // 1..6","label":null,"prefix":null,"suffix":null,"section":"Course 2","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":4,"display":"4"},{"text":"course2_grade = 3.3 // 0..4 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Course 2","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.1},"value":3.3,"display":"3.3"},{"text":"# Course 3","label":null,"prefix":null,"suffix":null,"section":"Course 3","hero":false,"slider":null,"value":null,"display":null},{"text":"course3_credits = 3 // 1..6","label":null,"prefix":null,"suffix":null,"section":"Course 3","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":3,"display":"3"},{"text":"course3_grade = 4.0 // 0..4 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Course 3","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.1},"value":4,"display":"4"},{"text":"# Course 4","label":null,"prefix":null,"suffix":null,"section":"Course 4","hero":false,"slider":null,"value":null,"display":null},{"text":"course4_credits = 3 // 1..6","label":null,"prefix":null,"suffix":null,"section":"Course 4","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":3,"display":"3"},{"text":"course4_grade = 2.7 // 0..4 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Course 4","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.1},"value":2.7,"display":"2.7"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"total_credits = course1_credits + course2_credits + course3_credits + course4_credits","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":13,"display":"13"},{"text":"total_grade_points = course1_credits * course1_grade + course2_credits * course2_grade + course3_credits * course3_grade + course4_credits * course4_grade","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":44.4,"display":"44.4"},{"text":"gpa = round(total_grade_points / total_credits * 100) / 100","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":true,"slider":null,"value":3.42,"display":"3.42"}]},{"id":"grade-calculator","title":"Grade Calculator","description":"Find what score you need on the final to hit your target 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Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"coursework_weight = 100 - final_weight","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"coursework_contribution = current_grade * (coursework_weight / 100)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":59.5,"display":"59.5"},{"text":"needed_from_final = target_grade - coursework_contribution","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":30.5,"display":"30.5"},{"text":"needed_final_score = round(needed_from_final / (final_weight / 100) * 10) / 10 // %","label":null,"prefix":null,"suffix":"%","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":101.7,"display":"101.7"}]},{"id":"grass-seed-coverage","title":"Grass Seed Coverage","description":"Calculate weight of grass seed needed for your lawn area.","category":"everyday","icon":"sprout","tags":["garden","seed"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"area_square_meters = 250 // square meters","label":null,"prefix":null,"suffix":"square meters","section":null,"hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"seed_rate_grams_per_square_meter = 35 // grams","label":null,"prefix":null,"suffix":"grams","section":null,"hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"total_seed_needed_kg = (area_square_meters * seed_rate_grams_per_square_meter) / 1000 // kg @hero","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":true,"slider":null,"value":8.75,"display":"8.75"}]},{"id":"gravel-weight-calculator","title":"Gravel Weight Calculator","description":"Calculate gravel weight in tons and truck loads from cubic yards.","category":"health","icon":"activity","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Gravel Volume","label":null,"prefix":null,"suffix":null,"section":"Gravel Volume","hero":false,"slider":null,"value":null,"display":null},{"text":"volume cubic yards = 5 // 0.5..100 by 0.5","label":null,"prefix":null,"suffix":null,"section":"Gravel Volume","hidden":false,"hero":false,"slider":{"min":0.5,"max":100,"step":0.5},"value":5,"display":"5"},{"text":"# Weight Calculations","label":null,"prefix":null,"suffix":null,"section":"Weight Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"# Average density is approx 2800 lbs per cubic yard","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hero":false,"slider":null,"value":null,"display":null},{"text":"pounds per cubic yard = 2800 // 2.4k..3.2k","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hidden":false,"hero":false,"slider":{"min":2400,"max":3200,"step":1},"value":2800,"display":"2,800"},{"text":"_total_weight_pounds = volume cubic yards * pounds per cubic yard","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hidden":true,"hero":false,"slider":null,"value":14000,"display":"14,000"},{"text":"total weight tons = round(total_weight_pounds / 2000, 2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hidden":false,"hero":true,"slider":null,"value":7,"display":"7"},{"text":"# Delivery","label":null,"prefix":null,"suffix":null,"section":"Delivery","hero":false,"slider":null,"value":null,"display":null},{"text":"# Typical small dump truck capacity is 5 tons","label":null,"prefix":null,"suffix":null,"section":"Typical small dump truck capacity is 5 tons","hero":false,"slider":null,"value":null,"display":null},{"text":"truck loads = roundup(total weight tons / 5)","label":null,"prefix":null,"suffix":null,"section":"Typical small dump truck capacity is 5 tons","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"}]},{"id":"gravitational-potential-energy-orbital","title":"Gravitational Potential Energy Orbital","description":"Calculate gravitational potential energy of an object in orbit.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"mass_object = 100 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"mass_planet = 5.972e24 // kg (Earth)","label":null,"prefix":null,"suffix":"kg (Earth)","section":null,"hidden":false,"hero":false,"slider":null,"value":5.972e+24,"display":"5.972e24"},{"text":"radius_orbit = 6771000 // meters (LEO)","label":null,"prefix":null,"suffix":"meters (LEO)","section":null,"hidden":false,"hero":false,"slider":null,"value":6771000,"display":"6,771,000"},{"text":"_G = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"potential_energy = -G * mass_planet * mass_object / radius_orbit // Joules @hero","label":null,"prefix":null,"suffix":"Joules","section":null,"hidden":false,"hero":true,"slider":null,"value":-5886446315.167628,"display":"-5,886,446,315.17"}]},{"id":"great-circle-distance-advanced","title":"Great Circle Distance Advanced","description":"Calculate great-circle distance between two coordinates using the haversine formula.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"radius_of_earth_kilometers = 6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"lat1_degrees = 40.71","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40.71,"display":"40.71"},{"text":"lon1_degrees = -74.00","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-74,"display":"-74"},{"text":"lat2_degrees = 34.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":34.05,"display":"34.05"},{"text":"lon2_degrees = -118.24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-118.24,"display":"-118.24"},{"text":"dlat = lat2_degrees - lat1_degrees","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-6.66,"display":"-6.66"},{"text":"dlon = lon2_degrees - lon1_degrees","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-44.24,"display":"-44.24"},{"text":"a = (sin(dlat/2))^2 + cos(lat1_degrees) * cos(lat2_degrees) * (sin(dlon/2))^2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.09242515272053431,"display":"0.0924"},{"text":"c = 2 * atan2(sqrt(a), sqrt(1-a)) * pi / 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.6178087507443442,"display":"0.6178"},{"text":"distance_kilometers = radius_of_earth_kilometers * c // kilometers @hero","label":null,"prefix":null,"suffix":"kilometers","section":null,"hidden":false,"hero":true,"slider":null,"value":3936.059550992217,"display":"3,936.0596"}]},{"id":"great-circle-distance-haversine","title":"Great Circle Distance Haversine","description":"Calculate great-circle distance between two latitude/longitude points.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"lat1 = 40.7128","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40.7128,"display":"40.71"},{"text":"lon1 = -74.0060","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-74.006,"display":"-74.01"},{"text":"lat2 = 34.0522","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":34.0522,"display":"34.05"},{"text":"lon2 = -118.2437","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-118.2437,"display":"-118.24"},{"text":"r = 6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"dlat = lat2 - lat1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-6.6606,"display":"-6.661"},{"text":"dlon = lon2 - lon1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-44.2377,"display":"-44.24"},{"text":"a = sin(dlat / 2)**2 + cos(lat1) * cos(lat2) * sin(dlon / 2)**2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.09241091078348553,"display":"0.0924"},{"text":"c = 2 * atan2(a**0.5, (1 - a)**0.5) * pi / 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.6177595753586126,"display":"0.6178"},{"text":"distance = r * c","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3935.746254609721,"display":"3,935.7463"}]},{"id":"greenhouse-ventilation-requirement","title":"Greenhouse Ventilation","description":"Calculate required airflow for greenhouse cooling.","category":"engineering","icon":"fan","tags":["engineering","garden"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"greenhouse_volume_cubic_meters = 100 // m3","label":null,"prefix":null,"suffix":"m3","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"target_air_changes_per_hour = 60 // 1 per minute during summer","label":null,"prefix":null,"suffix":"1 per minute during summer","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"required_airflow_cubic_meters_per_minute = greenhouse_volume_cubic_meters * target_air_changes_per_hour / 60 // m3/min @hero","label":null,"prefix":null,"suffix":"m3/min","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"greywater-recycling-potential","title":"Greywater Recycling Potential","description":"Calculate how much greywater you can reuse daily.","category":"everyday","icon":"droplet","tags":["eco","water"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"daily_shower_liters = 60 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"daily_laundry_liters = 20 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"recyclable_fraction = 70 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"daily_greywater_available_liters = (daily_shower_liters + daily_laundry_liters) * (recyclable_fraction / 100) // liters @hero","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":56,"display":"56"}]},{"id":"grid-calculator","title":"Grid Calculator","description":"Calculate CSS grid column widths from container and gap.","category":"design","icon":"grid","tags":["layout"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Container","label":null,"prefix":null,"suffix":null,"section":"Container","hero":false,"slider":null,"value":null,"display":null},{"text":"container width = 1200 // px 320..2560 by 10","label":null,"prefix":null,"suffix":"px","section":"Container","hidden":false,"hero":false,"slider":{"min":320,"max":2560,"step":10},"value":1200,"display":"1,200"},{"text":"columns = 12 // 1..24","label":null,"prefix":null,"suffix":null,"section":"Container","hidden":false,"hero":false,"slider":{"min":1,"max":24,"step":1},"value":12,"display":"12"},{"text":"gap = 24 // px 0..80 by 2","label":null,"prefix":null,"suffix":"px","section":"Container","hidden":false,"hero":false,"slider":{"min":0,"max":80,"step":2},"value":24,"display":"24"},{"text":"# Grid Calculations","label":null,"prefix":null,"suffix":null,"section":"Grid Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"total gap space = gap * (columns - 1) // px","label":null,"prefix":null,"suffix":"px","section":"Grid Calculations","hidden":false,"hero":false,"slider":null,"value":264,"display":"264"},{"text":"column width = round((container width - total gap space) / columns * 100) / 100 // px @hero","label":null,"prefix":null,"suffix":"px","section":"Grid Calculations","hidden":false,"hero":true,"slider":null,"value":78,"display":"78"},{"text":"# Span Widths","label":null,"prefix":null,"suffix":null,"section":"Span Widths","hero":false,"slider":null,"value":null,"display":null},{"text":"span 2 = round((column width * 2 + gap * 1) * 100) / 100 // px @label(2-column span)","label":"2-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"span 3 = round((column width * 3 + gap * 2) * 100) / 100 // px @label(3-column span)","label":"3-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":282,"display":"282"},{"text":"span 4 = round((column width * 4 + gap * 3) * 100) / 100 // px @label(4-column span)","label":"4-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":384,"display":"384"},{"text":"span 6 = round((column width * 6 + gap * 5) * 100) / 100 // px @label(6-column span)","label":"6-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":588,"display":"588"},{"text":"# Percentages","label":null,"prefix":null,"suffix":null,"section":"Percentages","hero":false,"slider":null,"value":null,"display":null},{"text":"col width pct = round((column width / container width) * 100 * 100) / 100 // % @label(Column width %)","label":"Column width %","prefix":null,"suffix":"%","section":"Percentages","hidden":false,"hero":false,"slider":null,"value":6.5,"display":"6.5"},{"text":"gap pct = round((total gap space / container width) * 100 * 100) / 100 // % @label(Total gap %)","label":"Total gap %","prefix":null,"suffix":"%","section":"Percentages","hidden":false,"hero":false,"slider":null,"value":22,"display":"22"}]},{"id":"grit-score-estimator","title":"Grit Score Estimator","description":"Estimate a grit score from perseverance and passion ratings.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"perseverance_score = 4.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4.5,"display":"4.5"},{"text":"passion_score = 4.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"grit_score = (perseverance_score + passion_score) / 2 // score 1-5 @hero","label":null,"prefix":null,"suffix":"score 1-5","section":null,"hidden":false,"hero":true,"slider":null,"value":4.25,"display":"4.25"}]},{"id":"gross-rent-multiplier","title":"Gross Rent Multiplier","description":"Quick valuation tool for comparing rental properties in an area.","category":"real-estate","icon":"ratio","tags":["rent"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"propertyPrice = 350000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":350000,"display":"350,000"},{"text":"grossAnnualRent = 42000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":42000,"display":"42,000"},{"text":"grm = propertyPrice / grossAnnualRent // ratio @hero","label":null,"prefix":null,"suffix":"ratio","section":null,"hidden":false,"hero":true,"slider":null,"value":8.333333333333334,"display":"8.333"}]},{"id":"groupthink-risk-indicator","title":"Groupthink Risk Indicator","description":"Estimate groupthink risk from group size, homogeneity, and isolation 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Sheet (Model / Qty / Price) and totals it. 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Live `import()` resolves in the interactive editor (Calc/Present), not a baked gallery snapshot.","category":"business","icon":"table","tags":["demo"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-28T04:41:58.382Z"},"rows":[{"text":"items = import(\"https://docs.google.com/spreadsheets/d/1qd-x1DIDHYXLGV8wpvWTAYoemvFPDm7bYdNRoo37t_8/export?format=csv\") // @hidden","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"line items = sum(map(items, r => 1)) // @label(Line items)","label":"Line items","prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"total quantity = sum(map(items, r => r.Qty)) // @label(Total quantity)","label":"Total quantity","prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true},{"text":"$total value = sum(map(items, r => r.Qty * r.Price)) // @hero @label(Total order value) @prefix($)","label":"Total order value","prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":null,"display":null,"loading":true},{"text":"$average unit price = total_quantity > 0 ? total_value / total_quantity : 0 // @label(Avg unit price) @prefix($)","label":"Avg unit price","prefix":"$","suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"$0.00"},{"text":"$most expensive = max(map(items, r => r.Price)) // @label(Priciest item) @prefix($)","label":"Priciest item","prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":null,"display":null,"loading":true}]},{"id":"guild-contribution-point-ratio","title":"Guild Contribution Point Ratio","description":"Calculate contribution points earned from 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L/s","label":null,"prefix":null,"suffix":"L/s","section":null,"hidden":false,"hero":false,"slider":null,"value":2.7777777777777777,"display":"2.778"},{"text":"gutter_slope_percent = 0.5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"required_gutter_cross_section_sq_cm = (total_flow_liters_per_second * 10) / (gutter_slope_percent^0.5) // sq cm @hero","label":null,"prefix":null,"suffix":"sq cm","section":null,"hidden":false,"hero":true,"slider":null,"value":39.2837100659193,"display":"39.28"}]},{"id":"habit-cue-reward-timing","title":"Habit Cue Reward Timing","description":"Calculate habit reinforcement strength based on cue-to-reward delay.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"cue_time_seconds = 0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"reward_delay_seconds = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"reinforcement_strength = 1 / (1 + reward_delay_seconds) // strength factor @hero","label":null,"prefix":null,"suffix":"strength factor","section":null,"hidden":false,"hero":true,"slider":null,"value":0.03225806451612903,"display":"0.0323"}]},{"id":"habit-streak-projected-milestones","title":"Habit Streak Projected Milestones","description":"Calculate days remaining to reach a habit streak milestone.","category":"productivity","icon":"clock","tags":["streak"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"current_streak_days = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"target_milestone_days = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"days_remaining = target_milestone_days - current_streak_days // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":85,"display":"85"},{"text":"weeks_to_milestone = days_remaining / 7 // weeks @hero","label":null,"prefix":null,"suffix":"weeks","section":null,"hidden":false,"hero":true,"slider":null,"value":12.142857142857142,"display":"12.14"}]},{"id":"half-life-advanced","title":"Half Life Advanced","description":"Calculate remaining radioactive material after time elapsed using half-life.","category":"science","icon":"flask-conical","tags":["life","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Decay Stats","label":null,"prefix":null,"suffix":null,"section":"Decay Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"initial amount = 100 // grams 0.1..10k","label":null,"prefix":null,"suffix":"grams","section":"Decay Stats","hidden":false,"hero":false,"slider":{"min":0.1,"max":10000,"step":100},"value":100,"display":"100"},{"text":"half life = 5730 // years 0.1..1e9","label":null,"prefix":null,"suffix":"years","section":"Decay Stats","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000000000,"step":10000000},"value":5730,"display":"5,730"},{"text":"time elapsed = 1000 // years 0..1e9","label":null,"prefix":null,"suffix":"years","section":"Decay Stats","hidden":false,"hero":false,"slider":{"min":0,"max":1000000000,"step":10000000},"value":1000,"display":"1,000"},{"text":"# Formula: N(t) = N0 * (0.5)^(t / t_half)","label":null,"prefix":null,"suffix":null,"section":"Formula: N(t) = N0 * (0.5)^(t / t_half)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"remaining amount = initial amount * (0.5^(time elapsed / half life)) // grams @hero","label":null,"prefix":null,"suffix":"grams","section":"Result","hidden":false,"hero":true,"slider":null,"value":88.60622295433987,"display":"88.61"},{"text":"# Progress","label":null,"prefix":null,"suffix":null,"section":"Progress","hero":false,"slider":null,"value":null,"display":null},{"text":"decay constant = 0.693147 / half life","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":0.00012096806282722514,"display":"0.000121"},{"text":"percent remaining = (remaining amount / initial amount) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Progress","hidden":false,"hero":false,"slider":null,"value":88.60622295433987,"display":"88.61"},{"text":"amount lost = initial amount - remaining amount","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":11.39377704566013,"display":"11.39"},{"text":"fractional remaining = remaining amount / initial amount","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":0.8860622295433987,"display":"0.8861"}]},{"id":"half-life-radioactive-atoms-remaining","title":"Half Life Radioactive Atoms Remaining","description":"Calculate radioactive atoms remaining after a number of half-lives.","category":"education","icon":"book-open","tags":["life","radioactive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"initial_atoms = 1000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"half_life_seconds = 60 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"time_elapsed_seconds = 180 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"_number_of_half_lives = time_elapsed_seconds / half_life_seconds","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"atoms_remaining = initial_atoms * (0.5)^number_of_half_lives // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":125000,"display":"125,000"}]},{"id":"half-life","title":"Half-Life","description":"Remaining amount after time t given half-life: N(t) = N₀ · (1/2)^(t/T½).","category":"formulas","icon":"timer","tags":["half-life"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"initial_amount = 100 // 0..1M","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"half_life = 5 // 0.01..10k","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.01,"max":10000,"step":100},"value":5,"display":"5"},{"text":"time = 10 // 0..100k","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":1000},"value":10,"display":"10"},{"text":"# Remaining amount","label":null,"prefix":null,"suffix":null,"section":"Remaining amount","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = initial_amount * (1 / 2)^(time / half_life) // @hero @label(N(t))","label":"N(t)","prefix":null,"suffix":null,"section":"Remaining amount","hidden":false,"hero":true,"slider":null,"value":25,"display":"25"},{"text":"decay_constant = log(2) / half_life // @label(Decay constant λ)","label":"Decay constant λ","prefix":null,"suffix":null,"section":"Remaining amount","hidden":false,"hero":false,"slider":null,"value":0.060205999132796235,"display":"0.0602"}]},{"id":"halo-effect-bias-estimate","title":"Halo Effect Bias Estimate","description":"Estimate perceived intelligence boost from the halo effect of attractiveness.","category":"health","icon":"brain","tags":["effect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"attractiveness_rating = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"perceived_intelligence_boost = attractiveness_rating * 0.5 // bias points @hero","label":null,"prefix":null,"suffix":"bias points","section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"hammock-hang-angle-tension","title":"Hammock Hang Angle Tension","description":"Calculate cord tension based on body weight and hang angle.","category":"everyday","icon":"anchor","tags":["everyday","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"body_weight_lbs = 180 // lbs","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"hang_angle_degrees = 30 // degrees (30 is ideal)","label":null,"prefix":null,"suffix":"degrees (30 is ideal)","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"cord_tension_lbs = (body_weight_lbs / 2) / sin(hang_angle_degrees) // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":true,"slider":null,"value":180.00000000000003,"display":"180"}]},{"id":"hamster-life-stage","title":"Hamster Life Stage","description":"Calculate a hamster's equivalent human age from months lived vs average lifespan.","category":"health","icon":"activity","tags":["life","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"hamster_age_months = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"average_lifespan_months = 24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"life_percentage = (hamster_age_months / average_lifespan_months) * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"equivalent_human_age = life_percentage * 0.8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":40,"display":"40"}]},{"id":"happiness-set-point-adjuster","title":"Happiness Set Point Adjuster","description":"Calculate a total happiness score from baseline, circumstances, and intentional activity.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"baseline_happiness = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"circumstances_impact = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"intentional_activity_impact = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"total_happiness = baseline_happiness + circumstances_impact + intentional_activity_impact // scale 0-100 @hero","label":null,"prefix":null,"suffix":"scale 0-100","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"hard-drive-life-expectancy-stats","title":"Hard Drive Life Expectancy Stats","description":"Calculate probability of hard drive failure over a number of years.","category":"math","icon":"infinity","tags":["drive","life","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"drive_age_years = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"annual_failure_rate = 0.015","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.015,"display":"0.015"},{"text":"probability_of_failure = 1 - (1 - annual_failure_rate) ** drive_age_years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.044328375,"display":"0.0443"}]},{"id":"hard-money-loan-cost","title":"Hard Money Loan Cost","description":"Estimate the total cost of interest and points for short-term loans.","category":"real-estate","icon":"dollar-sign","tags":["loan"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"loanAmount = 150000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":150000,"display":"150,000"},{"text":"interestRateAnnual = 12 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"loanPoints = 2 // points","label":null,"prefix":null,"suffix":"points","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"loanTermMonths = 6 // months","label":null,"prefix":null,"suffix":"months","section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"_interestCost = (loanAmount * (interestRateAnnual / 100) / 12) * loanTermMonths","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":9000,"display":"9,000"},{"text":"_pointsCost = loanAmount * (loanPoints / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"totalLoanCost = interestCost + pointsCost // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12000,"display":"12,000"}]},{"id":"hash-collision","title":"Hash Collision Probability","description":"Calculate collision probability using the birthday problem for any hash size.","category":"programming","icon":"fingerprint-pattern","tags":["birthday","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Hash Parameters","label":null,"prefix":null,"suffix":null,"section":"Hash Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"hash size = 128 // bits 8..512 by 8","label":null,"prefix":null,"suffix":"bits","section":"Hash Parameters","hidden":false,"hero":false,"slider":{"min":8,"max":512,"step":8},"value":128,"display":"128"},{"text":"number of items hashed = 1000000 // 1..100M","label":null,"prefix":null,"suffix":null,"section":"Hash Parameters","hidden":false,"hero":false,"slider":{"min":1,"max":100000000,"step":1000000},"value":1000000,"display":"1,000,000"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"total hash space = 2^hash_size","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":3.402823669209385e+38,"display":"3.4028e38"},{"text":"expected collisions = (number_of_items_hashed^2) / (2 * total_hash_space)","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":1.4693679385278594e-27,"display":"1.4694e-27"},{"text":"# Birthday Problem","label":null,"prefix":null,"suffix":null,"section":"Birthday Problem","hero":false,"slider":null,"value":null,"display":null},{"text":"prob no collision = E^(-(number_of_items_hashed * (number_of_items_hashed - 1)) / (2 * total_hash_space)) // @label(P(no collision))","label":"P(no collision)","prefix":null,"suffix":null,"section":"Birthday Problem","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"prob at least one collision = 1 - prob_no_collision // @hero @label(P(at least one collision))","label":"P(at least one collision)","prefix":null,"suffix":null,"section":"Birthday Problem","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"},{"text":"# 50% Collision Threshold","label":null,"prefix":null,"suffix":null,"section":"50% Collision Threshold","hero":false,"slider":null,"value":null,"display":null},{"text":"items needed for 50 pct collision chance = sqrt(2 * total_hash_space * ln(2))","label":null,"prefix":null,"suffix":null,"section":"50% Collision Threshold","hidden":false,"hero":false,"slider":null,"value":21719381355163560000,"display":"2.1719e19"}]},{"id":"health-savings-account-hsa-growth","title":"Health Savings Account Hsa Growth","description":"Calculate the future value of HSA contributions invested over 20 years.","category":"finance","icon":"heart","tags":["health","account","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"annual_contribution = 3850","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3850,"display":"3,850"},{"text":"years = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"expected_return = 0.07","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.07,"display":"0.07"},{"text":"future_value = annual_contribution * (((1 + expected_return) ** years - 1) / expected_return)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":157832.64543674007,"display":"157,832.65"}]},{"id":"heart-rate-zones","title":"Heart Rate Zones","description":"Find your training heart rate zones using the Karvonen method.","category":"health","icon":"heart-pulse","tags":["training"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Your Info","label":null,"prefix":null,"suffix":null,"section":"Your Info","hero":false,"slider":null,"value":null,"display":null},{"text":"age = 30 // years 15..85","label":null,"prefix":null,"suffix":"years","section":"Your Info","hidden":false,"hero":false,"slider":{"min":15,"max":85,"step":1},"value":30,"display":"30"},{"text":"resting heart rate = 65 // bpm 40..100","label":null,"prefix":null,"suffix":"bpm","section":"Your Info","hidden":false,"hero":false,"slider":{"min":40,"max":100,"step":1},"value":65,"display":"65"},{"text":"# Max Heart Rate","label":null,"prefix":null,"suffix":null,"section":"Max Heart Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"estimated max heart rate = 220 - age // bpm @hero","label":null,"prefix":null,"suffix":"bpm","section":"Max Heart Rate","hidden":false,"hero":true,"slider":null,"value":190,"display":"190"},{"text":"heart rate reserve = estimated_max_heart_rate - resting_heart_rate // bpm","label":null,"prefix":null,"suffix":"bpm","section":"Max Heart Rate","hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"# Training Zones (Karvonen Method)","label":null,"prefix":null,"suffix":null,"section":"Training Zones (Karvonen Method)","hero":false,"slider":null,"value":null,"display":null},{"text":"zone 1 recovery low = resting_heart_rate + heart_rate_reserve * 0.50 // bpm @label(Zone 1: Recovery (50%))","label":"Zone 1: Recovery (50%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":127.5,"display":"127.5"},{"text":"zone 1 recovery high = resting_heart_rate + heart_rate_reserve * 0.60 // bpm @label(Zone 1: Recovery (60%))","label":"Zone 1: Recovery (60%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":140,"display":"140"},{"text":"zone 2 aerobic low = resting_heart_rate + heart_rate_reserve * 0.60 // bpm @label(Zone 2: Aerobic (60%))","label":"Zone 2: Aerobic (60%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":140,"display":"140"},{"text":"zone 2 aerobic high = resting_heart_rate + heart_rate_reserve * 0.70 // bpm @label(Zone 2: Aerobic (70%))","label":"Zone 2: Aerobic (70%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":152.5,"display":"152.5"},{"text":"zone 3 tempo low = resting_heart_rate + heart_rate_reserve * 0.70 // bpm @label(Zone 3: Tempo (70%))","label":"Zone 3: Tempo (70%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":152.5,"display":"152.5"},{"text":"zone 3 tempo high = resting_heart_rate + heart_rate_reserve * 0.80 // bpm @label(Zone 3: Tempo (80%))","label":"Zone 3: Tempo (80%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":165,"display":"165"},{"text":"zone 4 threshold low = resting_heart_rate + heart_rate_reserve * 0.80 // bpm @label(Zone 4: Threshold (80%))","label":"Zone 4: Threshold (80%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":165,"display":"165"},{"text":"zone 4 threshold high = resting_heart_rate + heart_rate_reserve * 0.90 // bpm @label(Zone 4: Threshold (90%))","label":"Zone 4: Threshold (90%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":177.5,"display":"177.5"},{"text":"zone 5 max low = resting_heart_rate + heart_rate_reserve * 0.90 // bpm @label(Zone 5: Max (90%))","label":"Zone 5: Max (90%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":177.5,"display":"177.5"},{"text":"zone 5 max high = estimated_max_heart_rate // bpm @label(Zone 5: Max (100%))","label":"Zone 5: Max (100%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":190,"display":"190"}]},{"id":"heart-rate","title":"Heart Beats","description":"Beats per day, year, and lifetime from a resting heart rate.","category":"health","icon":"heart","tags":["biology","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Heart Rate","label":null,"prefix":null,"suffix":null,"section":"Heart Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"resting bpm = 70 // bpm 30..150","label":null,"prefix":null,"suffix":"bpm","section":"Heart Rate","hidden":false,"hero":false,"slider":{"min":30,"max":150,"step":1},"value":70,"display":"70"},{"text":"age years = 35 // years 0..120","label":null,"prefix":null,"suffix":"years","section":"Heart Rate","hidden":false,"hero":false,"slider":{"min":0,"max":120,"step":1},"value":35,"display":"35"},{"text":"# Daily","label":null,"prefix":null,"suffix":null,"section":"Daily","hero":false,"slider":null,"value":null,"display":null},{"text":"beats per hour = resting bpm * 60","label":null,"prefix":null,"suffix":null,"section":"Daily","hidden":false,"hero":false,"slider":null,"value":4200,"display":"4,200"},{"text":"beats per day = resting bpm * 60 * 24 // @hero","label":null,"prefix":null,"suffix":null,"section":"Daily","hidden":false,"hero":true,"slider":null,"value":100800,"display":"100,800"},{"text":"# Longer","label":null,"prefix":null,"suffix":null,"section":"Longer","hero":false,"slider":null,"value":null,"display":null},{"text":"beats per year = beats per day * 365","label":null,"prefix":null,"suffix":null,"section":"Longer","hidden":false,"hero":false,"slider":null,"value":36792000,"display":"36,792,000"},{"text":"lifetime years = 80 // years 1..120","label":null,"prefix":null,"suffix":"years","section":"Longer","hidden":false,"hero":false,"slider":{"min":1,"max":120,"step":1},"value":80,"display":"80"},{"text":"lifetime beats = beats per year * lifetime years","label":null,"prefix":null,"suffix":null,"section":"Longer","hidden":false,"hero":false,"slider":null,"value":2943360000,"display":"2,943,360,000"},{"text":"# Beats So Far","label":null,"prefix":null,"suffix":null,"section":"Beats So Far","hero":false,"slider":null,"value":null,"display":null},{"text":"beats so far = round(beats per year * age years) // @label(Beats so far in your life)","label":"Beats so far in your life","prefix":null,"suffix":null,"section":"Beats So Far","hidden":false,"hero":false,"slider":null,"value":1287720000,"display":"1,287,720,000"}]},{"id":"heat-exchanger-log-mean-temp-difference","title":"Heat Exchanger LMTD","description":"Calculate Log Mean Temperature Difference.","category":"engineering","icon":"thermometer","tags":["engineering","fluids"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"hot_inlet_temp_celsius = 80 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"hot_outlet_temp_celsius = 40 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"cold_inlet_temp_celsius = 20 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"cold_outlet_temp_celsius = 35 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"delta_t1 = hot_inlet_temp_celsius - cold_outlet_temp_celsius","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"delta_t2 = hot_outlet_temp_celsius - cold_inlet_temp_celsius","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"lmtd_celsius = (delta_t1 - delta_t2) / log(delta_t1 / delta_t2) // C @hero","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":true,"slider":null,"value":70.98591984084466,"display":"70.99"}]},{"id":"heat-index","title":"Heat Index","description":"Apparent temperature from heat and humidity (NOAA Rothfusz formula).","category":"everyday","icon":"thermometer","tags":["temperature","humidity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Conditions","label":null,"prefix":null,"suffix":null,"section":"Conditions","hero":false,"slider":null,"value":null,"display":null},{"text":"temperature f = 90 // °F 70..120","label":null,"prefix":null,"suffix":"°F","section":"Conditions","hidden":false,"hero":false,"slider":{"min":70,"max":120,"step":1},"value":90,"display":"90"},{"text":"relative humidity = 80 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Conditions","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":80,"display":"80"},{"text":"# Rothfusz Heat Index (NOAA full formula, valid above 80°F)","label":null,"prefix":null,"suffix":null,"section":"Rothfusz Heat Index (NOAA full formula, valid above 80°F)","hero":false,"slider":null,"value":null,"display":null},{"text":"_t = temperature f","label":null,"prefix":null,"suffix":null,"section":"Rothfusz Heat Index (NOAA full formula, valid above 80°F)","hidden":true,"hero":false,"slider":null,"value":90,"display":"90"},{"text":"_r = relative humidity","label":null,"prefix":null,"suffix":null,"section":"Rothfusz Heat Index (NOAA full formula, valid above 80°F)","hidden":true,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"_hi_raw = -42.379 + 2.04901523 * t + 10.14333127 * r - 0.22475541 * t * r - 0.00683783 * t^2 - 0.05481717 * r^2 + 0.00122874 * t^2 * r + 0.00085282 * t * r^2 - 0.00000199 * t^2 * r^2","label":null,"prefix":null,"suffix":null,"section":"Rothfusz Heat Index (NOAA full formula, valid above 80°F)","hidden":true,"hero":false,"slider":null,"value":113.3298493,"display":"113.33"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"feels like f = round(hi_raw, 0) // °F @hero @label(Feels like) @suffix(°F)","label":"Feels like","prefix":null,"suffix":"°F","section":"Result","hidden":false,"hero":true,"slider":null,"value":113,"display":"113"},{"text":"feels like c = round((feels like f - 32) * 5 / 9, 1) // °C @label(Feels like) @suffix(°C)","label":"Feels like","prefix":null,"suffix":"°C","section":"Result","hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"# Difference","label":null,"prefix":null,"suffix":null,"section":"Difference","hero":false,"slider":null,"value":null,"display":null},{"text":"extra degrees = round(feels like f - temperature f, 0) // °F @label(Heat index above real temp)","label":"Heat index above real temp","prefix":null,"suffix":"°F","section":"Difference","hidden":false,"hero":false,"slider":null,"value":23,"display":"23"}]},{"id":"heat-sink-thermal-resistance","title":"Heat Sink Thermal Resistance","description":"Calculate required thermal resistance for cooling.","category":"engineering","icon":"thermometer-snowflake","tags":["engineering","electronics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"power_dissipation_watts = 10 // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"max_junction_temp_celsius = 125 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"ambient_temp_celsius = 25 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"total_thermal_resistance = (max_junction_temp_celsius - ambient_temp_celsius) / power_dissipation_watts // C/W","label":null,"prefix":null,"suffix":"C/W","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"case_to_sink_resistance = 0.5 // C/W","label":null,"prefix":null,"suffix":"C/W","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"junction_to_case_resistance = 1.2 // C/W","label":null,"prefix":null,"suffix":"C/W","section":null,"hidden":false,"hero":false,"slider":null,"value":1.2,"display":"1.2"},{"text":"required_sink_to_ambient_resistance = total_thermal_resistance - junction_to_case_resistance - case_to_sink_resistance // C/W @hero","label":null,"prefix":null,"suffix":"C/W","section":null,"hidden":false,"hero":true,"slider":null,"value":8.3,"display":"8.3"}]},{"id":"heat-transfer","title":"Heat Transfer","description":"Calculate heat flow through walls using Fourier's Law with R-value and energy costs.","category":"engineering","icon":"thermometer","tags":["heat","insulation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Surface Properties","label":null,"prefix":null,"suffix":null,"section":"Surface Properties","hero":false,"slider":null,"value":null,"display":null},{"text":"wall_area = 10 // m² 1..100","label":null,"prefix":null,"suffix":"m²","section":"Surface Properties","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":10,"display":"10"},{"text":"wall thickness = 0.05 // m 0.01..0.5 by 0.01","label":null,"prefix":null,"suffix":"m","section":"Surface Properties","hidden":false,"hero":false,"slider":{"min":0.01,"max":0.5,"step":0.01},"value":0.05,"display":"0.05"},{"text":"thermal conductivity = 0.04 // W/m·K 0.01..2 by 0.01","label":null,"prefix":null,"suffix":"W/m·K","section":"Surface Properties","hidden":false,"hero":false,"slider":{"min":0.01,"max":2,"step":0.01},"value":0.04,"display":"0.04"},{"text":"# Temperatures","label":null,"prefix":null,"suffix":null,"section":"Temperatures","hero":false,"slider":null,"value":null,"display":null},{"text":"hot side temperature = 25 // °C -20..60","label":null,"prefix":null,"suffix":"°C","section":"Temperatures","hidden":false,"hero":false,"slider":{"min":-20,"max":60,"step":1},"value":25,"display":"25"},{"text":"cold side temperature = -5 // °C -40..40","label":null,"prefix":null,"suffix":"°C","section":"Temperatures","hidden":false,"hero":false,"slider":{"min":-40,"max":40,"step":1},"value":-5,"display":"-5"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"temperature difference = hot_side_temperature - cold_side_temperature // °C","label":null,"prefix":null,"suffix":"°C","section":"Results","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"heat transfer rate = thermal_conductivity * wall_area * temperature_difference / wall_thickness // W @hero @label(Heat Transfer Rate (Fourier's Law))","label":"Heat Transfer Rate (Fourier's Law)","prefix":null,"suffix":"W","section":"Results","hidden":false,"hero":true,"slider":null,"value":240,"display":"240"},{"text":"R value = wall_thickness / thermal_conductivity // m²·K/W @label(R-Value (Thermal Resistance))","label":"R-Value (Thermal Resistance)","prefix":null,"suffix":"m²·K/W","section":"Results","hidden":false,"hero":false,"slider":null,"value":1.25,"display":"1.25"},{"text":"daily energy loss = heat_transfer_rate * 24 / 1000 // kWh/day","label":null,"prefix":null,"suffix":"kWh/day","section":"Results","hidden":false,"hero":false,"slider":null,"value":5.76,"display":"5.76"},{"text":"$monthly cost at 12c per kWh = daily_energy_loss * 30 * 0.12","label":null,"prefix":"$","suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":20.736,"display":"$20.74"}]},{"id":"heater-wattage-sizing","title":"Heater Wattage Sizing","description":"Calculate heater wattage needed for a room from area and insulation quality.","category":"health","icon":"activity","tags":["heater","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Room Info","label":null,"prefix":null,"suffix":null,"section":"Room Info","hero":false,"slider":null,"value":null,"display":null},{"text":"length = 15 // feet","label":null,"prefix":null,"suffix":"feet","section":"Room Info","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"width = 12 // feet","label":null,"prefix":null,"suffix":"feet","section":"Room Info","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"insulation quality = 1.0 // 0.8 (great) to 1.5 (poor)","label":null,"prefix":null,"suffix":"0.8 (great) to 1.5 (poor)","section":"Room Info","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Wattage Calculations","label":null,"prefix":null,"suffix":null,"section":"Wattage Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_area = length * width","label":null,"prefix":null,"suffix":null,"section":"Wattage Calculations","hidden":true,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"_base_watts = area * 10","label":null,"prefix":null,"suffix":null,"section":"Wattage Calculations","hidden":true,"hero":false,"slider":null,"value":1800,"display":"1,800"},{"text":"total watts needed = roundup(base_watts * insulation quality) // @hero","label":null,"prefix":null,"suffix":null,"section":"Wattage Calculations","hidden":false,"hero":true,"slider":null,"value":1800,"display":"1,800"},{"text":"# BTU Conversion","label":null,"prefix":null,"suffix":null,"section":"BTU Conversion","hero":false,"slider":null,"value":null,"display":null},{"text":"# 1 Watt = 3.41 BTU/hr","label":null,"prefix":null,"suffix":null,"section":"1 Watt = 3.41 BTU/hr","hero":false,"slider":null,"value":null,"display":null},{"text":"total btu per hour = round(total watts needed * 3.41)","label":null,"prefix":null,"suffix":null,"section":"1 Watt = 3.41 BTU/hr","hidden":false,"hero":false,"slider":null,"value":6138,"display":"6,138"}]},{"id":"heloc-interest-calculator","title":"HELOC Interest","description":"Estimate monthly interest payments for a line of credit.","category":"real-estate","icon":"credit-card","tags":["interest"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"outstandingBalance = 25000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":25000,"display":"25,000"},{"text":"apr = 7.5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":7.5,"display":"7.5"},{"text":"monthlyInterestPayment = (outstandingBalance * (apr / 100)) / 12 // @prefix($) @suffix(/mo) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":156.25,"display":"156.25"}]},{"id":"heloc-payment","title":"Heloc Payment","description":"Calculate HELOC monthly payment for interest-only or amortizing 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Only: 1, Principal and Interest: 2})","label":null,"prefix":null,"suffix":null,"section":"HELOC Terms","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_monthly_interest_payment = heloc balance * (interest rate / 100 / 12)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":354.16666666666663,"display":"$354.17"},{"text":"$_monthly_principal_and_interest = heloc balance * (interest rate/1200 * (1+interest rate/1200)^240) / ((1+interest rate/1200)^240 - 1) // assumes 20yr","label":null,"prefix":"$","suffix":"assumes 20yr","section":"Calculations","hidden":true,"hero":false,"slider":null,"value":433.91161668276703,"display":"$433.91"},{"text":"# 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dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"feePerSquareFoot = 0.05 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"estimatedInspectionCost = baseFee + (squareFootage * feePerSquareFoot) // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":400,"display":"400"}]},{"id":"home-insulation-roi","title":"Home Insulation ROI","description":"Calculate savings and break-even point for home insulation.","category":"finance","icon":"home","tags":["finance","insulation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"insulation_cost = 2000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"annual_energy_savings_dollars = 400 // dollars per year","label":null,"prefix":null,"suffix":"dollars per year","section":null,"hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"years_to_break_even = insulation_cost / annual_energy_savings_dollars // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"twenty_year_total_savings = (annual_energy_savings_dollars * 20) - insulation_cost // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":6000,"display":"6,000"}]},{"id":"homebrew-og-fg-abv","title":"Homebrew Og Fg Abv","description":"Calculate beer ABV, attenuation, and calories from original and final 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@hero","label":null,"prefix":null,"suffix":"ounces","section":"Result","hidden":false,"hero":true,"slider":null,"value":124,"display":"124"},{"text":"water in liters = total daily water goal * 0.0295735","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":3.667114,"display":"3.667"}]},{"id":"hydraulic-cylinder-force","title":"Hydraulic Cylinder Force","description":"Calculate extension and retraction force for hydraulics.","category":"engineering","icon":"settings-2","tags":["engineering"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"bore_diameter_inches = 3 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"system_pressure_psi = 2000 // psi","label":null,"prefix":null,"suffix":"psi","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"piston_area = 3.14159 * ((bore_diameter_inches / 2)^2) // sq inches","label":null,"prefix":null,"suffix":"sq inches","section":null,"hidden":false,"hero":false,"slider":null,"value":7.0685775,"display":"7.069"},{"text":"extension_force_lbs = system_pressure_psi * piston_area // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":true,"slider":null,"value":14137.155,"display":"14,137.16"},{"text":"retraction_force_lbs = extension_force_lbs * 0.8 // assuming rod takes 20% area","label":null,"prefix":null,"suffix":"assuming rod takes 20% area","section":null,"hidden":false,"hero":false,"slider":null,"value":11309.724,"display":"11,309.72"}]},{"id":"hyperfocal-distance","title":"Hyperfocal Distance","description":"Calculate hyperfocal distance for a lens from focal length, aperture, and crop factor.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Optical Stats","label":null,"prefix":null,"suffix":null,"section":"Optical Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"focal length = 50 // mm 10..600","label":null,"prefix":null,"suffix":"mm","section":"Optical Stats","hidden":false,"hero":false,"slider":{"min":10,"max":600,"step":1},"value":50,"display":"50"},{"text":"aperture = 8.0 // f-number 1.0..64","label":null,"prefix":null,"suffix":"f-number","section":"Optical Stats","hidden":false,"hero":false,"slider":{"min":1,"max":64,"step":1},"value":8,"display":"8"},{"text":"sensor crop factor = 1.5 // 1..2","label":null,"prefix":null,"suffix":null,"section":"Optical Stats","hidden":false,"hero":false,"slider":{"min":1,"max":2,"step":0.01},"value":1.5,"display":"1.5"},{"text":"# Circle of Confusion (Commonly 0.03mm for 35mm)","label":null,"prefix":null,"suffix":null,"section":"Circle of Confusion (Commonly 0.03mm for 35mm)","hero":false,"slider":null,"value":null,"display":null},{"text":"coc = 0.03 / sensor crop factor","label":null,"prefix":null,"suffix":null,"section":"Circle of Confusion (Commonly 0.03mm for 35mm)","hidden":false,"hero":false,"slider":null,"value":0.02,"display":"0.02"},{"text":"# Formula: H = (f^2 / (N * c)) + f","label":null,"prefix":null,"suffix":null,"section":"Formula: H = (f^2 / (N * c)) + f","hero":false,"slider":null,"value":null,"display":null},{"text":"hyperfocal mm = (focal length^2 / (aperture * coc)) + focal length","label":null,"prefix":null,"suffix":null,"section":"Formula: H = (f^2 / (N * c)) + f","hidden":false,"hero":false,"slider":null,"value":15675,"display":"15,675"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"hyperfocal distance = hyperfocal mm / 1000 // meters @hero","label":null,"prefix":null,"suffix":"meters","section":"Result","hidden":false,"hero":true,"slider":null,"value":15.675,"display":"15.68"},{"text":"distance in feet = hyperfocal distance * 3.28084","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":51.427167,"display":"51.43"},{"text":"near limit at focus = hyperfocal distance / 2 // meters","label":null,"prefix":null,"suffix":"meters","section":"Result","hidden":false,"hero":false,"slider":null,"value":7.8375,"display":"7.838"},{"text":"far limit at focus = 9999 // infinity","label":null,"prefix":null,"suffix":"infinity","section":"Result","hidden":false,"hero":false,"slider":null,"value":9999,"display":"9,999"}]},{"id":"ice-cube-melt-time","title":"Ice Cube Melt Time","description":"Estimate ice cube melt time in minutes from size and ambient temperature.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"cube_side_cm = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"ambient_temp_c = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"melt_rate_factor = 0.01","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"time_minutes = (cube_side_cm^2) / (melt_rate_factor * (ambient_temp_c)) // minutes @hero","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"ideal-gas-law","title":"Ideal Gas Law","description":"Solve PV=nRT for any variable — pressure, volume, temperature, or moles.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Conditions","label":null,"prefix":null,"suffix":null,"section":"Conditions","hero":false,"slider":null,"value":null,"display":null},{"text":"pressure = 1 // atm 0.1..100","label":null,"prefix":null,"suffix":"atm","section":"Conditions","hidden":false,"hero":false,"slider":{"min":0.1,"max":100,"step":1},"value":1,"display":"1"},{"text":"volume = 22.4 // L 0.1..1k","label":null,"prefix":null,"suffix":"L","section":"Conditions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":22.4,"display":"22.4"},{"text":"temperature = 273.15 // K 1..1k","label":null,"prefix":null,"suffix":"K","section":"Conditions","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":273.15,"display":"273.15"},{"text":"# Constants","label":null,"prefix":null,"suffix":null,"section":"Constants","hero":false,"slider":null,"value":null,"display":null},{"text":"gas constant R = 0.08206 // L·atm/mol·K","label":null,"prefix":null,"suffix":"L·atm/mol·K","section":"Constants","hidden":false,"hero":false,"slider":null,"value":0.08206,"display":"0.0821"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"moles of gas = (pressure * volume) / (gas_constant_R * temperature) // mol @hero @label(Amount of Gas (n = PV/RT))","label":"Amount of Gas (n = PV/RT)","prefix":null,"suffix":"mol","section":"Results","hidden":false,"hero":true,"slider":null,"value":0.9993446708093965,"display":"0.9993"},{"text":"number of molecules = moles_of_gas * 6.022e23","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":6.0180536076141854e+23,"display":"6.0181e23"},{"text":"mass if O2 = moles_of_gas * 32 // g @label(Mass if O₂ (MW=32))","label":"Mass if O₂ (MW=32)","prefix":null,"suffix":"g","section":"Results","hidden":false,"hero":false,"slider":null,"value":31.979029465900684,"display":"31.98"},{"text":"mass if N2 = moles_of_gas * 28 // g @label(Mass if N₂ (MW=28))","label":"Mass if N₂ (MW=28)","prefix":null,"suffix":"g","section":"Results","hidden":false,"hero":false,"slider":null,"value":27.9816507826631,"display":"27.98"}]},{"id":"image-resize","title":"Image Resize","description":"Calculate new dimensions when resizing an image.","category":"design","icon":"image","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"# Original Image","label":null,"prefix":null,"suffix":null,"section":"Original Image","hero":false,"slider":null,"value":null,"display":null},{"text":"original width = 4032 // px 1..10k","label":null,"prefix":null,"suffix":"px","section":"Original Image","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":4032,"display":"4,032"},{"text":"original height = 3024 // px 1..10k","label":null,"prefix":null,"suffix":"px","section":"Original Image","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":3024,"display":"3,024"},{"text":"# Target","label":null,"prefix":null,"suffix":null,"section":"Target","hero":false,"slider":null,"value":null,"display":null},{"text":"target width = 1200 // px 1..10k","label":null,"prefix":null,"suffix":"px","section":"Target","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":1200,"display":"1,200"},{"text":"# Calculated Dimensions","label":null,"prefix":null,"suffix":null,"section":"Calculated Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"target height = round(original height * (target width / original width)) // px @hero","label":null,"prefix":null,"suffix":"px","section":"Calculated Dimensions","hidden":false,"hero":true,"slider":null,"value":900,"display":"900"},{"text":"scale factor = round(target width / original width * 10000) / 10000","label":null,"prefix":null,"suffix":null,"section":"Calculated Dimensions","hidden":false,"hero":false,"slider":null,"value":0.2976,"display":"0.2976"},{"text":"# File Size Estimate","label":null,"prefix":null,"suffix":null,"section":"File Size Estimate","hero":false,"slider":null,"value":null,"display":null},{"text":"original megapixels = round((original width * original height) / 1000000 * 100) / 100 // MP","label":null,"prefix":null,"suffix":"MP","section":"File Size Estimate","hidden":false,"hero":false,"slider":null,"value":12.19,"display":"12.19"},{"text":"new megapixels = round((target width * target height) / 1000000 * 100) / 100 // MP","label":null,"prefix":null,"suffix":"MP","section":"File Size Estimate","hidden":false,"hero":false,"slider":null,"value":1.08,"display":"1.08"},{"text":"size reduction pct = round((1 - (new megapixels / original megapixels)) * 100 * 10) / 10 // % @label(Pixel reduction)","label":"Pixel reduction","prefix":null,"suffix":"%","section":"File Size Estimate","hidden":false,"hero":false,"slider":null,"value":91.1,"display":"91.1"},{"text":"# Aspect Ratio","label":null,"prefix":null,"suffix":null,"section":"Aspect Ratio","hero":false,"slider":null,"value":null,"display":null},{"text":"ratio = round(original width / original height * 10000) / 10000 // @label(Aspect ratio (decimal))","label":"Aspect ratio (decimal)","prefix":null,"suffix":null,"section":"Aspect Ratio","hidden":false,"hero":false,"slider":null,"value":1.3333,"display":"1.333"}]},{"id":"inbound-freight-cost","title":"Inbound Freight Cost","description":"Track the average cost of shipments coming into your facility.","category":"business","icon":"corner-down-left","tags":["freight"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"totalInboundFreight = 8000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":8000,"display":"8,000"},{"text":"totalInboundShipments = 40 // shipments","label":null,"prefix":null,"suffix":"shipments","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"averageInboundCost = totalInboundFreight / totalInboundShipments // dollars per shipment @hero","label":null,"prefix":null,"suffix":"dollars per shipment","section":null,"hidden":false,"hero":true,"slider":null,"value":200,"display":"200"}]},{"id":"inductor-energy-storage","title":"Inductor Energy Storage","description":"Calculate energy stored in an inductor from inductance and current.","category":"health","icon":"activity","tags":["storage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"inductance_millihenries = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"current_amps = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"energy_stored_joules = 0.5 * (inductance_millihenries / 1000) * current_amps ** 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.2,"display":"0.2"}]},{"id":"inflation-adjusted-salary-history","title":"Inflation Adjusted Salary History","description":"Adjust a historical salary to today's dollars using CPI ratios.","category":"finance","icon":"dollar-sign","tags":["inflation","salary","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.442Z"},"rows":[{"text":"past_salary = 50000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"past_cpi = 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"current_cpi = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"adjusted_salary = past_salary * (current_cpi / past_cpi)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":83333.33333333334,"display":"83,333.33"}]},{"id":"inflation-calculator","title":"Inflation Calculator","description":"See how inflation erodes purchasing power over time.","category":"finance","icon":"arrow-up-right","tags":["inflation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"$amount today = 1000 // 1..1M","label":null,"prefix":"$","suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":1000000,"step":10000},"value":1000,"display":"$1,000.00"},{"text":"inflation rate = 3 // % 0.5..15 by 0.5","label":null,"prefix":null,"suffix":"%","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.5,"max":15,"step":0.5},"value":3,"display":"3"},{"text":"years = 10 // 1..50","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":10,"display":"10"},{"text":"# Future Cost","label":null,"prefix":null,"suffix":null,"section":"Future Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$future equivalent = round(amount today * (1 + inflation rate / 100)^years * 100) / 100 // @label(Cost of Same Goods in Future) @hero","label":"Cost of Same Goods in Future","prefix":"$","suffix":null,"section":"Future Cost","hidden":false,"hero":true,"slider":null,"value":1343.92,"display":"$1,343.92"},{"text":"# Purchasing Power","label":null,"prefix":null,"suffix":null,"section":"Purchasing Power","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchasing power = round(amount today / (1 + inflation rate / 100)^years * 100) / 100 // @label(What Your Money Will Buy)","label":"What Your Money Will Buy","prefix":"$","suffix":null,"section":"Purchasing Power","hidden":false,"hero":false,"slider":null,"value":744.09,"display":"$744.09"},{"text":"$value lost = round((amount today - purchasing power) * 100) / 100 // @label(Purchasing Power Lost)","label":"Purchasing Power Lost","prefix":"$","suffix":null,"section":"Purchasing Power","hidden":false,"hero":false,"slider":null,"value":255.91,"display":"$255.91"},{"text":"loss pct = round((value lost / amount today) * 100 * 10) / 10 // % @label(Loss %)","label":"Loss %","prefix":null,"suffix":"%","section":"Purchasing Power","hidden":false,"hero":false,"slider":null,"value":25.6,"display":"25.6"}]},{"id":"information-overload-content-threshold","title":"Information Overload Content Threshold","description":"Calculate cognitive capacity utilization from items processed vs limit.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"items_processed_per_hour = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"cognitive_limit_per_hour = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"capacity_utilization_percent = (items_processed_per_hour / cognitive_limit_per_hour) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"information-ratio-investment","title":"Information Ratio Investment","description":"Calculate the information ratio for a portfolio from excess return and tracking error.","category":"math","icon":"ratio","tags":["investment","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"portfolio_return = 0.12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"benchmark_return = 0.10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"tracking_error = 0.04","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"},{"text":"information_ratio = (portfolio_return - benchmark_return) / tracking_error","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"insta-calc-completion-celebration","title":"Insta Calc Completion Celebration","description":"Calculate the completion percentage of an Instacalc gallery milestone.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"calculators_completed = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"target_goal = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"completion_percent = (calculators_completed / target_goal) * 100 // percent complete! 1000/1000 @suffix(%) @hero","label":null,"prefix":null,"suffix":"percent complete! 1000/1000","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"insulation-savings-r-value","title":"Insulation Savings R Value","description":"Estimate annual heating savings from upgrading attic insulation R-value.","category":"finance","icon":"dollar-sign","tags":["insulation","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"current_r_value = 11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":11,"display":"11"},{"text":"target_r_value = 38","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":38,"display":"38"},{"text":"attic_area_square_feet = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"heating_degree_days = 4000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4000,"display":"4,000"},{"text":"cost_per_therm = 1.20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.2,"display":"1.2"},{"text":"annual_heat_loss_reduction_therms = (attic_area_square_feet * heating_degree_days * 24) / 100000 * (1/current_r_value - 1/target_r_value)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":62.00956937799045,"display":"62.01"},{"text":"annual_savings_dollars = annual_heat_loss_reduction_therms * cost_per_therm // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":74.41148325358854,"display":"74.41"}]},{"id":"integral-power-rule","title":"Integral — Power Rule","description":"Evaluate ∫a·xⁿ dx = a·x^(n+1)/(n+1) at a given x.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Function: f(x) = a · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 4 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":4,"display":"4"},{"text":"x = 2 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":2,"display":"2"},{"text":"# Antiderivative at x","label":null,"prefix":null,"suffix":null,"section":"Antiderivative at x","hero":false,"slider":null,"value":null,"display":null},{"text":"antiderivative = a * x^(n + 1) / (n + 1) // @label(∫f(x) dx)","label":"∫f(x) dx","prefix":null,"suffix":null,"section":"Antiderivative at x","hidden":false,"hero":true,"slider":null,"value":19.2,"display":"19.2"}]},{"id":"intellectual-property-portfolio-value","title":"IP Portfolio Value","description":"Estimate the combined value of patents and trademarks.","category":"other","icon":"briefcase","tags":["property"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"numberOfPatents = 5 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"averageValuePerPatent = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"numberOfTrademarks = 3 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"averageValuePerTrademark = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"totalPortfolioValue = (numberOfPatents * averageValuePerPatent) + (numberOfTrademarks * averageValuePerTrademark) // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":295000,"display":"295,000"}]},{"id":"internal-rate-of-return-real-estate","title":"Real Estate IRR Estimator","description":"Estimate the internal rate of return for a property investment.","category":"real-estate","icon":"trending-up","tags":["estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"initialInvestment = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"saleProceeds = 150000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":150000,"display":"150,000"},{"text":"yearsHeld = 5 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"estimatedIRR = ((saleProceeds / initialInvestment) ^ (1 / yearsHeld) - 1) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8.44717711976986,"display":"8.447"}]},{"id":"internal-rate-of-return","title":"Internal Rate of Return","description":"Calculate internal rate of return (IRR) from initial and final investment values.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Investment Return (CAGR Proxy for IRR)","label":null,"prefix":null,"suffix":null,"section":"Investment Return (CAGR Proxy for IRR)","hero":false,"slider":null,"value":null,"display":null},{"text":"$initial investment = 10000 // 100..1M","label":null,"prefix":"$","suffix":null,"section":"Investment Return (CAGR Proxy for IRR)","hidden":false,"hero":false,"slider":{"min":100,"max":1000000,"step":10000},"value":10000,"display":"$10,000.00"},{"text":"$final value = 15000 // 100..2M","label":null,"prefix":"$","suffix":null,"section":"Investment Return (CAGR Proxy for IRR)","hidden":false,"hero":false,"slider":{"min":100,"max":2000000,"step":20000},"value":15000,"display":"$15,000.00"},{"text":"years held = 3 // years 1..30","label":null,"prefix":null,"suffix":"years","section":"Investment Return (CAGR Proxy for IRR)","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":3,"display":"3"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"internal rate of return = ((final value / initial investment)^(1 / years held) - 1) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":14.471424255333181,"display":"14.47"},{"text":"$total profit = final value - initial 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500000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500000,"display":"500,000"},{"text":"cost_of_goods_sold = 2000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000000,"display":"2,000,000"},{"text":"inventory_days = (average_inventory / cost_of_goods_sold) * 365","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":91.25,"display":"91.25"}]},{"id":"inventory-space-weight-capacity","title":"Inventory Space Weight Capacity","description":"Calculate remaining inventory weight capacity.","category":"productivity","icon":"archive","tags":["gaming","inventory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Inventory Settings","label":null,"prefix":null,"suffix":null,"section":"Inventory 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Octets","hidden":false,"hero":false,"slider":{"min":0,"max":255,"step":1},"value":1,"display":"1"},{"text":"octet 4 = 1 // 0..255","label":null,"prefix":null,"suffix":null,"section":"IP Octets","hidden":false,"hero":false,"slider":{"min":0,"max":255,"step":1},"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"decimal value = (octet 1 * 2^24) + (octet 2 * 2^16) + (octet 3 * 2^8) + octet 4","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":3232235777,"display":"3,232,235,777"}]},{"id":"ironman-finish-time-estimate","title":"Ironman Finish Time Estimate","description":"Estimate Ironman finish time in hours from swim, bike, run, and transition 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@hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12.083333333333334,"display":"12.08"}]},{"id":"irrigation-run-time","title":"Irrigation Run Time","description":"Calculate how many minutes to run sprinklers for target depth.","category":"everyday","icon":"sprinklers","tags":["garden","water"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"target_water_depth_mm = 25 // mm (typically 1 inch per week)","label":null,"prefix":null,"suffix":"mm (typically 1 inch per week)","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"sprinkler_output_liters_per_minute = 10 // liters per minute","label":null,"prefix":null,"suffix":"liters per minute","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"area_square_meters = 100 // square meters","label":null,"prefix":null,"suffix":"square 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Details","hidden":false,"hero":false,"slider":{"min":1,"max":24,"step":1},"value":8,"display":"8"},{"text":"drop factor = 20 // gtt/ml 10..60","label":null,"prefix":null,"suffix":"gtt/ml","section":"Infusion Details","hidden":false,"hero":false,"slider":{"min":10,"max":60,"step":1},"value":20,"display":"20"},{"text":"# Formula","label":null,"prefix":null,"suffix":null,"section":"Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"total minutes = time duration * 60","label":null,"prefix":null,"suffix":null,"section":"Formula","hidden":false,"hero":false,"slider":null,"value":480,"display":"480"},{"text":"iv drip rate = (total volume * drop factor) / total minutes // gtt/min @hero","label":null,"prefix":null,"suffix":"gtt/min","section":"Formula","hidden":false,"hero":true,"slider":null,"value":41.666666666666664,"display":"41.67"},{"text":"# Hourly Rate","label":null,"prefix":null,"suffix":null,"section":"Hourly 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light.","category":"education","icon":"book-open","tags":["relativistic"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"mass = 1 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"velocity = 0.5 // fraction of light speed (c)","label":null,"prefix":null,"suffix":"fraction of light speed (c)","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_c = 299792458 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":true,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"_v = velocity * c","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":149896229,"display":"149,896,229"},{"text":"_gamma = 1 / sqrt(1 - (v/c)^2)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":1.1547005383792517,"display":"1.155"},{"text":"relativistic_kinetic_energy = (gamma - 1) * mass * c^2 // Joules @hero","label":null,"prefix":null,"suffix":"Joules","section":null,"hidden":false,"hero":true,"slider":null,"value":13903791002172618,"display":"13,903,791,002,172,618"}]},{"id":"kinetic-energy","title":"Kinetic Energy","description":"KE = ½ · m · v² — kinetic energy of a moving object.","category":"formulas","icon":"zap","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"mass = 10 // kg 0.001..10k","label":null,"prefix":null,"suffix":"kg","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000,"step":100},"value":10,"display":"10"},{"text":"velocity = 5 // m/s 0..1k","label":null,"prefix":null,"suffix":"m/s","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":5,"display":"5"},{"text":"# Kinetic energy","label":null,"prefix":null,"suffix":null,"section":"Kinetic energy","hero":false,"slider":null,"value":null,"display":null},{"text":"kinetic_energy = 0.5 * mass * velocity^2 // @label(KE) @suffix(J)","label":"KE","prefix":null,"suffix":null,"section":"Kinetic energy","hidden":false,"hero":true,"slider":null,"value":125,"display":"125"}]},{"id":"kinetic-friction-force","title":"Kinetic Friction Force","description":"Calculate kinetic friction force from normal force and friction 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temperatures.","category":"cooking","icon":"chef-hat","tags":["temperature"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Volume Conversions","label":null,"prefix":null,"suffix":null,"section":"Volume Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"cups = 2 // cups 0.25..20 by 0.25","label":null,"prefix":null,"suffix":"cups","section":"Volume Conversions","hidden":false,"hero":false,"slider":{"min":0.25,"max":20,"step":0.25},"value":2,"display":"2"},{"text":"tablespoons = cups * 16 // tbsp","label":null,"prefix":null,"suffix":"tbsp","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"teaspoons = cups * 48 // tsp","label":null,"prefix":null,"suffix":"tsp","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"fluid ounces = cups * 8 // fl oz","label":null,"prefix":null,"suffix":"fl oz","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"milliliters = cups * 236.588 // mL @hero","label":null,"prefix":null,"suffix":"mL","section":"Volume Conversions","hidden":false,"hero":true,"slider":null,"value":473.176,"display":"473.18"},{"text":"liters = milliliters / 1000 // L","label":null,"prefix":null,"suffix":"L","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":0.473176,"display":"0.4732"},{"text":"# Weight Conversions","label":null,"prefix":null,"suffix":null,"section":"Weight Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"weight in ounces = 8 // oz 0.5..128 by 0.5","label":null,"prefix":null,"suffix":"oz","section":"Weight Conversions","hidden":false,"hero":false,"slider":{"min":0.5,"max":128,"step":0.5},"value":8,"display":"8"},{"text":"grams = weight_in_ounces * 28.3495 // g","label":null,"prefix":null,"suffix":"g","section":"Weight Conversions","hidden":false,"hero":false,"slider":null,"value":226.796,"display":"226.8"},{"text":"kilograms = grams / 1000 // kg","label":null,"prefix":null,"suffix":"kg","section":"Weight Conversions","hidden":false,"hero":false,"slider":null,"value":0.226796,"display":"0.2268"},{"text":"pounds = weight_in_ounces / 16 // lbs","label":null,"prefix":null,"suffix":"lbs","section":"Weight Conversions","hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"# Temperature","label":null,"prefix":null,"suffix":null,"section":"Temperature","hero":false,"slider":null,"value":null,"display":null},{"text":"fahrenheit = 350 // °F 100..550 by 5","label":null,"prefix":null,"suffix":"°F","section":"Temperature","hidden":false,"hero":false,"slider":{"min":100,"max":550,"step":5},"value":350,"display":"350"},{"text":"celsius = (fahrenheit - 32) * 5 / 9 // °C","label":null,"prefix":null,"suffix":"°C","section":"Temperature","hidden":false,"hero":false,"slider":null,"value":176.66666666666666,"display":"176.67"},{"text":"gas mark approx = (celsius - 121) / 14","label":null,"prefix":null,"suffix":null,"section":"Temperature","hidden":false,"hero":false,"slider":null,"value":3.976190476190476,"display":"3.976"}]},{"id":"kitchen-island-clearance","title":"Kitchen Island Clearance","description":"Calculate total floor footprint including aisle clearance.","category":"design","icon":"layout","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"island_width_inches = 36 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"island_length_inches = 72 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":72,"display":"72"},{"text":"surrounding_aisle_clearance_inches = 42 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":42,"display":"42"},{"text":"total_footprint_square_inches = (island_width_inches + 2 * surrounding_aisle_clearance_inches) * (island_length_inches + 2 * surrounding_aisle_clearance_inches) // sq inches @hero","label":null,"prefix":null,"suffix":"sq inches","section":null,"hidden":false,"hero":true,"slider":null,"value":18720,"display":"18,720"},{"text":"total_footprint_square_feet = total_footprint_square_inches / 144 // sq ft","label":null,"prefix":null,"suffix":"sq ft","section":null,"hidden":false,"hero":false,"slider":null,"value":130,"display":"130"}]},{"id":"knitting-stitch-calculator","title":"Knitting Stitch Calculator","description":"Calculate total stitches needed for a 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20","label":null,"prefix":null,"suffix":null,"section":"Project","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_stitches_per_inch = stitches in swatch / swatch width inches","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"total stitches needed = desired width inches * stitches_per_inch","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"knitting-yarn-weight-gauge","title":"Knitting Yarn Weight Gauge","description":"Calculate yards per 100 grams of yarn from total length and 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days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"reviewProcessDays = 3 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"approvalWaitDays = 1 // day","label":null,"prefix":null,"suffix":"day","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"totalKYCTime = documentCollectionDays + reviewProcessDays + approvalWaitDays // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":6,"display":"6"}]},{"id":"landfill-waste-volume-density","title":"Landfill Waste Volume Density","description":"Calculate the volume of waste based on its weight and 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60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"_stopTimeMinutes = stopsInRoute * timePerStop","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"totalDeliveryTime = transitTimeMinutes + stopTimeMinutes // minutes @hero","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":true,"slider":null,"value":51,"display":"51"}]},{"id":"latent-heat-phase-change","title":"Latent Heat Phase Change","description":"Calculate energy required for a phase change using latent heat of fusion.","category":"education","icon":"book-open","tags":["heat"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"mass = 2 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"latent_heat_of_fusion = 334000 // J/kg (ice to water)","label":null,"prefix":null,"suffix":"J/kg (ice to water)","section":null,"hidden":false,"hero":false,"slider":null,"value":334000,"display":"334,000"},{"text":"energy_required = mass * latent_heat_of_fusion // Joules @hero","label":null,"prefix":null,"suffix":"Joules","section":null,"hidden":false,"hero":true,"slider":null,"value":668000,"display":"668,000"}]},{"id":"law-of-cosines","title":"Law of Cosines","description":"Find the third side of a triangle: c² = a² + b² − 2ab·cos C.","category":"formulas","icon":"triangle","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Two sides and the included angle (degrees)","label":null,"prefix":null,"suffix":null,"section":"Two sides and the included angle 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@label(c²)","label":"c²","prefix":null,"suffix":null,"section":"Third side","hidden":false,"hero":false,"slider":null,"value":38.99999999999999,"display":"39"},{"text":"c = sqrt(c_squared) // @label(Side c)","label":"Side c","prefix":null,"suffix":null,"section":"Third side","hidden":false,"hero":true,"slider":null,"value":6.244997998398397,"display":"6.245"}]},{"id":"law-of-sines","title":"Law of Sines","description":"Solve for an unknown side using the law of sines: a/sin A = b/sin B.","category":"formulas","icon":"triangle","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Known: side a, opposite angle A; angle B opposite unknown side b (degrees)","label":null,"prefix":null,"suffix":null,"section":"Known: side a, opposite angle A; angle B opposite unknown side b (degrees)","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Known: 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b","hidden":false,"hero":true,"slider":null,"value":17.320508075688775,"display":"17.32"}]},{"id":"lawn-mowing-time-estimator","title":"Lawn Mowing Time Estimator","description":"Estimate lawn mowing time from area, mower width, and walking speed.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"lawn_area_square_feet = 5000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"mower_width_inches = 21","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":21,"display":"21"},{"text":"mowing_speed_miles_per_hour = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"mowing_efficiency_percentage = 80","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"mowing_speed_feet_per_minute = mowing_speed_miles_per_hour * 5280 / 60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":264,"display":"264"},{"text":"effective_mower_width_feet = (mower_width_inches / 12) * (mowing_efficiency_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.4,"display":"1.4"},{"text":"area_mowed_per_minute = effective_mower_width_feet * mowing_speed_feet_per_minute","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":369.6,"display":"369.6"},{"text":"estimated_mowing_time_minutes = lawn_area_square_feet / area_mowed_per_minute","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":13.528138528138529,"display":"13.53"}]},{"id":"lcm-least-common-multiple","title":"LCM (Least Common Multiple)","description":"Find the least common multiple of two integers: LCM(a, b) = |a·b| / GCD(a, b).","category":"formulas","icon":"sigma","tags":["number-theory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Two integers","label":null,"prefix":null,"suffix":null,"section":"Two integers","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 12 // 1..10k","label":null,"prefix":null,"suffix":null,"section":"Two integers","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":12,"display":"12"},{"text":"b = 18 // 1..10k","label":null,"prefix":null,"suffix":null,"section":"Two integers","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":18,"display":"18"},{"text":"# LCM","label":null,"prefix":null,"suffix":null,"section":"LCM","hero":false,"slider":null,"value":null,"display":null},{"text":"result = lcm(a, b) // @label(LCM)","label":"LCM","prefix":null,"suffix":null,"section":"LCM","hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"lean-body-mass","title":"Lean Body Mass","description":"Calculate lean body mass using the Boer formula from weight, height, and sex.","category":"health","icon":"activity","tags":["body","mass","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Measurements","label":null,"prefix":null,"suffix":null,"section":"Measurements","hero":false,"slider":null,"value":null,"display":null},{"text":"weight = 180 // lbs 100..400","label":null,"prefix":null,"suffix":"lbs","section":"Measurements","hidden":false,"hero":false,"slider":{"min":100,"max":400,"step":1},"value":180,"display":"180"},{"text":"height = 70 // inches 48..84","label":null,"prefix":null,"suffix":"inches","section":"Measurements","hidden":false,"hero":false,"slider":{"min":48,"max":84,"step":1},"value":70,"display":"70"},{"text":"is male = 1 // dropdown({Male: 1, Female: 0})","label":null,"prefix":null,"suffix":null,"section":"Measurements","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Boer Formula","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"weight kg = weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":81.64656,"display":"81.65"},{"text":"height cm = height * 2.54","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":177.8,"display":"177.8"},{"text":"lean body mass male = 0.407 * weight kg + 0.267 * height cm - 19.2","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":61.50274992,"display":"61.5"},{"text":"lean body mass female = 0.252 * weight kg + 0.473 * height cm - 48.3","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":56.37433312,"display":"56.37"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"lean body mass kg = is male * lean body mass male + (1 - is male) * lean body mass female","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":61.50274992,"display":"61.5"},{"text":"lean body mass lbs = lean body mass kg * 2.20462","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":135.5901925286304,"display":"135.59"}]},{"id":"lease-buyback-analysis","title":"Lease Buyback Analysis","description":"Analyze profit potential of buying out a car lease versus market value.","category":"other","icon":"calculator","tags":["lease"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Lease Buyback","label":null,"prefix":null,"suffix":null,"section":"Lease Buyback","hero":false,"slider":null,"value":null,"display":null},{"text":"$lease residual value = 22000 // 5k..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Lease Buyback","hidden":false,"hero":false,"slider":{"min":5000,"max":100000,"step":500},"value":22000,"display":"$22,000.00"},{"text":"$estimated market value = 26000 // 5k..120k by 500","label":null,"prefix":"$","suffix":null,"section":"Lease Buyback","hidden":false,"hero":false,"slider":{"min":5000,"max":120000,"step":500},"value":26000,"display":"$26,000.00"},{"text":"$purchase fees and taxes = 1800 // 0..10k","label":null,"prefix":"$","suffix":null,"section":"Lease Buyback","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":1800,"display":"$1,800.00"},{"text":"loan interest rate = 6.0 // % 0..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Lease Buyback","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.1},"value":6,"display":"6"},{"text":"loan term = 48 // months 12..84","label":null,"prefix":null,"suffix":"months","section":"Lease Buyback","hidden":false,"hero":false,"slider":{"min":12,"max":84,"step":1},"value":48,"display":"48"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_cost_to_buy = lease residual value + purchase fees and taxes","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":23800,"display":"$23,800.00"},{"text":"$_instant_equity = estimated market value - total_cost_to_buy","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2200,"display":"$2,200.00"},{"text":"_r = loan interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.005,"display":"0.005"},{"text":"$_monthly_loan_payment = total_cost_to_buy * (r * (1 + r)^loan term) / ((1 + r)^loan term - 1)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":558.9436913408782,"display":"$558.94"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$potential profit on resale = estimated market value - total_cost_to_buy // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":2200,"display":"$2,200.00"},{"text":"$total amount paid over loan = monthly_loan_payment * loan term","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":26829.297184362153,"display":"$26,829.30"},{"text":"equity percentage = (instant_equity / estimated market value) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":8.461538461538462,"display":"8.462"},{"text":"decision = if(instant_equity > 0, \"Buyback likely profitable\", \"Market value too low\")","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Buyback likely profitable","display":"Buyback likely profitable"}]},{"id":"led-bulb-co2-reduction","title":"LED Bulb CO2 Reduction","description":"Calculate CO2 and cost savings from switching to LED bulbs.","category":"science","icon":"lightbulb","tags":["eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"old_bulb_watts = 60 // watts","label":null,"prefix":null,"suffix":"watts","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"led_bulb_watts = 9 // watts","label":null,"prefix":null,"suffix":"watts","section":null,"hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"hours_used_per_day = 5 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"days_per_year = 365 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":365,"display":"365"},{"text":"annual_kwh_saved = (old_bulb_watts - led_bulb_watts) * hours_used_per_day * days_per_year / 1000 // kWh","label":null,"prefix":null,"suffix":"kWh","section":null,"hidden":false,"hero":false,"slider":null,"value":93.075,"display":"93.08"},{"text":"co2_per_kwh = 0.4 // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"annual_co2_reduction_kg = annual_kwh_saved * co2_per_kwh // kg CO2 @hero","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":true,"slider":null,"value":37.23,"display":"37.23"}]},{"id":"led-resistor-calculator","title":"Led Resistor Calculator","description":"Calculate required resistor ohms for an LED from supply voltage and current.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"supply_voltage = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"led_forward_voltage = 3.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.2,"display":"3.2"},{"text":"desired_led_current_milliamps = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"required_resistor_ohms = (supply_voltage - led_forward_voltage) / (desired_led_current_milliamps / 1000)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":440,"display":"440"}]},{"id":"legal-fee-hourly-vs-flat-rate","title":"Legal Fee Comparison","description":"Compare total costs between hourly billing and flat rate quotes.","category":"other","icon":"dollar-sign","tags":["fee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"hourlyRate = 250 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"estimatedHours = 10 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"flatRateQuote = 2000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"_totalHourlyCost = hourlyRate * estimatedHours","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":2500,"display":"2,500"},{"text":"savingsWithFlatRate = totalHourlyCost - flatRateQuote // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":500,"display":"500"}]},{"id":"legal-retainer-burn-rate","title":"Legal Retainer Burn Rate","description":"Track how many months your legal retainer will last.","category":"other","icon":"trending-down","tags":["burn"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"initialRetainer = 10000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"monthlyFees = 2500 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2500,"display":"2,500"},{"text":"monthsRemaining = initialRetainer / monthlyFees // months @hero","label":null,"prefix":null,"suffix":"months","section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"lenses-focal-length-equation","title":"Lenses Focal Length Equation","description":"Calculate lens focal length and magnification from object and image distances.","category":"education","icon":"book-open","tags":["equation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"object_distance = 10 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"image_distance = 15 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"focal_length = 1 / (1 / object_distance + 1 / image_distance) // cm @hero","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":true,"slider":null,"value":5.999999999999999,"display":"6"},{"text":"magnification = -image_distance / object_distance // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":-1.5,"display":"-1.5"}]},{"id":"life-expectancy-simple","title":"Life Expectancy Simple","description":"Calculate remaining years, weeks, and days based on current age and life expectancy.","category":"math","icon":"infinity","tags":["life","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Personal Stats","label":null,"prefix":null,"suffix":null,"section":"Personal Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"current age = 30 // 0..100","label":null,"prefix":null,"suffix":null,"section":"Personal Stats","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":30,"display":"30"},{"text":"average life expectancy = 79 // years","label":null,"prefix":null,"suffix":"years","section":"Personal Stats","hidden":false,"hero":false,"slider":null,"value":79,"display":"79"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"remaining years = average life expectancy - current age // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":49,"display":"49"},{"text":"weeks remaining = remaining years * 52.17 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":2556.33,"display":"2,556.33"},{"text":"days remaining = remaining years * 365.25 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":17897.25,"display":"17,897.25"}]},{"id":"life-insurance-needs-estimator","title":"Life Insurance Needs Estimator","description":"Estimate total life insurance needs from income replacement years and total debt.","category":"other","icon":"calculator","tags":["life","insurance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"annual_income = 80000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80000,"display":"80,000"},{"text":"years_to_replace = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"total_debt = 250000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250000,"display":"250,000"},{"text":"total_needs = (annual_income * years_to_replace) + total_debt","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1050000,"display":"1,050,000"}]},{"id":"life-path-number","title":"Life Path Number","description":"Calculate a numerology life path number from birth date digits.","category":"everyday","icon":"smile","tags":["life"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"birth_day = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"birth_month = 6","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"birth_year = 1990","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1990,"display":"1,990"},{"text":"sum_digits = (floor(birth_day / 10) + mod(birth_day, 10)) + (floor(birth_month / 10) + mod(birth_month, 10)) + (floor(birth_year / 1000) + mod(floor(birth_year / 100), 10) + mod(floor(birth_year / 10), 10) + mod(birth_year, 10))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":31,"display":"31"},{"text":"life_path = mod(sum_digits - 1, 9) + 1 // number @hero","label":null,"prefix":null,"suffix":"number","section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"lift-coefficient","title":"Lift Coefficient","description":"Calculate aircraft lift coefficient from lift force, velocity, and wing area.","category":"other","icon":"calculator","tags":["coefficient"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Aerodynamics","label":null,"prefix":null,"suffix":null,"section":"Aerodynamics","hero":false,"slider":null,"value":null,"display":null},{"text":"lift force = 2500 // lbs 100..100k","label":null,"prefix":null,"suffix":"lbs","section":"Aerodynamics","hidden":false,"hero":false,"slider":{"min":100,"max":100000,"step":1000},"value":2500,"display":"2,500"},{"text":"air density = 0.0023769 // slugs/ft3 (standard sea level)","label":null,"prefix":null,"suffix":"slugs/ft3 (standard sea level)","section":"Aerodynamics","hidden":false,"hero":false,"slider":null,"value":0.0023769,"display":"0.002377"},{"text":"velocity = 150 // knots 40..600","label":null,"prefix":null,"suffix":"knots","section":"Aerodynamics","hidden":false,"hero":false,"slider":{"min":40,"max":600,"step":1},"value":150,"display":"150"},{"text":"wing area = 200 // sq ft 50..2k","label":null,"prefix":null,"suffix":"sq ft","section":"Aerodynamics","hidden":false,"hero":false,"slider":{"min":50,"max":2000,"step":20},"value":200,"display":"200"},{"text":"# Formula: Cl = L / (0.5 * rho * v^2 * S)","label":null,"prefix":null,"suffix":null,"section":"Formula: Cl = L / (0.5 * rho * v^2 * S)","hero":false,"slider":null,"value":null,"display":null},{"text":"velocity fps = velocity * 1.68781","label":null,"prefix":null,"suffix":null,"section":"Formula: Cl = L / (0.5 * rho * v^2 * S)","hidden":false,"hero":false,"slider":null,"value":253.1715,"display":"253.17"},{"text":"dynamic pressure = 0.5 * air density * (velocity fps^2)","label":null,"prefix":null,"suffix":null,"section":"Formula: Cl = L / (0.5 * rho * v^2 * S)","hidden":false,"hero":false,"slider":null,"value":76.17466350753853,"display":"76.17"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"lift coefficient = lift force / (dynamic pressure * wing area) // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":0.1640965568395711,"display":"0.1641"},{"text":"# Efficiency","label":null,"prefix":null,"suffix":null,"section":"Efficiency","hero":false,"slider":null,"value":null,"display":null},{"text":"required cl = lift coefficient","label":null,"prefix":null,"suffix":null,"section":"Efficiency","hidden":false,"hero":false,"slider":null,"value":0.1640965568395711,"display":"0.1641"},{"text":"stall cl = 1.5 // typical","label":null,"prefix":null,"suffix":"typical","section":"Efficiency","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"angle of attack estimate = lift coefficient / 0.1 // degrees (linear range)","label":null,"prefix":null,"suffix":"degrees (linear range)","section":"Efficiency","hidden":false,"hero":false,"slider":null,"value":1.640965568395711,"display":"1.641"},{"text":"induced drag coefficient = (lift coefficient^2) / (pi * 0.8 * 9) // estimate","label":null,"prefix":null,"suffix":"estimate","section":"Efficiency","hidden":false,"hero":false,"slider":null,"value":0.001190464825744835,"display":"0.00119"}]},{"id":"lift-to-drag-ratio","title":"Lift to Drag Ratio","description":"Calculate aerodynamic efficiency and glide angle.","category":"engineering","icon":"plane","tags":["engineering","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"lift_force_newtons = 5000 // N","label":null,"prefix":null,"suffix":"N","section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"drag_force_newtons = 250 // N","label":null,"prefix":null,"suffix":"N","section":null,"hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"lift_to_drag_ratio = lift_force_newtons / drag_force_newtons // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"},{"text":"glide_angle_degrees = atan(1 / lift_to_drag_ratio) // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":2.8624052261117474,"display":"2.8624"}]},{"id":"light-exposure-ev","title":"Light Exposure Ev","description":"Calculate photographic exposure value (EV) from f-number, shutter speed, and ISO.","category":"math","icon":"lightbulb","tags":["exposure","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Camera Settings","label":null,"prefix":null,"suffix":null,"section":"Camera Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"f number = 2.8 // 1..64","label":null,"prefix":null,"suffix":null,"section":"Camera Settings","hidden":false,"hero":false,"slider":{"min":1,"max":64,"step":1},"value":2.8,"display":"2.8"},{"text":"shutter speed = 0.01 // seconds (e.g., 1/100)","label":null,"prefix":null,"suffix":"seconds (e.g., 1/100)","section":"Camera Settings","hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"iso = 100 // 50..12.8k","label":null,"prefix":null,"suffix":null,"section":"Camera Settings","hidden":false,"hero":false,"slider":{"min":50,"max":12800,"step":200},"value":100,"display":"100"},{"text":"# EV Formula: log2(N^2 / t)","label":null,"prefix":null,"suffix":null,"section":"EV Formula: log2(N^2 / t)","hero":false,"slider":null,"value":null,"display":null},{"text":"ev at iso one hundred = log2(f number^2 / shutter speed)","label":null,"prefix":null,"suffix":null,"section":"EV Formula: log2(N^2 / t)","hidden":false,"hero":false,"slider":null,"value":9.614709844115207,"display":"9.615"},{"text":"iso adjustment = log2(iso / 100)","label":null,"prefix":null,"suffix":null,"section":"EV Formula: log2(N^2 / t)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"exposure value = ev at iso one hundred - iso adjustment // @hero","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":9.614709844115207,"display":"9.615"},{"text":"# Typical Benchmarks","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hero":false,"slider":null,"value":null,"display":null},{"text":"bright sunny = 15","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"cloudy bright = 13","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":13,"display":"13"},{"text":"indoor home = 5","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"moonlight = -3","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"night street = 8","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"}]},{"id":"limit-evaluation","title":"Limit Evaluation","description":"Evaluate lim x→a [c·xⁿ] = c·aⁿ for continuous polynomial functions.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Function: f(x) = c · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"c = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 2 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":2,"display":"2"},{"text":"a = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"# Limit (substitution for continuous functions)","label":null,"prefix":null,"suffix":null,"section":"Limit (substitution for continuous functions)","hero":false,"slider":null,"value":null,"display":null},{"text":"limit_value = c * a^n // @label(lim f(x))","label":"lim f(x)","prefix":null,"suffix":null,"section":"Limit (substitution for continuous functions)","hidden":false,"hero":true,"slider":null,"value":75,"display":"75"}]},{"id":"line-equation-from-two-points","title":"Line Equation From Two Points","description":"Find the slope and y-intercept of the line through two points.","category":"formulas","icon":"trending-up","tags":["equation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Two points","label":null,"prefix":null,"suffix":null,"section":"Two points","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"y1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"x2 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"y2 = 10 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":10,"display":"10"},{"text":"# Slope and intercept","label":null,"prefix":null,"suffix":null,"section":"Slope and intercept","hero":false,"slider":null,"value":null,"display":null},{"text":"slope = (y2 - y1) / (x2 - x1) // @hero @label(Slope m)","label":"Slope m","prefix":null,"suffix":null,"section":"Slope and intercept","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"},{"text":"y_intercept = y1 - slope * x1 // @hero @label(y-Intercept b)","label":"y-Intercept b","prefix":null,"suffix":null,"section":"Slope and intercept","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"line-height-optimal-typography","title":"Line Height Optimal Typography","description":"Calculate optimal CSS line-height from font size and ratio.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"font_size = 16 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"optimal_ratio = 1.5 // (1.4 to 1.6 recommended)","label":null,"prefix":null,"suffix":"(1.4 to 1.6 recommended)","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"line_height_pixels = font_size * optimal_ratio // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":24,"display":"24"}]},{"id":"linear-regression-slope","title":"Linear Regression Slope","description":"Slope of the least-squares regression line: m = cov(X,Y) / var(X).","category":"formulas","icon":"trending-up","tags":["slope","statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Dataset X","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"x2 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"x3 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"x4 = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"x5 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# Dataset Y","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hero":false,"slider":null,"value":null,"display":null},{"text":"y1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"y2 = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"y3 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"y4 = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"y5 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# Means","label":null,"prefix":null,"suffix":null,"section":"Means","hero":false,"slider":null,"value":null,"display":null},{"text":"_n = 5","label":null,"prefix":null,"suffix":null,"section":"Means","hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"mean_x = (x1 + x2 + x3 + x4 + x5) / n","label":null,"prefix":null,"suffix":null,"section":"Means","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"mean_y = (y1 + y2 + y3 + y4 + y5) / n","label":null,"prefix":null,"suffix":null,"section":"Means","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"# Slope (least squares)","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hero":false,"slider":null,"value":null,"display":null},{"text":"_num = (x1 - mean_x) * (y1 - mean_y) + (x2 - mean_x) * (y2 - mean_y) + (x3 - mean_x) * (y3 - mean_y) + (x4 - mean_x) * (y4 - mean_y) + (x5 - mean_x) * (y5 - mean_y)","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":true,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"_denom = (x1 - mean_x)^2 + (x2 - mean_x)^2 + (x3 - mean_x)^2 + (x4 - mean_x)^2 + (x5 - mean_x)^2","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":true,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"slope = num / denom // @hero","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":false,"hero":true,"slider":null,"value":0.6,"display":"0.6"},{"text":"intercept = mean_y - slope * mean_x // @hero","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":false,"hero":true,"slider":null,"value":2.2,"display":"2.2"}]},{"id":"liquid-net-worth-calculator","title":"Liquid Net Worth Calculator","description":"Calculate liquid net worth from cash, investments, and discounted retirement accounts.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"cash_savings = 15000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"stock_investments = 50000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"retirement_accounts = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"retirement_liquidity_factor = 0.70","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.7,"display":"0.7"},{"text":"liquid_net_worth = cash_savings + stock_investments + (retirement_accounts * retirement_liquidity_factor)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":135000,"display":"135,000"}]},{"id":"livestock-feed-conversion-ratio","title":"Livestock Feed Conversion Ratio","description":"Calculate feed conversion ratio from total feed consumed and weight gained.","category":"finance","icon":"ratio","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"total_feed_consumed_pounds = 500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"total_weight_gain_pounds = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"feed_conversion_ratio = total_feed_consumed_pounds / total_weight_gain_pounds // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"loan-payment","title":"Loan Payment","description":"Monthly payment for a fixed-rate loan: P = L · i / (1 − (1 + i)^−n).","category":"formulas","icon":"dollar-sign","tags":["mortgage","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Loan terms","label":null,"prefix":null,"suffix":null,"section":"Loan terms","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan_amount = 300000 // 1k..10M","label":null,"prefix":"$","suffix":null,"section":"Loan terms","hidden":false,"hero":false,"slider":{"min":1000,"max":10000000,"step":100000},"value":300000,"display":"$300,000.00"},{"text":"annual_rate = 6.5 // % 0..30","label":null,"prefix":null,"suffix":"%","section":"Loan terms","hidden":false,"hero":false,"slider":{"min":0,"max":30,"step":1},"value":6.5,"display":"6.5"},{"text":"$term_years = 30 // 1..50","label":null,"prefix":"$","suffix":null,"section":"Loan terms","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":30,"display":"$30.00"},{"text":"# Monthly payment","label":null,"prefix":null,"suffix":null,"section":"Monthly payment","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly_rate = annual_rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"total_payments = term_years * 12","label":null,"prefix":null,"suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"$monthly_payment = loan_amount * monthly_rate / (1 - (1 + monthly_rate)^(-total_payments)) // @hero","label":null,"prefix":"$","suffix":null,"section":"Monthly payment","hidden":false,"hero":true,"slider":null,"value":1896.2040704788958,"display":"$1,896.20"},{"text":"$total_paid = monthly_payment * total_payments","label":null,"prefix":"$","suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":682633.4653724026,"display":"$682,633.47"},{"text":"$total_interest = total_paid - loan_amount","label":null,"prefix":"$","suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":382633.4653724026,"display":"$382,633.47"}]},{"id":"loan-payoff","title":"Loan Payoff","description":"Find out how long to pay off a loan and how much interest you'll pay total.","category":"finance","icon":"credit-card","tags":["loan","payoff","debt","interest"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Loan Details","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hero":false,"slider":null,"value":null,"display":null},{"text":"current balance = $25000 // 500..200k by 500","label":null,"prefix":"$","suffix":null,"section":"Loan Details","hidden":false,"hero":false,"slider":{"min":500,"max":200000,"step":500},"value":25000,"display":"$25,000.00"},{"text":"annual interest rate = 6.5 // % 0.5..30 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":0.5,"max":30,"step":0.1},"value":6.5,"display":"6.5"},{"text":"monthly payment = $500 // 50..5k by 25","label":null,"prefix":"$","suffix":null,"section":"Loan Details","hidden":false,"hero":false,"slider":{"min":50,"max":5000,"step":25},"value":500,"display":"$500.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly rate = annual_interest_rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"months to pay off = -ln(1 - (current_balance * monthly_rate / monthly_payment)) / ln(1 + monthly_rate)","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":58.46909802580794,"display":"58.47"},{"text":"years to pay off = months_to_pay_off / 12 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":4.872424835483995,"display":"4.872"},{"text":"# Cost Summary","label":null,"prefix":null,"suffix":null,"section":"Cost Summary","hero":false,"slider":null,"value":null,"display":null},{"text":"$total amount paid = monthly_payment * months_to_pay_off","label":null,"prefix":"$","suffix":null,"section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":29234.54901290397,"display":"$29,234.55"},{"text":"$total interest paid = total_amount_paid - current_balance","label":null,"prefix":"$","suffix":null,"section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":4234.54901290397,"display":"$4,234.55"},{"text":"interest as pct of principal = (total_interest_paid / current_balance) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":16.93819605161588,"display":"16.94"}]},{"id":"loan-target-payoff","title":"Loan: Target a Payoff Date","description":"Standard loan math says monthly payment P = L · r / (1 − (1+r)^−n). Want to be debt-free by year 7 — what monthly payment do you need?","category":"finance","icon":"dollar-sign","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Loan setup","label":null,"prefix":null,"suffix":null,"section":"Loan setup","hero":false,"slider":null,"value":null,"display":null},{"text":"loan = 250000 // 1k..1M — principal ($)","label":null,"prefix":null,"suffix":"1k..1M — principal ($)","section":"Loan setup","hidden":false,"hero":false,"slider":null,"value":250000,"display":"250,000"},{"text":"apr = 0.065 // 0..0.2 — annual rate","label":null,"prefix":null,"suffix":"0..0.2 — annual rate","section":"Loan setup","hidden":false,"hero":false,"slider":null,"value":0.065,"display":"0.065"},{"text":"years = 7 // 1..30 — payoff target","label":null,"prefix":null,"suffix":"1..30 — payoff target","section":"Loan setup","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"# Derived","label":null,"prefix":null,"suffix":null,"section":"Derived","hero":false,"slider":null,"value":null,"display":null},{"text":"_r = apr / 12","label":null,"prefix":null,"suffix":null,"section":"Derived","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"_n = years * 12","label":null,"prefix":null,"suffix":null,"section":"Derived","hidden":true,"hero":false,"slider":null,"value":84,"display":"84"},{"text":"# Required payment (closed-form)","label":null,"prefix":null,"suffix":null,"section":"Required payment (closed-form)","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly = loan * _r / (1 - (1 + _r)^(-_n))","label":null,"prefix":null,"suffix":null,"section":"Required payment (closed-form)","hidden":false,"hero":false,"slider":null,"value":3712.359117957795,"display":"3,712.36"},{"text":"# Total interest paid over the loan","label":null,"prefix":null,"suffix":null,"section":"Total interest paid over the loan","hero":false,"slider":null,"value":null,"display":null},{"text":"total_interest = monthly * _n - loan","label":null,"prefix":null,"suffix":null,"section":"Total interest paid over the loan","hidden":false,"hero":false,"slider":null,"value":61838.1659084548,"display":"61,838.17"},{"text":"# Visualize remaining balance over time","label":null,"prefix":null,"suffix":null,"section":"Visualize remaining balance over time","hero":false,"slider":null,"value":null,"display":null},{"text":"balance = t => loan * ((1 + _r)^_n - (1 + _r)^t) / ((1 + _r)^_n - 1)","label":null,"prefix":null,"suffix":null,"section":"Visualize remaining balance over time","hidden":false,"hero":true,"slider":null,"value":{"type":"function","params":["t"],"body":["div",["mul",["parenExpr",{"type":"id","value":"loan","text":"loan","offset":16,"lineBreaks":0,"line":1,"col":17,"canonicalName":"loan"}],["parenExpr",["sub",["power",["parenExpr",["add",{"type":"decimal","value":"1","text":"1","offset":26,"lineBreaks":0,"line":1,"col":27},["parenExpr",{"type":"id","value":"r","text":"r","offset":31,"lineBreaks":0,"line":1,"col":32,"canonicalName":"r"}]]],["parenExpr",{"type":"id","value":"n","text":"n","offset":36,"lineBreaks":0,"line":1,"col":37,"canonicalName":"n"}]],["power",["parenExpr",["add",{"type":"decimal","value":"1","text":"1","offset":42,"lineBreaks":0,"line":1,"col":43},["parenExpr",{"type":"id","value":"r","text":"r","offset":47,"lineBreaks":0,"line":1,"col":48,"canonicalName":"r"}]]],["parenExpr",{"type":"id","value":"t","text":"t","offset":52,"lineBreaks":0,"line":1,"col":53,"canonicalName":"t"}]]]]],["parenExpr",["sub",["power",["parenExpr",["add",{"type":"decimal","value":"1","text":"1","offset":60,"lineBreaks":0,"line":1,"col":61},["parenExpr",{"type":"id","value":"r","text":"r","offset":65,"lineBreaks":0,"line":1,"col":66,"canonicalName":"r"}]]],["parenExpr",{"type":"id","value":"n","text":"n","offset":70,"lineBreaks":0,"line":1,"col":71,"canonicalName":"n"}]],{"type":"decimal","value":"1","text":"1","offset":75,"lineBreaks":0,"line":1,"col":76}]]],"name":"balance"},"display":null},{"text":"# Same answer via goalseek — fix payment, solve for years.","label":null,"prefix":null,"suffix":null,"section":"Same answer via goalseek — fix payment, solve for years.","hero":false,"slider":null,"value":null,"display":null},{"text":"# Uncomment to find: \"if I can only afford $X/month, when am I done?\"","label":null,"prefix":null,"suffix":null,"section":"Uncomment to find: \"if I can only afford $X/month, when am I done?\"","hero":false,"slider":null,"value":null,"display":null},{"text":"# target_monthly = 2500","label":null,"prefix":null,"suffix":null,"section":"target_monthly = 2500","hero":false,"slider":null,"value":null,"display":null},{"text":"# set monthly = target_monthly using years","label":null,"prefix":null,"suffix":null,"section":"set monthly = target_monthly using years","hero":false,"slider":null,"value":null,"display":null}]},{"id":"loan-to-value-ratio-advanced","title":"Loan-to-Value Ratio","description":"Calculate the current LTV ratio based on loan balance and value.","category":"real-estate","icon":"percent","tags":["loan"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"mortgageBalance = 240000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":240000,"display":"240,000"},{"text":"appraisedValue = 300000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"ltvPercent = (mortgageBalance / appraisedValue) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"logarithm-any-base","title":"Logarithm Any Base","description":"Compute log base b of x: log_b(x) = ln(x) / ln(b).","category":"formulas","icon":"sigma","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"x = 100 // 0.001..1M","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"base = 10 // 2..1k","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":2,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"result = log(x) / log(base) // @label(log_b(x))","label":"log_b(x)","prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"logarithm-base-10","title":"Logarithm Base 10","description":"Calculate the base-10 logarithm of a number.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"number = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"result = log10(number)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"logic-gate-propagation-delay","title":"Logic Gate Propagation Delay","description":"Calculate total delay and max frequency for logic paths.","category":"engineering","icon":"cpu","tags":["engineering","electronics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"number_of_gates_in_path = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"delay_per_gate_nanoseconds = 0.5 // ns","label":null,"prefix":null,"suffix":"ns","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"total_propagation_delay_nanoseconds = number_of_gates_in_path * delay_per_gate_nanoseconds // ns @hero","label":null,"prefix":null,"suffix":"ns","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"max_frequency_mhz = 1000 / total_propagation_delay_nanoseconds // MHz","label":null,"prefix":null,"suffix":"MHz","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"}]},{"id":"logistics-labor-productivity","title":"Logistics Labor Productivity","description":"Measure units processed per labor hour in your warehouse.","category":"business","icon":"users","tags":["logistics","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"totalUnitsProcessed = 10000 // units","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"totalLaborHours = 500 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"productivityRate = totalUnitsProcessed / totalLaborHours // units per hour @hero","label":null,"prefix":null,"suffix":"units per hour","section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"loot-drop-probability","title":"Loot Drop Probability","description":"Calculate the probability of getting a specific loot drop.","category":"math","icon":"gift","tags":["gaming","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Loot Settings","label":null,"prefix":null,"suffix":null,"section":"Loot Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base drop rate percent = 2 // %","label":null,"prefix":null,"suffix":"%","section":"Loot Settings","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"luck stat = 50","label":null,"prefix":null,"suffix":null,"section":"Loot Settings","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"luck multiplier = 0.01","label":null,"prefix":null,"suffix":null,"section":"Loot Settings","hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"adjusted drop rate percent = base drop rate percent * (1 + (luck stat * luck multiplier))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"loss-aversion-impact","title":"Loss Aversion Impact","description":"Quantify perceived pain from loss using a loss-aversion coefficient.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"potential_gain = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"potential_loss = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"loss_aversion_coefficient = 2.25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.25,"display":"2.25"},{"text":"perceived_pain = potential_loss * loss_aversion_coefficient // perceived units of pain @hero","label":null,"prefix":null,"suffix":"perceived units of pain","section":null,"hidden":false,"hero":true,"slider":null,"value":225,"display":"225"},{"text":"perceived_pleasure = potential_gain","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"}]},{"id":"lottery-odds-calculator","title":"Lottery Odds Calculator","description":"Calculate lottery odds (1-in-X) for picking k correct numbers from n.","category":"other","icon":"calculator","tags":["odds"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Lottery Parameters","label":null,"prefix":null,"suffix":null,"section":"Lottery Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 49 // total numbers e.g. 49","label":null,"prefix":null,"suffix":"total numbers e.g. 49","section":"Lottery Parameters","hidden":false,"hero":false,"slider":null,"value":49,"display":"49"},{"text":"k = 6 // picks e.g. 6","label":null,"prefix":null,"suffix":"picks e.g. 6","section":"Lottery Parameters","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"# Calculation — combinations n! / (k! * (n-k)!)","label":null,"prefix":null,"suffix":null,"section":"Calculation — combinations n! / (k! * (n-k)!)","hero":false,"slider":null,"value":null,"display":null},{"text":"# For 6 of 49, it is roughly 1 in 13.9M","label":null,"prefix":null,"suffix":null,"section":"For 6 of 49, it is roughly 1 in 13.9M","hero":false,"slider":null,"value":null,"display":null},{"text":"odds = factorial(n) / (factorial(k) * factorial(n - k)) // 1 in X","label":null,"prefix":null,"suffix":"1 in X","section":"For 6 of 49, it is roughly 1 in 13.9M","hidden":false,"hero":true,"slider":null,"value":13983816.000000006,"display":"13,983,816"}]},{"id":"ltv-ratio","title":"Ltv Ratio","description":"Calculate loan-to-value (LTV) ratio and equity from loan amount and property value.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.446Z"},"rows":[{"text":"# Loan and Value","label":null,"prefix":null,"suffix":null,"section":"Loan and Value","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = 320000 // 10k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Loan and Value","hidden":false,"hero":false,"slider":{"min":10000,"max":1000000,"step":5000},"value":320000,"display":"$320,000.00"},{"text":"$appraised property value = 400000 // 10k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Loan and Value","hidden":false,"hero":false,"slider":{"min":10000,"max":1000000,"step":5000},"value":400000,"display":"$400,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"loan to value ratio = (loan amount / appraised property value) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":80,"display":"80"},{"text":"$equity in property = appraised property value - loan amount","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":80000,"display":"$80,000.00"},{"text":"status = if(loan to value ratio > 80, \"PMI likely required\", \"Standard loan\")","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Standard loan","display":"Standard loan"}]},{"id":"lumber-estimator","title":"Lumber Estimator","description":"Calculate board feet and lumber costs for your woodworking project.","category":"construction","icon":"hammer","tags":["woodworking"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Board Dimensions","label":null,"prefix":null,"suffix":null,"section":"Board Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"board length = 8 // ft 2..20","label":null,"prefix":null,"suffix":"ft","section":"Board Dimensions","hidden":false,"hero":false,"slider":{"min":2,"max":20,"step":0.2},"value":8,"display":"8"},{"text":"nominal width = 6 // in 2..12","label":null,"prefix":null,"suffix":"in","section":"Board Dimensions","hidden":false,"hero":false,"slider":{"min":2,"max":12,"step":0.1},"value":6,"display":"6"},{"text":"nominal thickness = 2 // in 1..6","label":null,"prefix":null,"suffix":"in","section":"Board Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":2,"display":"2"},{"text":"# Quantity","label":null,"prefix":null,"suffix":null,"section":"Quantity","hero":false,"slider":null,"value":null,"display":null},{"text":"number of boards = 24 // 1..200","label":null,"prefix":null,"suffix":null,"section":"Quantity","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":24,"display":"24"},{"text":"# Board Feet","label":null,"prefix":null,"suffix":null,"section":"Board Feet","hero":false,"slider":null,"value":null,"display":null},{"text":"board feet per board = (nominal_thickness * nominal_width * board_length * 12) / 144","label":null,"prefix":null,"suffix":null,"section":"Board Feet","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"total board feet = board_feet_per_board * number_of_boards // @hero","label":null,"prefix":null,"suffix":null,"section":"Board Feet","hidden":false,"hero":true,"slider":null,"value":192,"display":"192"},{"text":"# Cost","label":null,"prefix":null,"suffix":null,"section":"Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$price per board foot = 6.50 // 1..25 by 0.25","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":{"min":1,"max":25,"step":0.25},"value":6.5,"display":"$6.50"},{"text":"$total lumber cost = total_board_feet * price_per_board_foot","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":null,"value":1248,"display":"$1,248.00"},{"text":"waste allowance = 15 // % 0..30","label":null,"prefix":null,"suffix":"%","section":"Cost","hidden":false,"hero":false,"slider":{"min":0,"max":30,"step":1},"value":15,"display":"15"},{"text":"$cost with waste = total_lumber_cost * (1 + waste_allowance / 100)","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":null,"value":1435.2,"display":"$1,435.20"}]},{"id":"lunar-phase-percentage","title":"Lunar Phase Percentage","description":"Calculate moon illumination percentage from days since the last new moon.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"days_since_new_moon = 14.7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14.7,"display":"14.7"},{"text":"lunar_cycle_days = 29.53","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":29.53,"display":"29.53"},{"text":"illumination_percentage = (1 - cos(2 * pi * days_since_new_moon / lunar_cycle_days)) / 2 * 100 // percent illuminated @suffix(%) @hero","label":null,"prefix":null,"suffix":"percent illuminated","section":null,"hidden":false,"hero":true,"slider":null,"value":0.07448252690752,"display":"0.0745"}]},{"id":"mac-address-format","title":"Mac Address Format","description":"Calculate the total number of possible MAC addresses from 48-bit address space.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# MAC address is 48 bits","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hero":false,"slider":null,"value":null,"display":null},{"text":"_bits = 48","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hidden":true,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"total possible addresses = 2 ^ bits","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hidden":false,"hero":true,"slider":null,"value":281474976710656,"display":"281,474,976,710,656"},{"text":"_oui_bits = 24 // Organizationally Unique Identifier","label":null,"prefix":null,"suffix":"Organizationally Unique Identifier","section":"MAC address is 48 bits","hidden":true,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"_nic_specific_bits = 24","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hidden":true,"hero":false,"slider":null,"value":24,"display":"24"}]},{"id":"mach-number-supersonic","title":"Mach Number Supersonic","description":"Calculate Mach number based on speed and altitude.","category":"science","icon":"plane","tags":["science","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"object_speed_m_per_s = 600 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":600,"display":"600"},{"text":"ambient_temperature_celsius = -50 // C (high altitude)","label":null,"prefix":null,"suffix":"C (high altitude)","section":null,"hidden":false,"hero":false,"slider":null,"value":-50,"display":"-50"},{"text":"speed_of_sound = 331.3 * ((1 + ambient_temperature_celsius / 273.15)^0.5) // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":299.44652601450616,"display":"299.45"},{"text":"mach_number = object_speed_m_per_s / speed_of_sound // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.003696646562312,"display":"2.004"}]},{"id":"macro-tracker","title":"Macro Tracker","description":"Split your daily calories into protein, carbs, and fat gram targets.","category":"health","icon":"chart-pie","tags":["protein"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Daily Targets","label":null,"prefix":null,"suffix":null,"section":"Daily Targets","hero":false,"slider":null,"value":null,"display":null},{"text":"daily calorie target = 2000 // cal 1k..5k","label":null,"prefix":null,"suffix":"cal","section":"Daily Targets","hidden":false,"hero":false,"slider":{"min":1000,"max":5000,"step":50},"value":2000,"display":"2,000"},{"text":"# Macro Split","label":null,"prefix":null,"suffix":null,"section":"Macro Split","hero":false,"slider":null,"value":null,"display":null},{"text":"protein pct = 30 // % 5..60","label":null,"prefix":null,"suffix":"%","section":"Macro Split","hidden":false,"hero":false,"slider":{"min":5,"max":60,"step":1},"value":30,"display":"30"},{"text":"carbs pct = 40 // % 5..70","label":null,"prefix":null,"suffix":"%","section":"Macro Split","hidden":false,"hero":false,"slider":{"min":5,"max":70,"step":1},"value":40,"display":"40"},{"text":"fat pct = 100 - protein_pct - carbs_pct // %","label":null,"prefix":null,"suffix":"%","section":"Macro Split","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# Grams Per Day","label":null,"prefix":null,"suffix":null,"section":"Grams Per Day","hero":false,"slider":null,"value":null,"display":null},{"text":"protein = daily calorie target * protein pct / 100 / 4 // g @hero","label":null,"prefix":null,"suffix":"g","section":"Grams Per Day","hidden":false,"hero":true,"slider":null,"value":150,"display":"150"},{"text":"carbs = daily calorie target * carbs pct / 100 / 4 // g","label":null,"prefix":null,"suffix":"g","section":"Grams Per Day","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"fat = daily calorie target * fat pct / 100 / 9 // g","label":null,"prefix":null,"suffix":"g","section":"Grams Per Day","hidden":false,"hero":false,"slider":null,"value":66.66666666666667,"display":"66.67"},{"text":"# Calorie Check","label":null,"prefix":null,"suffix":null,"section":"Calorie Check","hero":false,"slider":null,"value":null,"display":null},{"text":"total calories check = protein * 4 + carbs * 4 + fat * 9 // cal","label":null,"prefix":null,"suffix":"cal","section":"Calorie Check","hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"}]},{"id":"magic-formula-investing-rank","title":"Magic Formula Investing Rank","description":"Calculate a Magic Formula investing composite score from earnings yield and ROC.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"earnings_yield = 0.12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"return_on_capital = 0.25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"composite_score = earnings_yield + return_on_capital","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.37,"display":"0.37"}]},{"id":"magnetic-force-moving-charge","title":"Magnetic Force Moving Charge","description":"Calculate magnetic force on a moving charged particle in a magnetic field.","category":"education","icon":"book-open","tags":["charge"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"charge = 1.6e-19 // Coulombs (proton)","label":null,"prefix":null,"suffix":"Coulombs (proton)","section":null,"hidden":false,"hero":false,"slider":null,"value":1.6e-19,"display":"1.6e-19"},{"text":"velocity = 1e6 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"magnetic_field = 0.5 // Tesla","label":null,"prefix":null,"suffix":"Tesla","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"angle_degrees = 90 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":90,"display":"90"},{"text":"magnetic_force = charge * velocity * magnetic_field * sin(angle_degrees) // Newtons @hero","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":true,"slider":null,"value":8e-14,"display":"8e-14"}]},{"id":"marathon-split-projector","title":"Marathon Split Projector","description":"Calculate per-mile split time needed to finish a marathon at a target time.","category":"productivity","icon":"clock","tags":["marathon","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"target_finish_time_hours = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"target_finish_time_minutes = 0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"total_minutes = (target_finish_time_hours * 60) + target_finish_time_minutes","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":240,"display":"240"},{"text":"mile_split_minutes = total_minutes / 26.2 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":9.16030534351145,"display":"9.16"}]},{"id":"marketing-cpa-calculator","title":"Marketing Cpa Calculator","description":"Calculate cost per acquisition (CPA) from total ad spend and conversions.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"total_ad_spend = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"total_conversions = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"cost_per_acquisition = total_ad_spend / total_conversions","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"markup-calculator","title":"Markup Calculator","description":"Calculate selling price, profit, and margin from cost and markup.","category":"business","icon":"tag","tags":["profit"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Product Cost","label":null,"prefix":null,"suffix":null,"section":"Product Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$cost = 45 // 0.01..10k","label":null,"prefix":"$","suffix":null,"section":"Product Cost","hidden":false,"hero":false,"slider":{"min":0.01,"max":10000,"step":100},"value":45,"display":"$45.00"},{"text":"markup percent = 60 // % 0..500","label":null,"prefix":null,"suffix":"%","section":"Product Cost","hidden":false,"hero":false,"slider":{"min":0,"max":500,"step":1},"value":60,"display":"60"},{"text":"# Selling Price","label":null,"prefix":null,"suffix":null,"section":"Selling Price","hero":false,"slider":null,"value":null,"display":null},{"text":"$markup amount = round(cost * markup percent / 100 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Selling Price","hidden":false,"hero":false,"slider":null,"value":27,"display":"$27.00"},{"text":"$selling price = round((cost + markup amount) * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Selling Price","hidden":false,"hero":true,"slider":null,"value":72,"display":"$72.00"},{"text":"$profit per unit = markup amount","label":null,"prefix":"$","suffix":null,"section":"Selling Price","hidden":false,"hero":false,"slider":null,"value":27,"display":"$27.00"},{"text":"# Margin Analysis","label":null,"prefix":null,"suffix":null,"section":"Margin Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"margin percent = round((markup amount / selling price) * 100 * 10) / 10 // %","label":null,"prefix":null,"suffix":"%","section":"Margin Analysis","hidden":false,"hero":false,"slider":null,"value":37.5,"display":"37.5"},{"text":"multiplier = round(selling price / cost * 100) / 100 // @label(Price multiplier)","label":"Price multiplier","prefix":null,"suffix":null,"section":"Margin Analysis","hidden":false,"hero":false,"slider":null,"value":1.6,"display":"1.6"},{"text":"# Volume","label":null,"prefix":null,"suffix":null,"section":"Volume","hero":false,"slider":null,"value":null,"display":null},{"text":"units sold = 100 // 1..10k","label":null,"prefix":null,"suffix":null,"section":"Volume","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":100,"display":"100"},{"text":"$total revenue = selling price * units sold","label":null,"prefix":"$","suffix":null,"section":"Volume","hidden":false,"hero":false,"slider":null,"value":7200,"display":"$7,200.00"},{"text":"$total profit = profit per unit * units sold","label":null,"prefix":"$","suffix":null,"section":"Volume","hidden":false,"hero":false,"slider":null,"value":2700,"display":"$2,700.00"}]},{"id":"mars-weight-comparison","title":"Mars Weight Comparison","description":"Calculate your equivalent weight on Mars from Earth weight and gravity ratio.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"earth_weight_pounds = 150","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"mars_gravity_ratio = 0.376","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.376,"display":"0.376"},{"text":"mars_weight = earth_weight_pounds * mars_gravity_ratio // pounds on Mars @hero","label":null,"prefix":null,"suffix":"pounds on Mars","section":null,"hidden":false,"hero":true,"slider":null,"value":56.4,"display":"56.4"}]},{"id":"mash-tun-water-volume","title":"Mash Tun Water Volume","description":"Calculate strike water gallons needed for a beer mash from grain weight and ratio.","category":"health","icon":"droplet","tags":["water","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"grain_weight_pounds = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"water_to_grain_ratio_quarts_per_pound = 1.25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.25,"display":"1.25"},{"text":"total_strike_water_gallons = (grain_weight_pounds * water_to_grain_ratio_quarts_per_pound) / 4 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3.75,"display":"3.75"}]},{"id":"matchstick-burn-speed","title":"Matchstick Burn Speed","description":"Calculate matchstick burn speed in cm per second from length and burn time.","category":"everyday","icon":"smile","tags":["burn"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"match_length_cm = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"burn_time_seconds = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"burn_speed_cm_per_s = match_length_cm / burn_time_seconds // cm per second @hero","label":null,"prefix":null,"suffix":"cm per second","section":null,"hidden":false,"hero":true,"slider":null,"value":0.2,"display":"0.2"}]},{"id":"math-notation-demo","title":"Math Notation with LaTeX","description":"Instacalc renders **LaTeX math** in any text row using `$...$` for inline and `$$...$$` for display equations.","category":"formulas","icon":"sigma","tags":["math","latex"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Quadratic Formula","label":null,"prefix":null,"suffix":null,"section":"Quadratic Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 1","label":null,"prefix":null,"suffix":null,"section":"Quadratic Formula","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"b = -5","label":null,"prefix":null,"suffix":null,"section":"Quadratic Formula","hidden":false,"hero":false,"slider":null,"value":-5,"display":"-5"},{"text":"c = 6","label":null,"prefix":null,"suffix":null,"section":"Quadratic 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299792458","label":null,"prefix":null,"suffix":null,"section":"Energy-Mass Equivalence","hidden":false,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"energy_joules = mass_kg * c_ms^2","label":null,"prefix":null,"suffix":null,"section":"Energy-Mass Equivalence","hidden":false,"hero":false,"slider":null,"value":89875517873681760,"display":"89,875,517,873,681,760"},{"text":"# Pythagorean Theorem","label":null,"prefix":null,"suffix":null,"section":"Pythagorean Theorem","hero":false,"slider":null,"value":null,"display":null},{"text":"leg_a = 3","label":null,"prefix":null,"suffix":null,"section":"Pythagorean Theorem","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"leg_b = 4","label":null,"prefix":null,"suffix":null,"section":"Pythagorean Theorem","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"hypotenuse = sqrt(leg_a^2 + leg_b^2)","label":null,"prefix":null,"suffix":null,"section":"Pythagorean 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-100..100","label":null,"prefix":null,"suffix":null,"section":"Matrix B [[e, f], [g, h]]","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":8,"display":"8"},{"text":"# Product C = A · B","label":null,"prefix":null,"suffix":null,"section":"Product C = A · B","hero":false,"slider":null,"value":null,"display":null},{"text":"c00 = a * e + b * g // @hero @label(C[0,0])","label":"C[0,0]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":19,"display":"19"},{"text":"c01 = a * f + b * h // @hero @label(C[0,1])","label":"C[0,1]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":22,"display":"22"},{"text":"c10 = c * e + d * g // @hero @label(C[1,0])","label":"C[1,0]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":43,"display":"43"},{"text":"c11 = c * f + d * h // @hero @label(C[1,1])","label":"C[1,1]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"}]},{"id":"maximum-allowable-offer","title":"Maximum Allowable Offer","description":"Calculate the maximum price an investor should pay for a flip.","category":"real-estate","icon":"shopping-cart","tags":["real-estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"afterRepairValue = 300000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"repairCosts = 40000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":40000,"display":"40,000"},{"text":"profitMarginPercentage = 70 // 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20 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":20,"display":"20"},{"text":"x3 = 30 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":30,"display":"30"},{"text":"x4 = 40 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":40,"display":"40"},{"text":"x5 = 50 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":50,"display":"50"},{"text":"# Mean","label":null,"prefix":null,"suffix":null,"section":"Mean","hero":false,"slider":null,"value":null,"display":null},{"text":"_n = 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0.2})","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"pounds_per_hour = 2 * smoker_type_offset","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total_wood_pounds = smoke_time_hours * pounds_per_hour // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12,"display":"12"}]},{"id":"mechanical-torque-lever-arm","title":"Mechanical Torque Lever Arm","description":"Calculate mechanical torque from force, lever arm length, and angle.","category":"education","icon":"book-open","tags":["mechanical"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"force = 50 // Newtons","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"lever_arm_length = 2 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"angle_degrees = 90 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":90,"display":"90"},{"text":"torque = force * lever_arm_length * sin(angle_degrees) // Newton-meters @hero","label":null,"prefix":null,"suffix":"Newton-meters","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"median","title":"Median (5 values)","description":"Find the median of 5 values — the middle value after sorting. Enter values in any order.","category":"formulas","icon":"sigma","tags":["statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Data points (any order)","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 7 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":7,"display":"7"},{"text":"x2 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"x3 = 9 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":9,"display":"9"},{"text":"x4 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"x5 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# For n=5 the median is the 3rd-largest value: take max-of-every 3-element min.","label":null,"prefix":null,"suffix":null,"section":"For n=5 the median is the 3rd-largest value: take max-of-every 3-element min.","hero":false,"slider":null,"value":null,"display":null},{"text":"median = max(min(x1, x2, x3), min(x1, x2, x4), min(x1, x2, x5), min(x1, x3, x4), min(x1, x3, x5), min(x1, x4, x5), min(x2, x3, x4), min(x2, x3, x5), min(x2, x4, x5), min(x3, x4, x5))","label":null,"prefix":null,"suffix":null,"section":"For n=5 the median is the 3rd-largest value: take max-of-every 3-element 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Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"weight kg = patient weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":74.84268,"display":"74.84"},{"text":"total dosage = dosage per kg * weight kg // mg @hero","label":null,"prefix":null,"suffix":"mg","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":1122.6402,"display":"1,122.64"},{"text":"# Liquid Form (Optional)","label":null,"prefix":null,"suffix":null,"section":"Liquid Form (Optional)","hero":false,"slider":null,"value":null,"display":null},{"text":"concentration = 100 // mg per 5ml","label":null,"prefix":null,"suffix":"mg per 5ml","section":"Liquid Form (Optional)","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"volume needed = (total dosage / concentration) * 5 // ml","label":null,"prefix":null,"suffix":"ml","section":"Liquid Form (Optional)","hidden":false,"hero":false,"slider":null,"value":56.13201,"display":"56.13"},{"text":"total grams = total dosage / 1000","label":null,"prefix":null,"suffix":null,"section":"Liquid Form (Optional)","hidden":false,"hero":false,"slider":null,"value":1.1226402,"display":"1.123"}]},{"id":"meeting-cost-person-hour-total","title":"Meeting Cost Person Hour Total","description":"Calculate the total dollar cost of a meeting from attendees, rate, and duration.","category":"productivity","icon":"clock","tags":["meeting"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"number_of_attendees = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"average_hourly_rate = 75 // dollars per hour","label":null,"prefix":null,"suffix":"dollars per 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@hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1500,"display":"1,500"}]},{"id":"megapixels-to-print-dimensions","title":"Megapixels To Print Dimensions","description":"Calculate maximum print dimensions in inches from camera megapixels and DPI.","category":"design","icon":"palette","tags":["print"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"megapixels = 24 // MP","label":null,"prefix":null,"suffix":"MP","section":null,"hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"aspect_ratio_width = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"aspect_ratio_height = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"dpi = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"_total_pixels = megapixels * 1000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":24000000,"display":"24,000,000"},{"text":"_pixel_width = sqrt(total_pixels * (aspect_ratio_width / aspect_ratio_height))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":6000,"display":"6,000"},{"text":"_pixel_height = total_pixels / pixel_width","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":4000,"display":"4,000"},{"text":"print_width_inches = pixel_width / dpi // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"},{"text":"print_height_inches = pixel_height / dpi // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":13.333333333333334,"display":"13.33"}]},{"id":"memory-retention-forgetting-curve","title":"Memory Retention Forgetting Curve","description":"Calculate retention percentage after time elapsed using the forgetting curve.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"time_days = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"retention_base = 0.9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.9,"display":"0.9"},{"text":"retention = retention_base * exp(-time_days / 10) // retention percentage @hero","label":null,"prefix":null,"suffix":"retention 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Watts","label":null,"prefix":null,"suffix":null,"section":"Conversion to Watts","hero":false,"slider":null,"value":null,"display":null},{"text":"_joules_per_kcal = 4184","label":null,"prefix":null,"suffix":null,"section":"Conversion to Watts","hidden":true,"hero":false,"slider":null,"value":4184,"display":"4,184"},{"text":"_seconds_per_day = 86400","label":null,"prefix":null,"suffix":null,"section":"Conversion to Watts","hidden":true,"hero":false,"slider":null,"value":86400,"display":"86,400"},{"text":"watts at rest = round(daily kcal * joules_per_kcal / seconds_per_day, 1) // W @label(Heat output at rest)","label":"Heat output at rest","prefix":null,"suffix":"W","section":"Conversion to Watts","hidden":false,"hero":false,"slider":null,"value":101.7,"display":"101.7"},{"text":"watts active = round(watts at rest * activity factor, 1) // W @hero @label(Heat output now)","label":"Heat output now","prefix":null,"suffix":"W","section":"Conversion to Watts","hidden":false,"hero":true,"slider":null,"value":101.7,"display":"101.7"},{"text":"# Room Heating","label":null,"prefix":null,"suffix":null,"section":"Room Heating","hero":false,"slider":null,"value":null,"display":null},{"text":"people in room = 10 // 1..200","label":null,"prefix":null,"suffix":null,"section":"Room Heating","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":10,"display":"10"},{"text":"total watts = round(watts active * people in room, 0) // W @label(Total body heat in room)","label":"Total body heat in room","prefix":null,"suffix":"W","section":"Room Heating","hidden":false,"hero":false,"slider":null,"value":1017,"display":"1,017"},{"text":"btu per hour = round(total watts * 3.412, 0) // BTU/hr @label(Equivalent BTU/hr)","label":"Equivalent BTU/hr","prefix":null,"suffix":"BTU/hr","section":"Room Heating","hidden":false,"hero":false,"slider":null,"value":3470,"display":"3,470"}]},{"id":"methane-emissions-from-landfill","title":"Methane 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= 1.25 // 0.1..1.4","label":null,"prefix":null,"suffix":null,"section":"Optics","hidden":false,"hero":false,"slider":{"min":0.1,"max":1.4,"step":0.02},"value":1.25,"display":"1.25"},{"text":"# Abbe Resolution Limit: d = lambda / (2 * NA)","label":null,"prefix":null,"suffix":null,"section":"Abbe Resolution Limit: d = lambda / (2 * NA)","hero":false,"slider":null,"value":null,"display":null},{"text":"resolution limit = light wavelength / (2 * numerical aperture) // nm @hero","label":null,"prefix":null,"suffix":"nm","section":"Abbe Resolution Limit: d = lambda / (2 * NA)","hidden":false,"hero":true,"slider":null,"value":220,"display":"220"},{"text":"# Theoretical Limits","label":null,"prefix":null,"suffix":null,"section":"Theoretical Limits","hero":false,"slider":null,"value":null,"display":null},{"text":"resolution in microns = resolution limit / 1000","label":null,"prefix":null,"suffix":null,"section":"Theoretical Limits","hidden":false,"hero":false,"slider":null,"value":0.22,"display":"0.22"},{"text":"max useful magnification = 1000 * numerical aperture","label":null,"prefix":null,"suffix":null,"section":"Theoretical Limits","hidden":false,"hero":false,"slider":null,"value":1250,"display":"1,250"},{"text":"empty magnification point = max useful magnification * 2","label":null,"prefix":null,"suffix":null,"section":"Theoretical Limits","hidden":false,"hero":false,"slider":null,"value":2500,"display":"2,500"},{"text":"pixel size target = (resolution limit / 2) // Nyquist","label":null,"prefix":null,"suffix":"Nyquist","section":"Theoretical Limits","hidden":false,"hero":false,"slider":null,"value":110,"display":"110"}]},{"id":"mid-point-calculator","title":"Mid Point Calculator","description":"Calculate the midpoint of two (x, y) coordinates.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Point 1","label":null,"prefix":null,"suffix":null,"section":"Point 1","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 0 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 1","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":0,"display":"0"},{"text":"y1 = 0 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 1","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":0,"display":"0"},{"text":"# Point 2","label":null,"prefix":null,"suffix":null,"section":"Point 2","hero":false,"slider":null,"value":null,"display":null},{"text":"x2 = 10 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 2","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":10,"display":"10"},{"text":"y2 = 20 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 2","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":20,"display":"20"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"midpoint x = (x1 + x2) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"midpoint y = (y1 + y2) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"midpoint-formula","title":"Midpoint Formula","description":"Find the midpoint of a line segment: M = ((x₁+x₂)/2, (y₁+y₂)/2).","category":"formulas","icon":"ruler","tags":["coordinate-geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Two endpoints","label":null,"prefix":null,"suffix":null,"section":"Two 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+ x2) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Midpoint","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"midpoint_y = (y1 + y2) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Midpoint","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"minecraft-item-stacks","title":"Minecraft Item Stacks","description":"Calculate how many 64-stacks and double chests a Minecraft item count fills.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Item Count","label":null,"prefix":null,"suffix":null,"section":"Item Count","hero":false,"slider":null,"value":null,"display":null},{"text":"total items = 1000 // count","label":null,"prefix":null,"suffix":"count","section":"Item Count","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"stacks = floor(total items / 64) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":15,"display":"15"},{"text":"remaining items = mod(total items, 64) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":40,"display":"40"},{"text":"total double chests = floor(stacks / 54) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"mirrors-reflection-magnification","title":"Mirrors Reflection Magnification","description":"Calculate image height through a curved mirror using the mirror equation.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"object_height = 5 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"object_distance = 20 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"focal_length = 10 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"_image_distance = 1 / (1 / focal_length - 1 / object_distance)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"image_height = object_height * (-image_distance / object_distance) // cm @hero","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":true,"slider":null,"value":-5,"display":"-5"}]},{"id":"mma-takedown-success-rate","title":"MMA Takedown Success Rate","description":"Calculate MMA takedown success rate.","category":"health","icon":"activity","tags":["sports"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Stats","label":null,"prefix":null,"suffix":null,"section":"Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"takedowns landed = 3","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"takedown attempts = 8","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"takedown success rate percentage = (takedowns landed / takedown attempts) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":37.5,"display":"37.5"}]},{"id":"mode","title":"Mode (5 values)","description":"Count occurrences of each value among 5 entries to find the mode.","category":"formulas","icon":"sigma","tags":["statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Data points","label":null,"prefix":null,"suffix":null,"section":"Data points","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"x2 = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"x3 = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"x4 = 7 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":7,"display":"7"},{"text":"x5 = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"# Most-frequent value via count comparisons","label":null,"prefix":null,"suffix":null,"section":"Most-frequent value via count comparisons","hero":false,"slider":null,"value":null,"display":null},{"text":"count_x1 = (x1 == x1) + (x2 == x1) + (x3 == x1) + (x4 == x1) + (x5 == x1) // @label(Count of x₁)","label":"Count of x₁","prefix":null,"suffix":null,"section":"Most-frequent value via count comparisons","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"count_x2 = (x1 == x2) + (x2 == x2) + (x3 == x2) + (x4 == x2) + (x5 == x2) // @label(Count of x₂)","label":"Count of x₂","prefix":null,"suffix":null,"section":"Most-frequent value via count comparisons","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"count_x3 = (x1 == x3) + (x2 == x3) + (x3 == x3) + (x4 == x3) + (x5 == x3) // @label(Count of x₃)","label":"Count of x₃","prefix":null,"suffix":null,"section":"Most-frequent value via count comparisons","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"count_x4 = (x1 == x4) + (x2 == x4) + (x3 == x4) + (x4 == x4) + (x5 == x4) // @label(Count of x₄)","label":"Count of x₄","prefix":null,"suffix":null,"section":"Most-frequent value via count comparisons","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"count_x5 = (x1 == x5) + (x2 == x5) + (x3 == x5) + (x4 == x5) + (x5 == x5) // @label(Count of x₅)","label":"Count of x₅","prefix":null,"suffix":null,"section":"Most-frequent value via count comparisons","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Mode is value with highest count (returns lowest-indexed if tied)","label":null,"prefix":null,"suffix":null,"section":"Mode is value with highest count (returns lowest-indexed if tied)","hero":false,"slider":null,"value":null,"display":null},{"text":"max_count = max(count_x1, count_x2, count_x3, count_x4, count_x5) // @label(Mode Frequency)","label":"Mode Frequency","prefix":null,"suffix":null,"section":"Mode is value with highest count (returns lowest-indexed if tied)","hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"modular-arithmetic","title":"Modular Arithmetic","description":"Compute a mod n — the remainder when a is divided by n.","category":"formulas","icon":"sigma","tags":["number-theory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Numbers","label":null,"prefix":null,"suffix":null,"section":"Numbers","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 17 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Numbers","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":17,"display":"17"},{"text":"n = 5 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Numbers","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":5,"display":"5"},{"text":"# Remainder","label":null,"prefix":null,"suffix":null,"section":"Remainder","hero":false,"slider":null,"value":null,"display":null},{"text":"result = a mod n // @hero @label(a mod n)","label":"a mod n","prefix":null,"suffix":null,"section":"Remainder","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"},{"text":"quotient = (a - result) / n","label":null,"prefix":null,"suffix":null,"section":"Remainder","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"}]},{"id":"molality-chemistry-concentration","title":"Molality Chemistry Concentration","description":"Calculate solution molality from moles of solute and kilograms of solvent.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"moles_of_solute = 0.5 // mol","label":null,"prefix":null,"suffix":"mol","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"mass_of_solvent_kg = 1.0 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"molality = moles_of_solute / mass_of_solvent_kg // mol/kg @hero","label":null,"prefix":null,"suffix":"mol/kg","section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"molarity-calculator","title":"Molarity Calculator","description":"Calculate solution molarity from moles of solute and volume in milliliters.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Solute and Solvent","label":null,"prefix":null,"suffix":null,"section":"Solute and Solvent","hero":false,"slider":null,"value":null,"display":null},{"text":"moles of solute = 0.5 // moles 0.01..10","label":null,"prefix":null,"suffix":"moles","section":"Solute and Solvent","hidden":false,"hero":false,"slider":{"min":0.01,"max":10,"step":0.1},"value":0.5,"display":"0.5"},{"text":"solution volume = 500 // milliliters 1..5k","label":null,"prefix":null,"suffix":"milliliters","section":"Solute and Solvent","hidden":false,"hero":false,"slider":{"min":1,"max":5000,"step":50},"value":500,"display":"500"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"volume liters = solution volume / 1000","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"molarity = moles of solute / volume liters // mol/l @hero","label":null,"prefix":null,"suffix":"mol/l","section":"Result","hidden":false,"hero":true,"slider":null,"value":1,"display":"1"},{"text":"# Details","label":null,"prefix":null,"suffix":null,"section":"Details","hero":false,"slider":null,"value":null,"display":null},{"text":"millimolarity = molarity * 1000","label":null,"prefix":null,"suffix":null,"section":"Details","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"micromolarity = molarity * 1000000","label":null,"prefix":null,"suffix":null,"section":"Details","hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"moles per liter = molarity","label":null,"prefix":null,"suffix":null,"section":"Details","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"}]},{"id":"mole-fraction","title":"Mole Fraction","description":"Calculate mole fractions of three components in a mixture.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Components","label":null,"prefix":null,"suffix":null,"section":"Components","hero":false,"slider":null,"value":null,"display":null},{"text":"moles component a = 2.5 // moles 0..100","label":null,"prefix":null,"suffix":"moles","section":"Components","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":2.5,"display":"2.5"},{"text":"moles component b = 7.5 // moles 0..100","label":null,"prefix":null,"suffix":"moles","section":"Components","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":7.5,"display":"7.5"},{"text":"moles component c = 0.0 // moles 0..100","label":null,"prefix":null,"suffix":"moles","section":"Components","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":0,"display":"0"},{"text":"# Totals","label":null,"prefix":null,"suffix":null,"section":"Totals","hero":false,"slider":null,"value":null,"display":null},{"text":"total moles = moles component a + moles component b + moles component c","label":null,"prefix":null,"suffix":null,"section":"Totals","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"mole fraction a = moles component a / total moles // @hero","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":0.25,"display":"0.25"},{"text":"# Fractions","label":null,"prefix":null,"suffix":null,"section":"Fractions","hero":false,"slider":null,"value":null,"display":null},{"text":"mole fraction b = moles component b / total moles","label":null,"prefix":null,"suffix":null,"section":"Fractions","hidden":false,"hero":false,"slider":null,"value":0.75,"display":"0.75"},{"text":"mole fraction c = moles component c / total moles","label":null,"prefix":null,"suffix":null,"section":"Fractions","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"total check = mole fraction a + mole fraction b + mole fraction c","label":null,"prefix":null,"suffix":null,"section":"Fractions","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"percentage a = mole fraction a * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Fractions","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"}]},{"id":"momentum","title":"Momentum","description":"p = m · v — linear momentum of a moving object.","category":"formulas","icon":"zap","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"mass = 10 // kg 0.001..10k","label":null,"prefix":null,"suffix":"kg","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000,"step":100},"value":10,"display":"10"},{"text":"velocity = 5 // m/s -1k..1k","label":null,"prefix":null,"suffix":"m/s","section":"Inputs","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# Momentum","label":null,"prefix":null,"suffix":null,"section":"Momentum","hero":false,"slider":null,"value":null,"display":null},{"text":"momentum = mass * velocity // @label(p) @suffix(kg·m/s)","label":"p","prefix":null,"suffix":null,"section":"Momentum","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"}]},{"id":"moon-phase-percent-illumination","title":"Moon Phase Percent Illumination","description":"Calculate moon illumination percentage from days since the last new moon.","category":"science","icon":"moon","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"days_since_new_moon = 14.7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14.7,"display":"14.7"},{"text":"lunar_cycle_days = 29.53","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":29.53,"display":"29.53"},{"text":"phase_angle = (days_since_new_moon / lunar_cycle_days) * 2 * pi","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.1277624116335905,"display":"3.128"},{"text":"illumination_fraction = (1 - cos(phase_angle)) / 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.0007448252690752,"display":"0.0007448"},{"text":"illumination_percentage = illumination_fraction * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.07448252690752,"display":"0.0745"}]},{"id":"moon-weight-comparison","title":"Moon Weight Comparison","description":"Calculate your equivalent weight on the Moon from Earth weight and gravity ratio.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"earth_weight_pounds = 150","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"moon_gravity_ratio = 0.165","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.165,"display":"0.165"},{"text":"moon_weight = earth_weight_pounds * moon_gravity_ratio // pounds on the Moon @hero","label":null,"prefix":null,"suffix":"pounds on the Moon","section":null,"hidden":false,"hero":true,"slider":null,"value":24.75,"display":"24.75"}]},{"id":"morse-code-duration","title":"Morse Code Duration","description":"Calculate total Morse code transmission time from dot and dash counts.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"number_of_dots = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"number_of_dashes = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"dot_duration_ms = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"dash_duration_ms = dot_duration_ms * 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"total_duration_seconds = (number_of_dots * dot_duration_ms + number_of_dashes * dash_duration_ms) / 1000 // seconds @hero","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"mortgage-calculator","title":"Mortgage Calculator","description":"Calculate monthly payments, total interest, and lifetime cost for any home loan.","category":"finance","icon":"house","tags":["mortgage","loan","housing","interest"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Loan Details","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = 400000 // 50k..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Loan Details","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":5000},"value":400000,"display":"$400,000.00"},{"text":"interest rate = 6.5 // % 1..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.1},"value":6.5,"display":"6.5"},{"text":"loan term = 30 // years 5..40","label":null,"prefix":null,"suffix":"years","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":5,"max":40,"step":1},"value":30,"display":"30"},{"text":"_monthly_rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"_num_payments = loan term * 12","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hidden":true,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"# Monthly Costs","label":null,"prefix":null,"suffix":null,"section":"Monthly Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$principal and interest = loan amount * (monthly_rate * (1 + monthly_rate)^num_payments) / ((1 + monthly_rate)^num_payments - 1)","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":null,"value":2528.2720939718615,"display":"$2,528.27"},{"text":"$property tax = 500 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":500,"display":"$500.00"},{"text":"$insurance = 150 // 0..1k","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":150,"display":"$150.00"},{"text":"$total monthly payment = principal and interest + property tax + insurance // @hero","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":true,"slider":null,"value":3178.2720939718615,"display":"$3,178.27"},{"text":"# Lifetime Totals","label":null,"prefix":null,"suffix":null,"section":"Lifetime Totals","hero":false,"slider":null,"value":null,"display":null},{"text":"$total amount paid = total monthly payment * num_payments","label":null,"prefix":"$","suffix":null,"section":"Lifetime Totals","hidden":false,"hero":false,"slider":null,"value":1144177.95382987,"display":"$1,144,177.95"},{"text":"$total interest paid = total amount paid - loan amount","label":null,"prefix":"$","suffix":null,"section":"Lifetime Totals","hidden":false,"hero":false,"slider":null,"value":744177.95382987,"display":"$744,177.95"}]},{"id":"mortgage-insurance-pmi-cost","title":"Mortgage Insurance PMI Cost","description":"Estimate monthly private mortgage insurance costs for your loan.","category":"real-estate","icon":"shield","tags":["mortgage","insurance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"loanAmount = 400000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":400000,"display":"400,000"},{"text":"pmiRateAnnual = 0.5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"annualPMICost = loanAmount * (pmiRateAnnual / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"monthlyPMICost = annualPMICost / 12 // @prefix($) @suffix(/mo) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":166.66666666666666,"display":"166.67"}]},{"id":"mortgage-interest-tax-deduction","title":"Mortgage Interest Tax Deduction","description":"Calculate income tax savings from the mortgage interest deduction.","category":"finance","icon":"home","tags":["mortgage","interest","tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"annual_interest_paid = 15000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"marginal_tax_rate = 0.24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.24,"display":"0.24"},{"text":"tax_savings = annual_interest_paid * marginal_tax_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3600,"display":"3,600"}]},{"id":"mortgage-payoff-acceleration","title":"Mortgage Payoff Acceleration","description":"Calculate years saved and interest saved by paying extra each month on a mortgage.","category":"finance","icon":"home","tags":["mortgage","payoff","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Mortgage Details","label":null,"prefix":null,"suffix":null,"section":"Mortgage Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$current balance = 350000 // 10k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":10000,"max":1000000,"step":5000},"value":350000,"display":"$350,000.00"},{"text":"interest rate = 6.5 // % 1..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.1},"value":6.5,"display":"6.5"},{"text":"years remaining = 25 // years 1..30","label":null,"prefix":null,"suffix":"years","section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":25,"display":"25"},{"text":"$extra monthly payment = 500 // 0..5k","label":null,"prefix":"$","suffix":null,"section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":50},"value":500,"display":"$500.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_monthly_rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"$_standard_monthly_payment = current balance * (monthly_rate * (1 + monthly_rate)^(years remaining * 12)) / ((1 + monthly_rate)^(years remaining * 12) - 1)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2363.225064716746,"display":"$2,363.23"},{"text":"$_total_monthly_payment = standard_monthly_payment + extra monthly payment","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2863.225064716746,"display":"$2,863.23"},{"text":"# Approximation for months remaining","label":null,"prefix":null,"suffix":null,"section":"Approximation for months remaining","hero":false,"slider":null,"value":null,"display":null},{"text":"# n = -ln(1 - (r*PV)/P) / ln(1 + r)","label":null,"prefix":null,"suffix":null,"section":"n = -ln(1 - (r*PV)/P) / ln(1 + r)","hero":false,"slider":null,"value":null,"display":null},{"text":"_months_remaining_with_extra = -ln(1 - (monthly_rate * current balance) / total_monthly_payment) / ln(1 + monthly_rate)","label":null,"prefix":null,"suffix":null,"section":"n = -ln(1 - (r*PV)/P) / ln(1 + r)","hidden":true,"hero":false,"slider":null,"value":200.86828948804973,"display":"200.87"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"years saved = years remaining - (months_remaining_with_extra / 12) // @hero years","label":null,"prefix":null,"suffix":"years","section":"Result","hidden":false,"hero":true,"slider":null,"value":8.260975875995857,"display":"8.261"},{"text":"$total interest saved = (standard_monthly_payment * years remaining * 12) - (total_monthly_payment * months_remaining_with_extra)","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":133836.3982460606,"display":"$133,836.40"},{"text":"new payoff time = months_remaining_with_extra / 12 // years","label":null,"prefix":null,"suffix":"years","section":"Result","hidden":false,"hero":false,"slider":null,"value":16.739024124004143,"display":"16.74"}]},{"id":"mosquito-repellent-duration","title":"Mosquito Repellent Duration","description":"Estimate hours of mosquito protection from a repellent's DEET concentration.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"deet_concentration_percent = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"estimated_protection_hours = deet_concentration_percent / 5 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"motor-torque-from-hp-rpm","title":"Motor Torque from HP and RPM","description":"Convert between horsepower and torque at a given RPM.","category":"engineering","icon":"settings","tags":["engineering","mechanical"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"horsepower = 5 // HP","label":null,"prefix":null,"suffix":"HP","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"rpm = 1750 // RPM","label":null,"prefix":null,"suffix":"RPM","section":null,"hidden":false,"hero":false,"slider":null,"value":1750,"display":"1,750"},{"text":"torque_lb_ft = (horsepower * 5252) / rpm // lb-ft @hero","label":null,"prefix":null,"suffix":"lb-ft","section":null,"hidden":false,"hero":true,"slider":null,"value":15.005714285714285,"display":"15.01"},{"text":"torque_nm = torque_lb_ft * 1.3558","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20.344747428571427,"display":"20.34"}]},{"id":"movement-speed-multiplier","title":"Movement Speed Multiplier","description":"Calculate final movement speed with various buffs.","category":"math","icon":"fast-forward","tags":["gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Speed Settings","label":null,"prefix":null,"suffix":null,"section":"Speed Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base speed = 300","label":null,"prefix":null,"suffix":null,"section":"Speed Settings","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"boots bonus percent = 15 // %","label":null,"prefix":null,"suffix":"%","section":"Speed Settings","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"haste buff percent = 20 // %","label":null,"prefix":null,"suffix":"%","section":"Speed Settings","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_multiplier = 1 + (boots bonus percent / 100) + (haste buff percent / 100)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.35,"display":"1.35"},{"text":"final speed = base speed * total_multiplier","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":405,"display":"405"}]},{"id":"moving-cost","title":"Moving Cost","description":"Estimate the cost of a DIY or professional move.","category":"real-estate","icon":"truck","tags":["truck"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Move Details","label":null,"prefix":null,"suffix":null,"section":"Move Details","hero":false,"slider":null,"value":null,"display":null},{"text":"distance = 500 // miles 10..3k by 10","label":null,"prefix":null,"suffix":"miles","section":"Move Details","hidden":false,"hero":false,"slider":{"min":10,"max":3000,"step":10},"value":500,"display":"500"},{"text":"bedrooms = 2 // 1..6","label":null,"prefix":null,"suffix":null,"section":"Move Details","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":2,"display":"2"},{"text":"is professional = 1 // dropdown({Professional: 1, DIY: 0}) @label(Moving Method)","label":"Moving Method","prefix":null,"suffix":null,"section":"Move Details","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# DIY Costs","label":null,"prefix":null,"suffix":null,"section":"DIY Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$truck rental = 40 + distance * 0.70 + bedrooms * 50","label":null,"prefix":"$","suffix":null,"section":"DIY Costs","hidden":false,"hero":false,"slider":null,"value":490,"display":"$490.00"},{"text":"$fuel for truck = distance * 2 / 10 * 3.89 // @label(Fuel (truck ~10mpg))","label":"Fuel (truck ~10mpg)","prefix":"$","suffix":null,"section":"DIY Costs","hidden":false,"hero":false,"slider":null,"value":389,"display":"$389.00"},{"text":"$diy total = truck rental + fuel for truck","label":null,"prefix":"$","suffix":null,"section":"DIY Costs","hidden":false,"hero":false,"slider":null,"value":879,"display":"$879.00"},{"text":"# Professional Costs","label":null,"prefix":null,"suffix":null,"section":"Professional Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$base labor = 800 + bedrooms * 400 // @label(Base Labor (crew + hours))","label":"Base Labor (crew + hours)","prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":1600,"display":"$1,600.00"},{"text":"$mileage charge = distance * 0.75 // @label(Long Distance Charge)","label":"Long Distance Charge","prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":375,"display":"$375.00"},{"text":"$packing materials = 100 + bedrooms * 75","label":null,"prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":250,"display":"$250.00"},{"text":"$pro total = base labor + mileage charge + packing materials","label":null,"prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":2225,"display":"$2,225.00"},{"text":"# Your Estimate","label":null,"prefix":null,"suffix":null,"section":"Your Estimate","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated cost = is professional * pro total + (1 - is professional) * diy total // @hero","label":null,"prefix":"$","suffix":null,"section":"Your Estimate","hidden":false,"hero":true,"slider":null,"value":2225,"display":"$2,225.00"},{"text":"$per bedroom = round(estimated cost / bedrooms) // @label(Cost Per Bedroom)","label":"Cost Per Bedroom","prefix":"$","suffix":null,"section":"Your Estimate","hidden":false,"hero":false,"slider":null,"value":1113,"display":"$1,113.00"}]},{"id":"mtu-overhead-overhead-percent","title":"Mtu Overhead Overhead Percent","description":"Calculate the network overhead percentage of headers within an MTU.","category":"other","icon":"percent","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"mtu_size_bytes = 1500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"header_size_bytes = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"overhead_percentage = (header_size_bytes / mtu_size_bytes) * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.666666666666667,"display":"2.667"}]},{"id":"mulch-volume-calculator","title":"Mulch Volume Calculator","description":"Estimate mulch in cubic yards and bags needed from area and depth.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Landscape Area","label":null,"prefix":null,"suffix":null,"section":"Landscape Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = 500 // square feet 1..5k","label":null,"prefix":null,"suffix":"square feet","section":"Landscape Area","hidden":false,"hero":false,"slider":{"min":1,"max":5000,"step":50},"value":500,"display":"500"},{"text":"depth = 3 // inches 1..12","label":null,"prefix":null,"suffix":"inches","section":"Landscape Area","hidden":false,"hero":false,"slider":{"min":1,"max":12,"step":0.2},"value":3,"display":"3"},{"text":"# Volume Calculations","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_depth_feet = depth / 12","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"_volume_cubic_feet = area * depth_feet","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"volume cubic yards = round(volume_cubic_feet / 27, 2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":false,"hero":true,"slider":null,"value":4.63,"display":"4.63"},{"text":"# Bags","label":null,"prefix":null,"suffix":null,"section":"Bags","hero":false,"slider":null,"value":null,"display":null},{"text":"# Small bag is typically 2 cubic feet","label":null,"prefix":null,"suffix":null,"section":"Small bag is typically 2 cubic feet","hero":false,"slider":null,"value":null,"display":null},{"text":"small bags needed = roundup(volume_cubic_feet / 2)","label":null,"prefix":null,"suffix":null,"section":"Small bag is typically 2 cubic feet","hidden":false,"hero":false,"slider":null,"value":63,"display":"63"},{"text":"# Large bag is typically 3 cubic feet","label":null,"prefix":null,"suffix":null,"section":"Large bag is typically 3 cubic feet","hero":false,"slider":null,"value":null,"display":null},{"text":"large bags needed = roundup(volume_cubic_feet / 3)","label":null,"prefix":null,"suffix":null,"section":"Large bag is typically 3 cubic feet","hidden":false,"hero":false,"slider":null,"value":42,"display":"42"}]},{"id":"music-chord-semitone-intervals","title":"Music Chord Semitone Intervals","description":"Calculate the semitone intervals between chord notes.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"root_note = 0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"third_note = 4 // major third","label":null,"prefix":null,"suffix":"major third","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"fifth_note = 7 // perfect fifth","label":null,"prefix":null,"suffix":"perfect fifth","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"interval_root_to_third = third_note - root_note // semitones @hero","label":null,"prefix":null,"suffix":"semitones","section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"},{"text":"interval_third_to_fifth = fifth_note - third_note // semitones @hero","label":null,"prefix":null,"suffix":"semitones","section":null,"hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"named-points-demo","title":"Named Points on Graph","description":"Mark and label specific points on a graph — intersections, maxima, reference levels. Each `point(x, y, \"name\")` renders as a labeled circle next to the curve. Mix as many as you need with any combination of curves.","category":"math","icon":"target","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# A parabola with three named points","label":null,"prefix":null,"suffix":null,"section":"A parabola with three named points","hero":false,"slider":null,"value":null,"display":null},{"text":"# Sine wave with key landmarks","label":null,"prefix":null,"suffix":null,"section":"Sine wave with key landmarks","hero":false,"slider":null,"value":null,"display":null},{"text":"# Linear function with the y-intercept and the point where it crosses x = 5","label":null,"prefix":null,"suffix":null,"section":"Linear function with the y-intercept and the point where it crosses x = 5","hero":false,"slider":null,"value":null,"display":null},{"text":"# Multiple curves with shared landmarks","label":null,"prefix":null,"suffix":null,"section":"Multiple curves with shared landmarks","hero":false,"slider":null,"value":null,"display":null},{"text":"# Styled points — pass {color, size, icon} for emphasis","label":null,"prefix":null,"suffix":null,"section":"Styled points — pass {color, size, icon} for emphasis","hero":false,"slider":null,"value":null,"display":null},{"text":"plot x^2, point(0, 0, {label: \"min\", color: \"info\"}), point(2, 4, {label: \"peak\", color: \"success\", size: \"lg\", icon: \"star\"}) from -3 to 3","label":null,"prefix":null,"suffix":null,"section":"Styled points — pass {color, size, icon} for emphasis","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"natural-logarithm","title":"Natural Logarithm","description":"Calculate the natural logarithm (ln) of a number.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"number = 2.71828","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.71828,"display":"2.718"},{"text":"result = log(number)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.4342941897738881,"display":"0.4343"}]},{"id":"nautical-mile-to-statute","title":"Nautical Mile To Statute","description":"Convert nautical miles to statute miles.","category":"other","icon":"calculator","tags":["statute"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"nautical_miles = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"statute_miles = nautical_miles * 1.15078 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11.5078,"display":"11.51"}]},{"id":"nda-breach-cost-estimate","title":"NDA Breach Cost","description":"Estimate the potential financial impact of an NDA violation.","category":"other","icon":"alert-triangle","tags":["breach"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"liquidatedDamages = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"estimatedLegalFees = 25000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":25000,"display":"25,000"},{"text":"potentialMarketLoss = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"totalBreachCost = liquidatedDamages + estimatedLegalFees + potentialMarketLoss // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":175000,"display":"175,000"}]},{"id":"net-operating-income","title":"Net Operating Income","description":"Calculate the annual profit of a property before taxes and debt.","category":"real-estate","icon":"briefcase","tags":["income"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"grossRentalIncome = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"otherIncome = 2000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"vacancyLoss = 2500 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2500,"display":"2,500"},{"text":"operatingExpenses = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"noi = (grossRentalIncome + otherIncome - vacancyLoss) - operatingExpenses // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":34500,"display":"34,500"}]},{"id":"net-present-value","title":"Net Present Value","description":"Calculate net present value (NPV) of a 5-year investment from cash flows and discount rate.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# NPV Project Analysis","label":null,"prefix":null,"suffix":null,"section":"NPV Project Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"$initial investment = 50000 // 1k..1M","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":1000,"max":1000000,"step":10000},"value":50000,"display":"$50,000.00"},{"text":"discount rate = 10 // % 1..25","label":null,"prefix":null,"suffix":"%","section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":1,"max":25,"step":1},"value":10,"display":"10"},{"text":"$year one cash flow = 15000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":15000,"display":"$15,000.00"},{"text":"$year two cash flow = 18000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":18000,"display":"$18,000.00"},{"text":"$year three cash flow = 22000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":22000,"display":"$22,000.00"},{"text":"$year four cash flow = 25000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":25000,"display":"$25,000.00"},{"text":"$year five cash flow = 30000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":30000,"display":"$30,000.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_r = discount rate / 100","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"$_pv1 = year one cash flow / (1 + r)^1","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":13636.363636363636,"display":"$13,636.36"},{"text":"$_pv2 = year two cash flow / (1 + r)^2","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":14876.033057851237,"display":"$14,876.03"},{"text":"$_pv3 = year three cash flow / (1 + r)^3","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":16528.925619834707,"display":"$16,528.93"},{"text":"$_pv4 = year four cash flow / (1 + r)^4","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":17075.33638412676,"display":"$17,075.34"},{"text":"$_pv5 = year five cash flow / (1 + r)^5","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":18627.63969177465,"display":"$18,627.64"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$net present value = pv1 + pv2 + pv3 + pv4 + pv5 - initial investment // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":30744.29838995099,"display":"$30,744.30"},{"text":"$total nominal cash flow = year one cash flow + year two cash flow + year three cash flow + year four cash flow + year five cash flow","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":110000,"display":"$110,000.00"},{"text":"profitability index = (net present value + initial investment) / initial investment","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":1.6148859677990197,"display":"1.615"}]},{"id":"net-promoter-score","title":"Net Promoter Score","description":"Calculate Net Promoter Score (NPS) from promoter, passive, and detractor counts.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Survey Results","label":null,"prefix":null,"suffix":null,"section":"Survey Results","hero":false,"slider":null,"value":null,"display":null},{"text":"total responses = 500 // 10..10k","label":null,"prefix":null,"suffix":null,"section":"Survey Results","hidden":false,"hero":false,"slider":{"min":10,"max":10000,"step":100},"value":500,"display":"500"},{"text":"number of promoters = 300 // 9-10 score 0..10000 by 1","label":null,"prefix":null,"suffix":"9-10 score","section":"Survey Results","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":1},"value":300,"display":"300"},{"text":"number of detractors = 50 // 0-6 score 0..10000 by 1","label":null,"prefix":null,"suffix":"0-6 score","section":"Survey Results","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":1},"value":50,"display":"50"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_percent_promoters = (number of promoters / total responses) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"_percent_detractors = (number of detractors / total responses) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"_number_of_passives = total responses - number of promoters - number of detractors","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"net promoter score = percent_promoters - percent_detractors // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"},{"text":"rating = if(net promoter score > 70, \"World Class\", if(net promoter score > 30, \"Good\", \"Needs Improvement\"))","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Good","display":"Good"},{"text":"percent passives = (number_of_passives / total responses) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"}]},{"id":"net-worth-growth-projection","title":"Net Worth Growth Projection","description":"Project future net worth from current value, annual contributions, and growth rate.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"current_net_worth = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"annual_contribution = 12000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12000,"display":"12,000"},{"text":"years = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"expected_growth = 0.06","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.06,"display":"0.06"},{"text":"future_value = current_net_worth * (1 + expected_growth) ** years + annual_contribution * (((1 + expected_growth) ** years - 1) / expected_growth)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":337254.30896285636,"display":"337,254.31"}]},{"id":"net-worth","title":"Net Worth","description":"Track your assets minus liabilities to see your net worth.","category":"finance","icon":"wallet","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Assets","label":null,"prefix":null,"suffix":null,"section":"Assets","hero":false,"slider":null,"value":null,"display":null},{"text":"$cash and savings = 15000 // 0..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":1000},"value":15000,"display":"$15,000.00"},{"text":"$investments = 50000 // 0..2M","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":20000},"value":50000,"display":"$50,000.00"},{"text":"$retirement accounts = 75000 // 0..3M","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":3000000,"step":50000},"value":75000,"display":"$75,000.00"},{"text":"$home value = 350000 // 0..2M by 10k","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":10000},"value":350000,"display":"$350,000.00"},{"text":"$other assets = 10000 // 0..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":1000},"value":10000,"display":"$10,000.00"},{"text":"# Liabilities","label":null,"prefix":null,"suffix":null,"section":"Liabilities","hero":false,"slider":null,"value":null,"display":null},{"text":"$mortgage balance = 280000 // 0..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":5000},"value":280000,"display":"$280,000.00"},{"text":"$car loans = 12000 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":12000,"display":"$12,000.00"},{"text":"$student loans = 25000 // 0..200k by 1k","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":200000,"step":1000},"value":25000,"display":"$25,000.00"},{"text":"$credit card debt = 3000 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":3000,"display":"$3,000.00"},{"text":"$other debts = 0 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":0,"display":"$0.00"},{"text":"# Summary","label":null,"prefix":null,"suffix":null,"section":"Summary","hero":false,"slider":null,"value":null,"display":null},{"text":"$total assets = cash and savings + investments + retirement accounts + home value + other assets","label":null,"prefix":"$","suffix":null,"section":"Summary","hidden":false,"hero":false,"slider":null,"value":500000,"display":"$500,000.00"},{"text":"$total liabilities = mortgage balance + car loans + student loans + credit card debt + other debts","label":null,"prefix":"$","suffix":null,"section":"Summary","hidden":false,"hero":false,"slider":null,"value":320000,"display":"$320,000.00"},{"text":"$net worth = total assets - total liabilities","label":null,"prefix":"$","suffix":null,"section":"Summary","hidden":false,"hero":true,"slider":null,"value":180000,"display":"$180,000.00"}]},{"id":"network-latency-delay","title":"Network Latency Delay","description":"Calculate one-way and round-trip latency over fiber optic cable.","category":"other","icon":"calculator","tags":["delay"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Journey","label":null,"prefix":null,"suffix":null,"section":"Journey","hero":false,"slider":null,"value":null,"display":null},{"text":"distance kilometers = 1000 // km","label":null,"prefix":null,"suffix":"km","section":"Journey","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"refraction index of fiber = 1.467 // speed of light is c/n","label":null,"prefix":null,"suffix":"speed of light is c/n","section":"Journey","hidden":false,"hero":false,"slider":null,"value":1.467,"display":"1.467"},{"text":"# Speed of light in vacuum (approx)","label":null,"prefix":null,"suffix":null,"section":"Speed of light in vacuum (approx)","hero":false,"slider":null,"value":null,"display":null},{"text":"_c_vacuum = 299792 // km/s","label":null,"prefix":null,"suffix":"km/s","section":"Speed of light in vacuum (approx)","hidden":true,"hero":false,"slider":null,"value":299792,"display":"299,792"},{"text":"_speed_in_fiber = c_vacuum / refraction index of fiber // km/s","label":null,"prefix":null,"suffix":"km/s","section":"Speed of light in vacuum (approx)","hidden":true,"hero":false,"slider":null,"value":204357.1915473756,"display":"204,357.19"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"one way delay milliseconds = (distance kilometers / speed_in_fiber) * 1000 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":4.893392752308267,"display":"4.893"},{"text":"roundtrip_time_milliseconds = one way delay milliseconds * 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":9.786785504616534,"display":"9.787"}]},{"id":"newsletter-subscriber-valuation","title":"Newsletter Subscriber Valuation","description":"Calculate the total valuation of a newsletter from subscriber count and revenue.","category":"business","icon":"briefcase","tags":["valuation","business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"total_subscribers = 5000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"average_monthly_revenue_per_subscriber = 0.50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"churn_rate_percentage = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"subscriber_lifetime_months = 1 / churn_rate_percentage","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":33.333333333333336,"display":"33.33"},{"text":"total_newsletter_valuation = total_subscribers * average_monthly_revenue_per_subscriber * subscriber_lifetime_months","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":83333.33333333334,"display":"83,333.33"}]},{"id":"newtons-second-law-acceleration","title":"Newtons Second Law Acceleration","description":"Calculate acceleration from force and mass using Newton's Second Law.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"force = 100 // Newtons","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"mass = 20 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"acceleration = force / mass // meters per second squared @hero","label":null,"prefix":null,"suffix":"meters per second squared","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"newtons-second-law","title":"Newton's Second Law","description":"F = m · a — force equals mass times acceleration.","category":"formulas","icon":"zap","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"mass = 10 // kg 0.001..10k","label":null,"prefix":null,"suffix":"kg","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000,"step":100},"value":10,"display":"10"},{"text":"acceleration = 9.8 // m/s² -100..100 by 0.01","label":null,"prefix":null,"suffix":"m/s²","section":"Inputs","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":0.01},"value":9.8,"display":"9.8"},{"text":"# Force","label":null,"prefix":null,"suffix":null,"section":"Force","hero":false,"slider":null,"value":null,"display":null},{"text":"force = mass * acceleration // @label(Force) @suffix(N)","label":"Force","prefix":null,"suffix":null,"section":"Force","hidden":false,"hero":true,"slider":null,"value":98,"display":"98"}]},{"id":"nitro-gas-mix-ppo2","title":"Nitro Gas Mix Ppo2","description":"Calculate partial pressure of oxygen (ppO2) for a nitrox mix at depth.","category":"everyday","icon":"home","tags":["gas","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"nitrox_oxygen_percent = 32","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"depth_feet = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"ata_pressure = (depth_feet / 33) + 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4.03030303030303,"display":"4.03"},{"text":"partial_pressure_oxygen = (nitrox_oxygen_percent / 100) * ata_pressure // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.2896969696969696,"display":"1.29"}]},{"id":"noise-exposure-limit-osha","title":"Noise Exposure Limit Osha","description":"Calculate permissible OSHA noise exposure hours from decibel level.","category":"math","icon":"infinity","tags":["exposure","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"noise_level_decibels = 95","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":95,"display":"95"},{"text":"permissible_exposure_hours = 8 / (2^((noise_level_decibels - 90) / 5)) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"normal-distribution-probability","title":"Normal Distribution Density","description":"Probability density of a normal distribution: f(x) = (1 / (σ√(2π))) · exp(−(x−μ)²/(2σ²)).","category":"formulas","icon":"sigma","tags":["statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Distribution parameters","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"mean = 0 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":0,"display":"0"},{"text":"standard_deviation = 1 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":1,"display":"1"},{"text":"x = 0 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":0,"display":"0"},{"text":"# PDF value at x","label":null,"prefix":null,"suffix":null,"section":"PDF value at x","hero":false,"slider":null,"value":null,"display":null},{"text":"_exponent = -(((x - mean)^2)) / (2 * (standard_deviation^2))","label":null,"prefix":null,"suffix":null,"section":"PDF value at x","hidden":true,"hero":false,"slider":null,"value":0,"display":"-0"},{"text":"density = (1 / (standard_deviation * sqrt(2 * pi))) * exp(exponent) // @label(f(x))","label":"f(x)","prefix":null,"suffix":null,"section":"PDF value at x","hidden":false,"hero":true,"slider":null,"value":0.3989422804014327,"display":"0.3989"}]},{"id":"notary-public-fee-limit","title":"Notary Fee Limit","description":"Calculate the maximum legal fee for notary services.","category":"other","icon":"file-check","tags":["fee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"numberOfSignatures = 3 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"maxFeePerSignature = 10 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"totalMaxNotaryFee = numberOfSignatures * maxFeePerSignature // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"numerology-destiny-number","title":"Numerology Destiny Number","description":"Reduce a name's numeric sum to a single-digit numerology destiny number.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"name_value_sum = 42","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":42,"display":"42"},{"text":"destiny_number = mod(name_value_sum - 1, 9) + 1 // number @hero","label":null,"prefix":null,"suffix":"number","section":null,"hidden":false,"hero":true,"slider":null,"value":6,"display":"6"}]},{"id":"nyquist-sampling-rate","title":"Nyquist Sampling Rate","description":"Calculate minimum sampling frequency to avoid aliasing.","category":"engineering","icon":"activity","tags":["engineering","electronics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"max_signal_frequency_hz = 20000 // Hz (audio)","label":null,"prefix":null,"suffix":"Hz (audio)","section":null,"hidden":false,"hero":false,"slider":null,"value":20000,"display":"20,000"},{"text":"minimum_sampling_rate_hz = 2 * max_signal_frequency_hz // Hz @hero","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":true,"slider":null,"value":40000,"display":"40,000"},{"text":"standard_cd_quality_rate = 44100 // Hz","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":false,"slider":null,"value":44100,"display":"44,100"}]},{"id":"ocean-acidification-ph-change","title":"Ocean Acidification pH Change","description":"Predict pH change based on atmospheric CO2 increases.","category":"science","icon":"droplet","tags":["science","ocean","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"initial_ph = 8.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8.1,"display":"8.1"},{"text":"carbon_dioxide_increase_percent = 20 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"ph_sensitivity_factor = 0.002 // change in pH per percent CO2 increase","label":null,"prefix":null,"suffix":"change in pH per percent CO2 increase","section":null,"hidden":false,"hero":false,"slider":null,"value":0.002,"display":"0.002"},{"text":"predicted_new_ph = initial_ph - (carbon_dioxide_increase_percent * ph_sensitivity_factor) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8.06,"display":"8.06"}]},{"id":"ocean-tide-height-estimate","title":"Ocean Tide Height Estimate","description":"Estimate relative tidal force on Earth from the Moon's mass and distance.","category":"science","icon":"globe","tags":["ocean"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"moon_distance_km = 384400","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":384400,"display":"384,400"},{"text":"moon_mass_kg = 7.34e22","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7.34e+22,"display":"7.34e22"},{"text":"earth_radius_km = 6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"tide_force_relative = (moon_mass_kg / moon_distance_km^3) * earth_radius_km // relative units @hero","label":null,"prefix":null,"suffix":"relative units","section":null,"hidden":false,"hero":true,"slider":null,"value":8232913036.222099,"display":"8,232,913,036.22"}]},{"id":"offshore-wind-farm-capacity","title":"Offshore Wind Farm Capacity","description":"Calculate energy generation and homes powered by offshore wind.","category":"engineering","icon":"fan","tags":["engineering","wind"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"number_of_turbines = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"turbine_capacity_mw = 8 // MW","label":null,"prefix":null,"suffix":"MW","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"capacity_factor = 40 // percent (efficiency in real conditions)","label":null,"prefix":null,"suffix":"percent (efficiency in real conditions)","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"total_annual_generation_gwh = number_of_turbines * turbine_capacity_mw * (capacity_factor / 100) * 8760 / 1000 // GWh @hero","label":null,"prefix":null,"suffix":"GWh","section":null,"hidden":false,"hero":true,"slider":null,"value":1401.6,"display":"1,401.6"},{"text":"homes_powered = total_annual_generation_gwh * 1000000 / 3500 // 3500 kWh per home","label":null,"prefix":null,"suffix":"3500 kWh per home","section":null,"hidden":false,"hero":false,"slider":null,"value":400457.14285714284,"display":"400,457.14"}]},{"id":"ohms-law","title":"Ohm's Law","description":"Calculate voltage, current, resistance, and power for electrical circuits.","category":"science","icon":"zap","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Circuit Values","label":null,"prefix":null,"suffix":null,"section":"Circuit Values","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage = 12 // V 0.1..240","label":null,"prefix":null,"suffix":"V","section":"Circuit Values","hidden":false,"hero":false,"slider":{"min":0.1,"max":240,"step":5},"value":12,"display":"12"},{"text":"resistance = 6 // Ω 0.1..1000 by 0.1","label":null,"prefix":null,"suffix":"Ω","section":"Circuit Values","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":0.1},"value":6,"display":"6"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"current = voltage / resistance // A @hero @label(Current (I = V/R))","label":"Current (I = V/R)","prefix":null,"suffix":"A","section":"Results","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"},{"text":"power = voltage * current // W @label(Power (P = V × I))","label":"Power (P = V × I)","prefix":null,"suffix":"W","section":"Results","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"power check = current^2 * resistance // W @label(Power (P = I²R))","label":"Power (P = I²R)","prefix":null,"suffix":"W","section":"Results","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"energy per hour = power * 1 // Wh","label":null,"prefix":null,"suffix":"Wh","section":"Results","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"}]},{"id":"oil-change-interval-recommendation","title":"Oil Change Interval Recommendation","description":"Estimate oil change interval based on driving conditions.","category":"engineering","icon":"settings","tags":["automotive","maintenance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Driving Conditions","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hero":false,"slider":null,"value":null,"display":null},{"text":"base interval miles = 7500","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":7500,"display":"7,500"},{"text":"short trips factor = 0.8","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"towing factor = 0.7","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":0.7,"display":"0.7"},{"text":"dusty conditions factor = 0.9","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":0.9,"display":"0.9"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"recommended interval miles = base interval miles * short trips factor * towing factor * dusty conditions factor","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":3780,"display":"3,780"}]},{"id":"on-time-delivery-rate","title":"On-Time Delivery Rate","description":"Monitor the percentage of orders delivered by the promised date.","category":"business","icon":"calendar","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"ordersDeliveredOnTime = 950 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":950,"display":"950"},{"text":"totalOrdersDelivered = 1000 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"onTimeDeliveryRatePercent = (ordersDeliveredOnTime / totalOrdersDelivered) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":95,"display":"95"}]},{"id":"one-rep-max-epley","title":"One Rep Max Epley","description":"Calculate one-rep max (1RM) using the Epley formula and training percentages.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Lift Details","label":null,"prefix":null,"suffix":null,"section":"Lift Details","hero":false,"slider":null,"value":null,"display":null},{"text":"weight lifted = 225 // lbs 5..1k","label":null,"prefix":null,"suffix":"lbs","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":5,"max":1000,"step":1},"value":225,"display":"225"},{"text":"reps performed = 5 // reps 1..30","label":null,"prefix":null,"suffix":"reps","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":5,"display":"5"},{"text":"# Epley Formula","label":null,"prefix":null,"suffix":null,"section":"Epley Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"one rep max = weight lifted * (1 + reps performed / 30) // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":"Epley Formula","hidden":false,"hero":true,"slider":null,"value":262.50000000000006,"display":"262.5"},{"text":"# Training Percentages","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hero":false,"slider":null,"value":null,"display":null},{"text":"ninety percent = one rep max * 0.9","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hidden":false,"hero":false,"slider":null,"value":236.25000000000003,"display":"236.25"},{"text":"eighty percent = one rep max * 0.8","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hidden":false,"hero":false,"slider":null,"value":210.00000000000003,"display":"210"},{"text":"seventy percent = one rep max * 0.7","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hidden":false,"hero":false,"slider":null,"value":183.75000000000003,"display":"183.75"}]},{"id":"one-rep-max","title":"One Rep Max","description":"Estimate your 1RM and training maxes from a submaximal lift.","category":"health","icon":"dumbbell","tags":["training"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Lift Details","label":null,"prefix":null,"suffix":null,"section":"Lift Details","hero":false,"slider":null,"value":null,"display":null},{"text":"weight lifted = 185 // lbs 5..1k by 5","label":null,"prefix":null,"suffix":"lbs","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":5,"max":1000,"step":5},"value":185,"display":"185"},{"text":"reps done = 5 // reps 1..30","label":null,"prefix":null,"suffix":"reps","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":5,"display":"5"},{"text":"# Estimated 1RM (Epley Formula)","label":null,"prefix":null,"suffix":null,"section":"Estimated 1RM (Epley Formula)","hero":false,"slider":null,"value":null,"display":null},{"text":"estimated 1rm = round(weight lifted * (1 + reps done / 30)) // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":"Estimated 1RM (Epley Formula)","hidden":false,"hero":true,"slider":null,"value":216,"display":"216"},{"text":"# Training Maxes","label":null,"prefix":null,"suffix":null,"section":"Training Maxes","hero":false,"slider":null,"value":null,"display":null},{"text":"ninety pct = round(estimated 1rm * 0.90) // lbs @label(90% Training Max)","label":"90% Training Max","prefix":null,"suffix":"lbs","section":"Training Maxes","hidden":false,"hero":false,"slider":null,"value":194,"display":"194"},{"text":"eighty five pct = round(estimated 1rm * 0.85) // lbs @label(85% Training Max)","label":"85% Training Max","prefix":null,"suffix":"lbs","section":"Training Maxes","hidden":false,"hero":false,"slider":null,"value":184,"display":"184"},{"text":"eighty pct = round(estimated 1rm * 0.80) // lbs @label(80% Training Max)","label":"80% Training Max","prefix":null,"suffix":"lbs","section":"Training Maxes","hidden":false,"hero":false,"slider":null,"value":173,"display":"173"}]},{"id":"op-amp-gain-non-inverting","title":"Op-Amp Gain Non-Inverting","description":"Calculate voltage gain for a non-inverting amplifier.","category":"engineering","icon":"activity","tags":["engineering","electronics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"resistor_feedback_ohms = 10000 // Rf","label":null,"prefix":null,"suffix":"Rf","section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"resistor_ground_ohms = 1000 // Rg","label":null,"prefix":null,"suffix":"Rg","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"voltage_gain = 1 + (resistor_feedback_ohms / resistor_ground_ohms) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11,"display":"11"},{"text":"input_voltage = 0.1 // volts","label":null,"prefix":null,"suffix":"volts","section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"output_voltage = input_voltage * voltage_gain // volts","label":null,"prefix":null,"suffix":"volts","section":null,"hidden":false,"hero":false,"slider":null,"value":1.1,"display":"1.1"}]},{"id":"openstax-algebra-trig-unit-circle","title":"OpenStax · Degrees, Radians & the Pythagorean Identity (Algebra and Trigonometry)","description":"Worked example in the style of OpenStax Algebra and Trigonometry 2e — evaluating unit-circle values and confirming sin²θ + cos²θ = 1, with a note on the degrees-vs-radians trap.","category":"education","icon":"book-open","tags":["trigonometry","unit-circle","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Angle mode matters","label":null,"prefix":null,"suffix":null,"section":"Angle mode matters","hero":false,"slider":null,"value":null,"display":null},{"text":"sin_30 = sin(30) // @label(sin 30°)","label":"sin 30°","prefix":null,"suffix":null,"section":"Angle mode matters","hidden":false,"hero":false,"slider":null,"value":0.49999999999999994,"display":"0.5"},{"text":"sin_pi_6 = sin(pi/6 rad) // @label(sin(π/6), radians)","label":"sin(π/6), radians","prefix":null,"suffix":null,"section":"Angle mode matters","hidden":false,"hero":false,"slider":null,"value":0.49999999999999994,"display":"0.5"},{"text":"# Common unit-circle values (degrees)","label":null,"prefix":null,"suffix":null,"section":"Common unit-circle values (degrees)","hero":false,"slider":null,"value":null,"display":null},{"text":"cos_60 = cos(60) // @label(cos 60°)","label":"cos 60°","prefix":null,"suffix":null,"section":"Common unit-circle values (degrees)","hidden":false,"hero":false,"slider":null,"value":0.5000000000000001,"display":"0.5"},{"text":"tan_45 = tan(45) // @label(tan 45°)","label":"tan 45°","prefix":null,"suffix":null,"section":"Common unit-circle values (degrees)","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Pythagorean identity","label":null,"prefix":null,"suffix":null,"section":"Pythagorean identity","hero":false,"slider":null,"value":null,"display":null},{"text":"identity = sin(45)^2 + cos(45)^2 // @hero @formula @label(sin²45° + cos²45°)","label":"sin²45° + cos²45°","prefix":null,"suffix":null,"section":"Pythagorean identity","hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"openstax-calculus-definite-integral-ftc","title":"OpenStax · Definite Integral via the FTC (Calculus I)","description":"Worked example in the style of OpenStax Calculus Volume 1 — evaluating a definite integral with the Fundamental Theorem of Calculus.","category":"education","icon":"book-open","tags":["calculus","integrals","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Find an antiderivative","label":null,"prefix":null,"suffix":null,"section":"Find an antiderivative","hero":false,"slider":null,"value":null,"display":null},{"text":"# Evaluate F at the bounds","label":null,"prefix":null,"suffix":null,"section":"Evaluate F at the bounds","hero":false,"slider":null,"value":null,"display":null},{"text":"F_upper = 3^3 - 3^2 // @label(F(3))","label":"F(3)","prefix":null,"suffix":null,"section":"Evaluate F at the bounds","hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"F_lower = 1^3 - 1^2 // @label(F(1))","label":"F(1)","prefix":null,"suffix":null,"section":"Evaluate F at the bounds","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# Apply the FTC","label":null,"prefix":null,"suffix":null,"section":"Apply the FTC","hero":false,"slider":null,"value":null,"display":null},{"text":"integral = F_upper - F_lower // @hero @formula @label(integral from 1 to 3)","label":"integral from 1 to 3","prefix":null,"suffix":null,"section":"Apply the FTC","hidden":false,"hero":true,"slider":null,"value":18,"display":"18"}]},{"id":"openstax-college-algebra-change-of-base","title":"OpenStax · Change-of-Base Formula (College Algebra)","description":"Worked example in the style of OpenStax College Algebra 2e — evaluating a logarithm to an unusual base with the change-of-base formula.","category":"education","icon":"book-open","tags":["algebra","logarithms","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Change of base","label":null,"prefix":null,"suffix":null,"section":"Change of base","hero":false,"slider":null,"value":null,"display":null},{"text":"result = log(100)/log(5) // @hero @formula @label(log base 5 of 100)","label":"log base 5 of 100","prefix":null,"suffix":null,"section":"Change of base","hidden":false,"hero":true,"slider":null,"value":2.8613531161467867,"display":"2.861"},{"text":"# Verify by exponentiating","label":null,"prefix":null,"suffix":null,"section":"Verify by exponentiating","hero":false,"slider":null,"value":null,"display":null},{"text":"check = 5^result // @label(5 ^ result)","label":"5 ^ result","prefix":null,"suffix":null,"section":"Verify by exponentiating","hidden":false,"hero":false,"slider":null,"value":100.00000000000009,"display":"100"}]},{"id":"openstax-college-algebra-compound-interest","title":"OpenStax · Compound Interest (College Algebra)","description":"Worked example in the style of OpenStax College Algebra 2e — the compound-interest formula A = P(1 + r/n)^(nt), evaluated end to end.","category":"education","icon":"book-open","tags":["algebra","finance","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Given values","label":null,"prefix":null,"suffix":null,"section":"Given values","hero":false,"slider":null,"value":null,"display":null},{"text":"P = 3000 // @label(principal) @prefix($)","label":"principal","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"r = 0.03 // @label(annual rate)","label":"annual rate","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"n = 4 // @label(compounds per year)","label":"compounds per year","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"t = 10 // @label(years)","label":"years","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"# Apply the compound-interest formula","label":null,"prefix":null,"suffix":null,"section":"Apply the compound-interest formula","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = P*(1 + r/n)^(n*t) // @hero @prefix($) @formula @label(balance after 10 years)","label":"balance after 10 years","prefix":null,"suffix":null,"section":"Apply the compound-interest formula","hidden":false,"hero":true,"slider":null,"value":4045.045837009249,"display":"4,045.05"}]},{"id":"openstax-college-algebra-log-laws","title":"OpenStax · The Laws of Logarithms (College Algebra)","description":"Worked example in the style of OpenStax College Algebra 2e — verifying the product, inverse, and change-of-base log laws numerically.","category":"education","icon":"book-open","tags":["logarithms","college-algebra","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.450Z"},"rows":[{"text":"# Product law: log(ab) = log a + log b","label":null,"prefix":null,"suffix":null,"section":"Product law: log(ab) = log a + log b","hero":false,"slider":null,"value":null,"display":null},{"text":"product_law = log(2) + log(50) // @hero @label(log 2 + log 50)","label":"log 2 + log 50","prefix":null,"suffix":null,"section":"Product law: log(ab) = log a + log b","hidden":false,"hero":true,"slider":null,"value":1.9999999999999998,"display":"2"},{"text":"# Logs and exponentials are inverses","label":null,"prefix":null,"suffix":null,"section":"Logs and exponentials are inverses","hero":false,"slider":null,"value":null,"display":null},{"text":"inverse_check = e^(ln(5)) // @label(e^(ln 5))","label":"e^(ln 5)","prefix":null,"suffix":null,"section":"Logs and exponentials are inverses","hidden":false,"hero":false,"slider":null,"value":4.999999999999999,"display":"5"},{"text":"# Change of base / power law: log_b(a) = log a / log b","label":null,"prefix":null,"suffix":null,"section":"Change of base / power law: log_b(a) = log a / log b","hero":false,"slider":null,"value":null,"display":null},{"text":"power_law = log(8) / log(2) // @label(log 8 / log 2)","label":"log 8 / log 2","prefix":null,"suffix":null,"section":"Change of base / power law: log_b(a) = log a / log b","hidden":false,"hero":false,"slider":null,"value":2.9999999999999996,"display":"3"}]},{"id":"openstax-elementary-algebra-mixture","title":"OpenStax · Mixture Problem (Elementary Algebra)","description":"Worked example in the style of OpenStax Elementary Algebra 2e — mixing two acid solutions to hit a target concentration, solved two ways that agree.","category":"education","icon":"book-open","tags":["algebra","openstax","worked-example"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Set up the equation","label":null,"prefix":null,"suffix":null,"section":"Set up the equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Method 1 — let the engine solve it","label":null,"prefix":null,"suffix":null,"section":"Method 1 — let the engine solve it","hero":false,"slider":null,"value":null,"display":null},{"text":"# Method 2 — isolate x by hand","label":null,"prefix":null,"suffix":null,"section":"Method 2 — isolate x by hand","hero":false,"slider":null,"value":null,"display":null},{"text":"liters_40 = (0.25*10 - 0.10*10) / (0.40 - 0.10) // @hero @label(liters of 40% solution)","label":"liters of 40% solution","prefix":null,"suffix":null,"section":"Method 2 — isolate x by hand","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"openstax-intermediate-algebra-factoring","title":"OpenStax · Factoring & Quadratic Roots (Intermediate Algebra)","description":"Worked example in the style of OpenStax Intermediate Algebra 2e — factor a trinomial, expand to check, solve the quadratic, and confirm the roots with Vieta's formulas.","category":"education","icon":"book-open","tags":["algebra","factoring","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Factor the trinomial","label":null,"prefix":null,"suffix":null,"section":"Factor the trinomial","hero":false,"slider":null,"value":null,"display":null},{"text":"# Expand to check","label":null,"prefix":null,"suffix":null,"section":"Expand to check","hero":false,"slider":null,"value":null,"display":null},{"text":"# Solve for the roots","label":null,"prefix":null,"suffix":null,"section":"Solve for the roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# A quadratic with no real roots","label":null,"prefix":null,"suffix":null,"section":"A quadratic with no real roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# Confirm with Vieta's formulas","label":null,"prefix":null,"suffix":null,"section":"Confirm with Vieta's formulas","hero":false,"slider":null,"value":null,"display":null},{"text":"product_of_roots = 2 * 3 // @hero @label(product of the roots)","label":"product of the roots","prefix":null,"suffix":null,"section":"Confirm with Vieta's formulas","hidden":false,"hero":true,"slider":null,"value":6,"display":"6"}]},{"id":"openstax-linear-algebra-matrices","title":"OpenStax · Matrices: Determinant, Inverse & a 2×2 System (Linear Algebra)","description":"Worked example in the style of OpenStax — matrix literals with [[...]] notation, the determinant and inverse, then solving a linear system as a matrix equation.","category":"education","icon":"book-open","tags":["linear-algebra","matrices","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Define a matrix","label":null,"prefix":null,"suffix":null,"section":"Define a matrix","hero":false,"slider":null,"value":null,"display":null},{"text":"A = [[2, 1], [1, 3]] // @label(matrix A)","label":"matrix A","prefix":null,"suffix":null,"section":"Define a matrix","hidden":false,"hero":false,"slider":null,"value":[[2,1],[1,3]],"display":null},{"text":"# Determinant and inverse","label":null,"prefix":null,"suffix":null,"section":"Determinant and inverse","hero":false,"slider":null,"value":null,"display":null},{"text":"detA = det(A) // @hero @label(det(A))","label":"det(A)","prefix":null,"suffix":null,"section":"Determinant and inverse","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"invA = inverse(A) // @label(A⁻¹)","label":"A⁻¹","prefix":null,"suffix":null,"section":"Determinant and inverse","hidden":false,"hero":false,"slider":null,"value":[[0.6,-0.2],[-0.2,0.4]],"display":null},{"text":"# Solve a system Bx = c via the inverse","label":null,"prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hero":false,"slider":null,"value":null,"display":null},{"text":"B = [[1, 1], [1, -1]] // @label(coefficient matrix)","label":"coefficient matrix","prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hidden":false,"hero":false,"slider":null,"value":[[1,1],[1,-1]],"display":null},{"text":"c = [[10], [2]] // @label(constants)","label":"constants","prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hidden":false,"hero":false,"slider":null,"value":[[10],[2]],"display":null},{"text":"solution = inverse(B) * c // @label(solution [x; y])","label":"solution [x; y]","prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hidden":false,"hero":false,"slider":null,"value":[[6],[4]],"display":null}]},{"id":"openstax-prealgebra-prime-factorization","title":"OpenStax · Prime Factorization, GCD & LCM (Prealgebra)","description":"Worked example in the style of OpenStax Prealgebra 2e — break a number into primes, then read off the greatest common divisor and least common multiple.","category":"education","icon":"book-open","tags":["prealgebra","number-theory","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Prime factorization of 360","label":null,"prefix":null,"suffix":null,"section":"Prime factorization of 360","hero":false,"slider":null,"value":null,"display":null},{"text":"prime_factors = factor(360) // @label(360 as primes)","label":"360 as primes","prefix":null,"suffix":null,"section":"Prime factorization of 360","hidden":false,"hero":false,"slider":null,"value":"2^3*3^2*5","display":"2^3*3^2*5"},{"text":"# Greatest common divisor of 48 and 180","label":null,"prefix":null,"suffix":null,"section":"Greatest common divisor of 48 and 180","hero":false,"slider":null,"value":null,"display":null},{"text":"gcd_value = gcd(48, 180) // @label(GCD)","label":"GCD","prefix":null,"suffix":null,"section":"Greatest common divisor of 48 and 180","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"# Least common multiple of 48 and 180","label":null,"prefix":null,"suffix":null,"section":"Least common multiple of 48 and 180","hero":false,"slider":null,"value":null,"display":null},{"text":"lcm_value = lcm(48, 180) // @hero @label(LCM)","label":"LCM","prefix":null,"suffix":null,"section":"Least common multiple of 48 and 180","hidden":false,"hero":true,"slider":null,"value":720,"display":"720"},{"text":"# Bonus: all divisors and a primality check","label":null,"prefix":null,"suffix":null,"section":"Bonus: all divisors and a primality check","hero":false,"slider":null,"value":null,"display":null},{"text":"all_divisors = divisors(36) // @label(divisors of 36)","label":"divisors of 36","prefix":null,"suffix":null,"section":"Bonus: all divisors and a primality check","hidden":false,"hero":false,"slider":null,"value":[1,2,3,4,6,9,12,18,36],"display":null},{"text":"is_97_prime = isprime(97) // @label(is 97 prime?)","label":"is 97 prime?","prefix":null,"suffix":null,"section":"Bonus: all divisors and a primality check","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"}]},{"id":"openstax-precalculus-complex-euler","title":"OpenStax · Complex Numbers & Euler's Identity (Precalculus)","description":"Worked example in the style of OpenStax Precalculus 2e — the imaginary unit, complex arithmetic and modulus, and Euler's identity e^(iπ) = −1.","category":"education","icon":"book-open","tags":["complex-numbers","precalculus","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# The imaginary unit","label":null,"prefix":null,"suffix":null,"section":"The imaginary unit","hero":false,"slider":null,"value":null,"display":null},{"text":"i_squared = i^2 // @label(i²)","label":"i²","prefix":null,"suffix":null,"section":"The imaginary unit","hidden":false,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Modulus and conjugate","label":null,"prefix":null,"suffix":null,"section":"Modulus and conjugate","hero":false,"slider":null,"value":null,"display":null},{"text":"modulus = abs(3 + 4i) // @hero @label(|3 + 4i|)","label":"|3 + 4i|","prefix":null,"suffix":null,"section":"Modulus and conjugate","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"# Euler's identity","label":null,"prefix":null,"suffix":null,"section":"Euler's identity","hero":false,"slider":null,"value":null,"display":null},{"text":"euler = e^(i*pi) // @label(e^(iπ))","label":"e^(iπ)","prefix":null,"suffix":null,"section":"Euler's identity","hidden":false,"hero":false,"slider":null,"value":-1,"display":"-1"}]},{"id":"openstax-precalculus-geometric-series","title":"OpenStax · Geometric Series Sum (Precalculus)","description":"Worked example in the style of OpenStax Precalculus 2e — summing a finite geometric series with the closed form, then checking term by term.","category":"education","icon":"book-open","tags":["precalculus","sequences","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Given","label":null,"prefix":null,"suffix":null,"section":"Given","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 3 // @label(first term)","label":"first term","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"r = 2 // @label(common ratio)","label":"common ratio","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"n = 8 // @label(number of terms)","label":"number of terms","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Closed form for the sum","label":null,"prefix":null,"suffix":null,"section":"Closed form for the sum","hero":false,"slider":null,"value":null,"display":null},{"text":"sum = a1*(1 - r^n)/(1 - r) // @hero @formula @label(sum of first 8 terms)","label":"sum of first 8 terms","prefix":null,"suffix":null,"section":"Closed form for the sum","hidden":false,"hero":true,"slider":null,"value":765,"display":"765"},{"text":"# Sanity check: add the terms directly","label":null,"prefix":null,"suffix":null,"section":"Sanity check: add the terms directly","hero":false,"slider":null,"value":null,"display":null},{"text":"check = 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 // @label(term-by-term)","label":"term-by-term","prefix":null,"suffix":null,"section":"Sanity check: add the terms directly","hidden":false,"hero":false,"slider":null,"value":765,"display":"765"}]},{"id":"openstax-precalculus-vectors","title":"OpenStax · Vectors: Dot Product, Cross Product & Angle (Precalculus)","description":"Worked example in the style of OpenStax Precalculus 2e — vector magnitude, dot product, the angle between two vectors, and the cross product, all in natural [x, y, z] notation.","category":"education","icon":"book-open","tags":["vectors","precalculus","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Define the vectors","label":null,"prefix":null,"suffix":null,"section":"Define the vectors","hero":false,"slider":null,"value":null,"display":null},{"text":"u = [1, 2, 2] // @label(vector u)","label":"vector u","prefix":null,"suffix":null,"section":"Define the vectors","hidden":false,"hero":false,"slider":null,"value":[1,2,2],"display":null},{"text":"v = [2, 0, 1] // @label(vector v)","label":"vector v","prefix":null,"suffix":null,"section":"Define the vectors","hidden":false,"hero":false,"slider":null,"value":[2,0,1],"display":null},{"text":"# Magnitudes","label":null,"prefix":null,"suffix":null,"section":"Magnitudes","hero":false,"slider":null,"value":null,"display":null},{"text":"mag_u = norm(u) // @label(|u|)","label":"|u|","prefix":null,"suffix":null,"section":"Magnitudes","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"mag_v = norm(v) // @label(|v|)","label":"|v|","prefix":null,"suffix":null,"section":"Magnitudes","hidden":false,"hero":false,"slider":null,"value":2.2360679775,"display":"2.236"},{"text":"# Dot product and the angle between","label":null,"prefix":null,"suffix":null,"section":"Dot product and the angle between","hero":false,"slider":null,"value":null,"display":null},{"text":"u_dot_v = dot(u, v) // @label(u · v)","label":"u · v","prefix":null,"suffix":null,"section":"Dot product and the angle between","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"angle_uv = angle(u, v) // @hero @label(angle between u and v)","label":"angle between u and v","prefix":null,"suffix":null,"section":"Dot product and the angle between","hidden":false,"hero":true,"slider":null,"value":53.39572355729035,"display":"53.3957"},{"text":"# Cross product (perpendicular to both)","label":null,"prefix":null,"suffix":null,"section":"Cross product (perpendicular to both)","hero":false,"slider":null,"value":null,"display":null},{"text":"u_cross_v = cross(u, v) // @label(u × v)","label":"u × v","prefix":null,"suffix":null,"section":"Cross product (perpendicular to both)","hidden":false,"hero":false,"slider":null,"value":[2,3,-4],"display":null}]},{"id":"openstax-statistics-normal-probability","title":"OpenStax · Normal Distribution Probability (Statistics)","description":"Worked example in the style of OpenStax Introductory Statistics 2e — a z-score and a normal-curve probability, with no printed Z-table needed.","category":"education","icon":"book-open","tags":["statistics","normal","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Given","label":null,"prefix":null,"suffix":null,"section":"Given","hero":false,"slider":null,"value":null,"display":null},{"text":"mu = 170 // @label(mean μ) @suffix(cm)","label":"mean μ","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":170,"display":"170"},{"text":"sigma = 8 // @label(std dev σ) @suffix(cm)","label":"std dev σ","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"x = 182 // @label(height of interest) @suffix(cm)","label":"height of interest","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":182,"display":"182"},{"text":"# Standardize to a z-score","label":null,"prefix":null,"suffix":null,"section":"Standardize to a z-score","hero":false,"slider":null,"value":null,"display":null},{"text":"z = (x - mu)/sigma // @formula @label(z-score)","label":"z-score","prefix":null,"suffix":null,"section":"Standardize to a z-score","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"# Probability from the standard normal CDF","label":null,"prefix":null,"suffix":null,"section":"Probability from the standard normal CDF","hero":false,"slider":null,"value":null,"display":null},{"text":"probability = normDist(x, mu, sigma, true) // @hero @formula @label(P(height < 182 cm))","label":"P(height < 182 cm)","prefix":null,"suffix":null,"section":"Probability from the standard normal CDF","hidden":false,"hero":true,"slider":null,"value":0.9331927690234977,"display":"0.9332"}]},{"id":"operant-conditioning-ratio","title":"Operant Conditioning Ratio","description":"Calculate the response-to-reward ratio in operant conditioning.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"responses = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"rewards = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"ratio = responses / rewards // responses per reward @hero","label":null,"prefix":null,"suffix":"responses per reward","section":null,"hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"operating-expense-ratio","title":"Operating Expense Ratio","description":"Compare operating expenses against effective gross income.","category":"real-estate","icon":"pie-chart","tags":["real-estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"operatingExpenses = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"effectiveGrossIncome = 40000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":40000,"display":"40,000"},{"text":"oerPercent = (operatingExpenses / effectiveGrossIncome) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":37.5,"display":"37.5"}]},{"id":"operating-leverage-degree","title":"Operating Leverage Degree","description":"Calculate the degree of operating leverage from contribution margin and operating income.","category":"health","icon":"activity","tags":["leverage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"contribution_margin = 1000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"operating_income = 400000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":400000,"display":"400,000"},{"text":"degree_of_operating_leverage = contribution_margin / operating_income","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"opportunity-zone-investment-gain","title":"Opportunity Zone Gain","description":"Estimate potential tax savings from Opportunity Zone investments.","category":"real-estate","icon":"map","tags":["investment"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"capitalGainAmount = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"taxRatePercentage = 20 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"deferralYears = 5 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"taxSavings = (capitalGainAmount * (taxRatePercentage / 100)) // dollars deferred @hero","label":null,"prefix":null,"suffix":"dollars deferred","section":null,"hidden":false,"hero":true,"slider":null,"value":20000,"display":"20,000"}]},{"id":"optimism-bias-margin","title":"Optimism Bias Margin","description":"Calculate the optimism bias margin between predicted and average success rates.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"predicted_success_rate = 0.8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"average_success_rate = 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"bias_margin = predicted_success_rate - average_success_rate // percentage points @hero","label":null,"prefix":null,"suffix":"percentage points","section":null,"hidden":false,"hero":true,"slider":null,"value":0.3,"display":"0.3"}]},{"id":"orbital-period","title":"Orbital Period","description":"Calculate orbital period in hours from semi-major axis and central body mass.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"semi_major_axis_kilometers = 42164 // Geostationary","label":null,"prefix":null,"suffix":"Geostationary","section":null,"hidden":false,"hero":false,"slider":null,"value":42164,"display":"42,164"},{"text":"planetary_mass_kilograms = 5.97e24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5.97e+24,"display":"5.97e24"},{"text":"gravitational_constant = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"period_seconds = 2 * pi * sqrt( (semi_major_axis_kilometers * 1000)^3 / (gravitational_constant * planetary_mass_kilograms) )","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":86181.15468591503,"display":"86,181.15"},{"text":"period_hours = period_seconds / 3600 // hours @hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":23.939209634976397,"display":"23.94"}]},{"id":"orbital-velocity","title":"Orbital Velocity","description":"Circular-orbit speed and period for any altitude around any body.","category":"science","icon":"orbit","tags":["orbit","physics","space"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Orbit","label":null,"prefix":null,"suffix":null,"section":"Orbit","hero":false,"slider":null,"value":null,"display":null},{"text":"body mass kg = 5.972e24 // kg 1e20..2e30","label":null,"prefix":null,"suffix":"kg","section":"Orbit","hidden":false,"hero":false,"slider":{"min":100000000000000000000,"max":2e+30,"step":2e+28},"value":5.972e+24,"display":"5.972e24"},{"text":"altitude km = 408 // km 100..400k","label":null,"prefix":null,"suffix":"km","section":"Orbit","hidden":false,"hero":false,"slider":{"min":100,"max":400000,"step":5000},"value":408,"display":"408"},{"text":"body radius km = 6371 // km 100..70k","label":null,"prefix":null,"suffix":"km","section":"Orbit","hidden":false,"hero":false,"slider":{"min":100,"max":70000,"step":1000},"value":6371,"display":"6,371"},{"text":"# Circular Orbit Math","label":null,"prefix":null,"suffix":null,"section":"Circular Orbit Math","hero":false,"slider":null,"value":null,"display":null},{"text":"_G = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":"Circular Orbit Math","hidden":true,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"_orbit_radius_m = (body radius km + altitude km) * 1000 // m","label":null,"prefix":null,"suffix":"m","section":"Circular Orbit Math","hidden":true,"hero":false,"slider":null,"value":6779000,"display":"6,779,000"},{"text":"velocity m per s = sqrt(G * body mass kg / orbit_radius_m) // m/s @label(Orbital velocity) @suffix(m/s)","label":"Orbital velocity","prefix":null,"suffix":"m/s","section":"Circular Orbit Math","hidden":false,"hero":false,"slider":null,"value":7667.789532332016,"display":"7,667.79"},{"text":"velocity km per s = velocity m per s / 1000 // km/s @hero @label(Orbital velocity (km/s))","label":"Orbital velocity (km/s)","prefix":null,"suffix":"km/s","section":"Circular Orbit Math","hidden":false,"hero":true,"slider":null,"value":7.667789532332016,"display":"7.668"},{"text":"# Orbital Period","label":null,"prefix":null,"suffix":null,"section":"Orbital Period","hero":false,"slider":null,"value":null,"display":null},{"text":"_period_seconds = 2 * pi * orbit_radius_m / velocity m per s // s","label":null,"prefix":null,"suffix":"s","section":"Orbital Period","hidden":true,"hero":false,"slider":null,"value":5554.8881483730975,"display":"5,554.89"},{"text":"period minutes = round(period_seconds / 60, 1) // min @label(Orbital period) @suffix(min)","label":"Orbital period","prefix":null,"suffix":"min","section":"Orbital Period","hidden":false,"hero":false,"slider":null,"value":92.6,"display":"92.6"},{"text":"orbits per day = round(1440 / period minutes, 1)","label":null,"prefix":null,"suffix":null,"section":"Orbital Period","hidden":false,"hero":false,"slider":null,"value":15.6,"display":"15.6"}]},{"id":"order-picking-accuracy","title":"Order Picking Accuracy","description":"Track the percentage of orders picked without any errors.","category":"business","icon":"check-circle","tags":["order"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"totalOrdersPicked = 1000 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"incorrectOrders = 5 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"accuracyRate = ((totalOrdersPicked - incorrectOrders) / totalOrdersPicked) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":99.5,"display":"99.5"}]},{"id":"origami-fold-thickness","title":"Origami Fold Thickness","description":"Calculate the thickness in millimeters of paper after N folds.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"initial_thickness_mm = 0.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"number_of_folds = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"final_thickness_mm = initial_thickness_mm * 2^number_of_folds // millimeters @hero","label":null,"prefix":null,"suffix":"millimeters","section":null,"hidden":false,"hero":true,"slider":null,"value":12.8,"display":"12.8"}]},{"id":"osha-incident-rate","title":"OSHA Incident Rate","description":"Calculate your company's safety incident rate per 100 employees.","category":"other","icon":"shield","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"numberOfIncidents = 5 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"totalHoursWorked = 200000 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"incidentRate = (numberOfIncidents * 200000) / totalHoursWorked // per 100 employees @hero","label":null,"prefix":null,"suffix":"per 100 employees","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"outbound-shipping-cost","title":"Outbound Shipping Cost","description":"Calculate the average cost to ship orders to your customers.","category":"business","icon":"send","tags":["shipping"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"totalOutboundFreight = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"totalOutboundOrders = 3000 // orders","label":null,"prefix":null,"suffix":"orders","section":null,"hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"averageOutboundCost = totalOutboundFreight / totalOutboundOrders // dollars per order @hero","label":null,"prefix":null,"suffix":"dollars per order","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"ovulation-calculator","title":"Ovulation Calculator","description":"Calculate days until ovulation and the fertile window from cycle data.","category":"health","icon":"activity","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Cycle Info","label":null,"prefix":null,"suffix":null,"section":"Cycle Info","hero":false,"slider":null,"value":null,"display":null},{"text":"days since last period = 14 // days 0..60","label":null,"prefix":null,"suffix":"days","section":"Cycle Info","hidden":false,"hero":false,"slider":{"min":0,"max":60,"step":1},"value":14,"display":"14"},{"text":"average cycle length = 28 // days 20..45","label":null,"prefix":null,"suffix":"days","section":"Cycle Info","hidden":false,"hero":false,"slider":{"min":20,"max":45,"step":1},"value":28,"display":"28"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"ovulation day = average cycle length - 14","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"days until ovulation = ovulation day - days since last period // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"},{"text":"# Fertility Window","label":null,"prefix":null,"suffix":null,"section":"Fertility Window","hero":false,"slider":null,"value":null,"display":null},{"text":"fertile window start = ovulation day - 5","label":null,"prefix":null,"suffix":null,"section":"Fertility Window","hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"fertile window end = ovulation day + 1","label":null,"prefix":null,"suffix":null,"section":"Fertility Window","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"}]},{"id":"ozone-layer-recovery-estimate","title":"Ozone Layer Recovery Estimate","description":"Predict years to ozone recovery based on chemical reduction.","category":"science","icon":"sun","tags":["science","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"current_ozone_depleting_substances_ppb = 3.2 // parts per billion","label":null,"prefix":null,"suffix":"parts per billion","section":null,"hidden":false,"hero":false,"slider":null,"value":3.2,"display":"3.2"},{"text":"target_level_ppb = 2.0 // level in 1980","label":null,"prefix":null,"suffix":"level in 1980","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"annual_reduction_rate_percent = 2 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"years_to_target_recovery = (log(target_level_ppb / current_ozone_depleting_substances_ppb)) / (log(1 - annual_reduction_rate_percent / 100)) // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":23.264388374233185,"display":"23.26"}]},{"id":"p-e-ratio","title":"P E Ratio","description":"Calculate price-to-earnings ratio and earnings yield from stock price and EPS.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Stock Data","label":null,"prefix":null,"suffix":null,"section":"Stock Data","hero":false,"slider":null,"value":null,"display":null},{"text":"$share_price = 150 // dollars 1..5k","label":null,"prefix":"$","suffix":"dollars","section":"Stock Data","hidden":false,"hero":false,"slider":{"min":1,"max":5000,"step":50},"value":150,"display":"$150.00"},{"text":"$earnings_per_share = 7.50 // dollars 0.01..500","label":null,"prefix":"$","suffix":"dollars","section":"Stock Data","hidden":false,"hero":false,"slider":{"min":0.01,"max":500,"step":5},"value":7.5,"display":"$7.50"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"price_to_earnings_ratio = share_price / earnings_per_share // @hero","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":20,"display":"20"},{"text":"earnings_yield = (earnings_per_share / share_price) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"valuation = if(price_to_earnings_ratio < 15, \"Potentially Undervalued\", if(price_to_earnings_ratio < 25, \"Fair Value\", \"Growth/Premium\"))","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Fair Value","display":"Fair Value"}]},{"id":"p-value-from-z","title":"P-Value from Z-Score (Two-Tailed)","description":"Approximate two-tailed p-value from a z-score using the normal CDF approximation.","category":"formulas","icon":"sigma","tags":["statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Z-score","label":null,"prefix":null,"suffix":null,"section":"Z-score","hero":false,"slider":null,"value":null,"display":null},{"text":"z = 1.96 // 0..5 by 0.01","label":null,"prefix":null,"suffix":null,"section":"Z-score","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.01},"value":1.96,"display":"1.96"},{"text":"# Abramowitz-Stegun approximation for normal CDF","label":null,"prefix":null,"suffix":null,"section":"Abramowitz-Stegun approximation for normal CDF","hero":false,"slider":null,"value":null,"display":null},{"text":"# Use the high-accuracy rational approximation","label":null,"prefix":null,"suffix":null,"section":"Use the high-accuracy rational approximation","hero":false,"slider":null,"value":null,"display":null},{"text":"abs_z = abs(z)","label":null,"prefix":null,"suffix":null,"section":"Use the high-accuracy rational approximation","hidden":false,"hero":false,"slider":null,"value":1.96,"display":"1.96"},{"text":"_t = 1 / (1 + 0.2316419 * abs_z)","label":null,"prefix":null,"suffix":null,"section":"Use the high-accuracy rational approximation","hidden":true,"hero":false,"slider":null,"value":0.6877493364725074,"display":"0.6877"},{"text":"_phi_z = 0.3989422804 * exp(-(abs_z^2) / 2)","label":null,"prefix":null,"suffix":null,"section":"Use the high-accuracy rational approximation","hidden":true,"hero":false,"slider":null,"value":0.05844094433324159,"display":"0.0584"},{"text":"_prob_one_tail = phi_z * (0.319381530 * t - 0.356563782 * t^2 + 1.781477937 * t^3 - 1.821255978 * t^4 + 1.330274429 * t^5)","label":null,"prefix":null,"suffix":null,"section":"Use the high-accuracy rational approximation","hidden":true,"hero":false,"slider":null,"value":0.024997825156545833,"display":"0.025"},{"text":"# Two-tailed p-value","label":null,"prefix":null,"suffix":null,"section":"Two-tailed p-value","hero":false,"slider":null,"value":null,"display":null},{"text":"p_value = 2 * prob_one_tail // @label(Two-tailed p)","label":"Two-tailed p","prefix":null,"suffix":null,"section":"Two-tailed p-value","hidden":false,"hero":true,"slider":null,"value":0.049995650313091666,"display":"0.05"}]},{"id":"p-value-z-test","title":"P Value Z Test","description":"Approximate a one-tailed p-value from a z-score for hypothesis testing.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"z score = 1.96 // 0..5 by 0.01","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.01},"value":1.96,"display":"1.96"},{"text":"# Approximation for one-tailed p-value","label":null,"prefix":null,"suffix":null,"section":"Approximation for one-tailed p-value","hero":false,"slider":null,"value":null,"display":null},{"text":"# Using a simple approximation for the area under the normal curve","label":null,"prefix":null,"suffix":null,"section":"Using a simple approximation for the area under the normal curve","hero":false,"slider":null,"value":null,"display":null},{"text":"p value approx = 0.5 * exp(-0.717 * z score - 0.416 * z score^2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Using a simple approximation for the area under the normal curve","hidden":false,"hero":true,"slider":null,"value":0.024808404786111647,"display":"0.0248"},{"text":"confidence level = (1 - p value approx) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Using a simple approximation for the area under the normal curve","hidden":false,"hero":false,"slider":null,"value":97.51915952138884,"display":"97.52"}]},{"id":"packet-loss-impact-tcp-throughput","title":"Packet Loss Impact Tcp Throughput","description":"Calculate maximum TCP throughput as constrained by RTT and packet loss.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"bandwidth_mbps = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"round_trip_time_ms = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"packet_loss_rate = 0.001","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.001,"display":"0.001"},{"text":"max_throughput = (1460 * 8) / (round_trip_time_ms * 0.001 * (packet_loss_rate ** 0.5))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":7387080.614153335,"display":"7,387,080.61"}]},{"id":"paint-coverage","title":"Paint Coverage","description":"Calculate how many gallons of paint you need for any room, minus doors and windows.","category":"construction","icon":"paintbrush","tags":["coverage"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Room Dimensions","label":null,"prefix":null,"suffix":null,"section":"Room Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"room length = 15 // ft 5..50","label":null,"prefix":null,"suffix":"ft","section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":15,"display":"15"},{"text":"room width = 12 // ft 5..50","label":null,"prefix":null,"suffix":"ft","section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":12,"display":"12"},{"text":"wall height = 9 // ft 7..20","label":null,"prefix":null,"suffix":"ft","section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":7,"max":20,"step":0.2},"value":9,"display":"9"},{"text":"number of doors = 1 // 0..6","label":null,"prefix":null,"suffix":null,"section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":0,"max":6,"step":0.1},"value":1,"display":"1"},{"text":"number of windows = 2 // 0..10","label":null,"prefix":null,"suffix":null,"section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":0,"max":10,"step":0.1},"value":2,"display":"2"},{"text":"# Wall Area","label":null,"prefix":null,"suffix":null,"section":"Wall Area","hero":false,"slider":null,"value":null,"display":null},{"text":"room perimeter = 2 * (room_length + room_width) // ft","label":null,"prefix":null,"suffix":"ft","section":"Wall Area","hidden":false,"hero":false,"slider":null,"value":54,"display":"54"},{"text":"gross wall area = room_perimeter * wall_height // sq ft","label":null,"prefix":null,"suffix":"sq ft","section":"Wall Area","hidden":false,"hero":false,"slider":null,"value":486,"display":"486"},{"text":"door area = number_of_doors * 21","label":null,"prefix":null,"suffix":null,"section":"Wall Area","hidden":false,"hero":false,"slider":null,"value":21,"display":"21"},{"text":"window area = number_of_windows * 12","label":null,"prefix":null,"suffix":null,"section":"Wall Area","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"paintable area = gross_wall_area - door_area - window_area // sq ft @hero","label":null,"prefix":null,"suffix":"sq ft","section":"Wall Area","hidden":false,"hero":true,"slider":null,"value":441,"display":"441"},{"text":"# Paint Needed","label":null,"prefix":null,"suffix":null,"section":"Paint Needed","hero":false,"slider":null,"value":null,"display":null},{"text":"coverage per gallon = 350 // sq ft 200..500 by 10","label":null,"prefix":null,"suffix":"sq ft","section":"Paint Needed","hidden":false,"hero":false,"slider":{"min":200,"max":500,"step":10},"value":350,"display":"350"},{"text":"number of coats = 2 // 1..4","label":null,"prefix":null,"suffix":null,"section":"Paint Needed","hidden":false,"hero":false,"slider":{"min":1,"max":4,"step":0.05},"value":2,"display":"2"},{"text":"gallons needed = (paintable_area * number_of_coats) / coverage_per_gallon","label":null,"prefix":null,"suffix":null,"section":"Paint Needed","hidden":false,"hero":false,"slider":null,"value":2.52,"display":"2.52"},{"text":"gallons to buy = roundup(gallons_needed)","label":null,"prefix":null,"suffix":null,"section":"Paint Needed","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"}]},{"id":"painting-coverage-gallons-required","title":"Painting Coverage Gallons Required","description":"Calculate gallons of paint needed from wall area, coverage rate, and coat count.","category":"design","icon":"palette","tags":["coverage"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"wall_area_square_feet = 400 // square feet","label":null,"prefix":null,"suffix":"square feet","section":null,"hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"paint_coverage_per_gallon = 350 // square feet per gallon","label":null,"prefix":null,"suffix":"square feet per gallon","section":null,"hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"number_of_coats = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total_gallons_required = (wall_area_square_feet / paint_coverage_per_gallon) * number_of_coats // gallons @hero","label":null,"prefix":null,"suffix":"gallons","section":null,"hidden":false,"hero":true,"slider":null,"value":2.2857142857142856,"display":"2.286"}]},{"id":"pallet-stack-height","title":"Pallet Stack Height","description":"Determine the total height of a pallet stack including the base.","category":"business","icon":"layers","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"palletBaseHeight = 0.15 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"boxHeight = 0.3 // 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2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"glide_ratio = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"horizontal_distance = launch_height_meters * glide_ratio","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"flight_speed_m_s = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"flight_time_seconds = horizontal_distance / flight_speed_m_s // seconds @hero","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":true,"slider":null,"value":3.3333333333333335,"display":"3.333"}]},{"id":"paper-recycling-water-saved","title":"Paper Recycling Water Saved","description":"Calculate water saved by recycling paper instead of 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C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"copper_thickness_oz = 1 // oz/ft2","label":null,"prefix":null,"suffix":"oz/ft2","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"required_trace_width_mils = (current_amperes / (0.048 * (temp_rise_celsius^0.44)))^(1/0.725) // mils @hero","label":null,"prefix":null,"suffix":"mils","section":null,"hidden":false,"hero":true,"slider":null,"value":42.39306714892737,"display":"42.39"}]},{"id":"pencil-writing-distance","title":"Pencil Writing Distance","description":"Calculate the total writing distance possible from a pencil's length.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"pencil_length_cm = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"km_per_cm = 2.4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.4,"display":"2.4"},{"text":"total_distance_km = pencil_length_cm * km_per_cm // kilometers @hero","label":null,"prefix":null,"suffix":"kilometers","section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"pendulum-period-large-angle","title":"Pendulum Period Large Angle","description":"Calculate pendulum period corrected for large swing amplitudes.","category":"education","icon":"book-open","tags":["pendulum","angle"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"length = 1 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"gravity = 9.80665 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(old/new)","prefix":null,"suffix":null,"section":"Ratios","hidden":false,"hero":false,"slider":null,"value":0.8065,"display":"0.8065"},{"text":"# Reverse","label":null,"prefix":null,"suffix":null,"section":"Reverse","hero":false,"slider":null,"value":null,"display":null},{"text":"reverse pct = round(((old value - new value) / new value) * 100 * 100) / 100 // % @label(% change back to original)","label":"% change back to original","prefix":null,"suffix":"%","section":"Reverse","hidden":false,"hero":false,"slider":null,"value":-19.35,"display":"-19.35"}]},{"id":"perfect-order-rate","title":"Perfect Order Rate","description":"Measure the percentage of orders that meet all requirements perfectly.","category":"business","icon":"award","tags":["order"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"ordersOnTime = 980 // 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ft²","label":null,"prefix":null,"suffix":"ft²","section":"Flow","hidden":false,"hero":false,"slider":null,"value":0.08726646259971647,"display":"0.0873"},{"text":"flow cfs = flow_rate / 449","label":null,"prefix":null,"suffix":null,"section":"Flow","hidden":false,"hero":false,"slider":null,"value":0.22271714922049,"display":"0.2227"},{"text":"flow velocity = flow_cfs / cross_section_area // ft/s @hero","label":null,"prefix":null,"suffix":"ft/s","section":"Flow","hidden":false,"hero":true,"slider":null,"value":2.5521505351038902,"display":"2.552"},{"text":"# Head Loss (Darcy-Weisbach approx)","label":null,"prefix":null,"suffix":null,"section":"Head Loss (Darcy-Weisbach approx)","hero":false,"slider":null,"value":null,"display":null},{"text":"reynolds number = flow_velocity * diameter_ft / 0.0000141","label":null,"prefix":null,"suffix":null,"section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":null,"value":60334.52801664043,"display":"60,334.53"},{"text":"friction factor approx = 0.025 // 0.005..0.1","label":null,"prefix":null,"suffix":null,"section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":{"min":0.005,"max":0.1,"step":0.001},"value":0.025,"display":"0.025"},{"text":"head loss = friction_factor_approx * (pipe_length / diameter_ft) * (flow_velocity^2) / (2 * 32.2) // ft","label":null,"prefix":null,"suffix":"ft","section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":null,"value":0.7585565629461652,"display":"0.7586"},{"text":"pressure drop = head_loss * 0.433 // psi","label":null,"prefix":null,"suffix":"psi","section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":null,"value":0.32845499175568954,"display":"0.3285"}]},{"id":"pipe-pressure-drop-hazen-williams","title":"Pipe Pressure Drop","description":"Calculate pressure loss in pipes using Hazen-Williams.","category":"engineering","icon":"droplet","tags":["engineering","plumbing","fluids"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"flow_rate_gpm = 50 // gallons per minute","label":null,"prefix":null,"suffix":"gallons per minute","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"pipe_diameter_inches = 2 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"pipe_length_feet = 100 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"roughness_coefficient_c = 140 // for PVC","label":null,"prefix":null,"suffix":"for PVC","section":null,"hidden":false,"hero":false,"slider":null,"value":140,"display":"140"},{"text":"pressure_drop_psi = 4.52 * pipe_length_feet * (flow_rate_gpm^1.85) / (roughness_coefficient_c^1.85 * pipe_diameter_inches^4.87) // psi @hero","label":null,"prefix":null,"suffix":"psi","section":null,"hidden":false,"hero":true,"slider":null,"value":2.300805982491716,"display":"2.301"}]},{"id":"pixel-converter","title":"Pixel Converter","description":"Convert between px, rem, em, and pt units.","category":"design","icon":"type","tags":["pixel","font"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Base Settings","label":null,"prefix":null,"suffix":null,"section":"Base Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base font size = 16 // px 8..32","label":null,"prefix":null,"suffix":"px","section":"Base Settings","hidden":false,"hero":false,"slider":{"min":8,"max":32,"step":1},"value":16,"display":"16"},{"text":"pixel value = 24 // px 1..200","label":null,"prefix":null,"suffix":"px","section":"Base Settings","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":24,"display":"24"},{"text":"# Conversions","label":null,"prefix":null,"suffix":null,"section":"Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"rem value = round(pixel value / base font size * 10000) / 10000 // rem @hero","label":null,"prefix":null,"suffix":"rem","section":"Conversions","hidden":false,"hero":true,"slider":null,"value":1.5,"display":"1.5"},{"text":"em value = round(pixel value / base font size * 10000) / 10000 // em @label(em (same as rem at root))","label":"em (same as rem at root)","prefix":null,"suffix":"em","section":"Conversions","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"pt value = round(pixel value * 0.75 * 100) / 100 // pt","label":null,"prefix":null,"suffix":"pt","section":"Conversions","hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"# Reverse: rem to px","label":null,"prefix":null,"suffix":null,"section":"Reverse: rem to px","hero":false,"slider":null,"value":null,"display":null},{"text":"rem input = 1.5 // rem 0.1..20 by 0.1","label":null,"prefix":null,"suffix":"rem","section":"Reverse: rem to px","hidden":false,"hero":false,"slider":{"min":0.1,"max":20,"step":0.1},"value":1.5,"display":"1.5"},{"text":"px from rem = round(rem input * base font size * 10) / 10 // px","label":null,"prefix":null,"suffix":"px","section":"Reverse: rem to px","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"# Common Sizes","label":null,"prefix":null,"suffix":null,"section":"Common Sizes","hero":false,"slider":null,"value":null,"display":null},{"text":"px for 1rem = base font size // px","label":null,"prefix":null,"suffix":"px","section":"Common Sizes","hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"px for 0.875rem = round(0.875 * base font size * 10) / 10 // px @label(0.875rem in px (small text))","label":"0.875rem in px (small text)","prefix":null,"suffix":"px","section":"Common Sizes","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"px for 1.25rem = round(1.25 * base font size * 10) / 10 // px @label(1.25rem in px (large text))","label":"1.25rem in px (large text)","prefix":null,"suffix":"px","section":"Common Sizes","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"}]},{"id":"pizza-slice-angle","title":"Pizza Slice Angle","description":"Calculate the angle in degrees of each slice in a divided pizza.","category":"everyday","icon":"smile","tags":["angle"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"number_of_slices = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"angle_degrees = 360 / number_of_slices // degrees per slice @hero","label":null,"prefix":null,"suffix":"degrees per slice","section":null,"hidden":false,"hero":true,"slider":null,"value":45,"display":"45"}]},{"id":"pizza-value","title":"Pizza Value","description":"Compare pizza sizes to find the best deal per square inch.","category":"everyday","icon":"pizza","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Small Pizza","label":null,"prefix":null,"suffix":null,"section":"Small Pizza","hero":false,"slider":null,"value":null,"display":null},{"text":"small diameter = 10 // inches 6..16","label":null,"prefix":null,"suffix":"inches","section":"Small Pizza","hidden":false,"hero":false,"slider":{"min":6,"max":16,"step":0.1},"value":10,"display":"10"},{"text":"$small price = 9.99 // 4..30","label":null,"prefix":"$","suffix":null,"section":"Small Pizza","hidden":false,"hero":false,"slider":{"min":4,"max":30,"step":1},"value":9.99,"display":"$9.99"},{"text":"small area = round(3.14159 * (small diameter / 2)^2 * 10) / 10 // sq in","label":null,"prefix":null,"suffix":"sq in","section":"Small Pizza","hidden":false,"hero":false,"slider":null,"value":78.5,"display":"78.5"},{"text":"# Large Pizza","label":null,"prefix":null,"suffix":null,"section":"Large Pizza","hero":false,"slider":null,"value":null,"display":null},{"text":"large diameter = 16 // inches 10..24","label":null,"prefix":null,"suffix":"inches","section":"Large Pizza","hidden":false,"hero":false,"slider":{"min":10,"max":24,"step":0.2},"value":16,"display":"16"},{"text":"$large price = 16.99 // 8..40","label":null,"prefix":"$","suffix":null,"section":"Large Pizza","hidden":false,"hero":false,"slider":{"min":8,"max":40,"step":1},"value":16.99,"display":"$16.99"},{"text":"large area = round(3.14159 * (large diameter / 2)^2 * 10) / 10 // sq in","label":null,"prefix":null,"suffix":"sq in","section":"Large Pizza","hidden":false,"hero":false,"slider":null,"value":201.1,"display":"201.1"},{"text":"# Value Comparison","label":null,"prefix":null,"suffix":null,"section":"Value Comparison","hero":false,"slider":null,"value":null,"display":null},{"text":"$small price per sq in = round(small price / small area * 1000) / 1000 // @label(Small: Price Per Sq Inch)","label":"Small: Price Per Sq Inch","prefix":"$","suffix":null,"section":"Value Comparison","hidden":false,"hero":false,"slider":null,"value":0.127,"display":"$0.13"},{"text":"$large price per sq in = round(large price / large area * 1000) / 1000 // @label(Large: Price Per Sq Inch)","label":"Large: Price Per Sq Inch","prefix":"$","suffix":null,"section":"Value Comparison","hidden":false,"hero":false,"slider":null,"value":0.084,"display":"$0.08"},{"text":"large vs small area = round(large area / small area * 10) / 10 // x more pizza @hero @label(Large Has X Times More Pizza)","label":"Large Has X Times More Pizza","prefix":null,"suffix":"x more pizza","section":"Value Comparison","hidden":false,"hero":true,"slider":null,"value":2.6,"display":"2.6"},{"text":"$savings per sq in = round((small price per sq in - large price per sq in) * 1000) / 1000 // @label(You Save Per Sq Inch With Large)","label":"You Save Per Sq Inch With Large","prefix":"$","suffix":null,"section":"Value Comparison","hidden":false,"hero":false,"slider":null,"value":0.043,"display":"$0.04"}]},{"id":"planetary-equilibrium-temperature","title":"Planetary Equilibrium Temperature","description":"Calculate a planet's equilibrium temperature from distance, albedo, and star luminosity.","category":"science","icon":"globe","tags":["planetary","temperature"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"distance_au = 1.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"albedo = 0.3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"star_luminosity_solar = 1.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"temperature_kelvin = 278 * (star_luminosity_solar^0.25) * sqrt((1 - albedo) / distance_au) // Kelvin @hero","label":null,"prefix":null,"suffix":"Kelvin","section":null,"hidden":false,"hero":true,"slider":null,"value":232.59148737647303,"display":"232.59"}]},{"id":"planetary-periods","title":"Planetary Periods","description":"Compare a planet's rotation and orbital period — when a day exceeds a year.","category":"science","icon":"globe","tags":["orbit"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Planet (default: Venus)","label":null,"prefix":null,"suffix":null,"section":"Planet (default: Venus)","hero":false,"slider":null,"value":null,"display":null},{"text":"rotation days = 243 // Earth days 0.1..10k","label":null,"prefix":null,"suffix":"Earth days","section":"Planet (default: Venus)","hidden":false,"hero":false,"slider":{"min":0.1,"max":10000,"step":100},"value":243,"display":"243"},{"text":"orbital days = 224.7 // Earth days 0.1..100k","label":null,"prefix":null,"suffix":"Earth days","section":"Planet (default: Venus)","hidden":false,"hero":false,"slider":{"min":0.1,"max":100000,"step":1000},"value":224.7,"display":"224.7"},{"text":"# Comparison","label":null,"prefix":null,"suffix":null,"section":"Comparison","hero":false,"slider":null,"value":null,"display":null},{"text":"day longer than year = rotation days - orbital days // days @hero @label(Day minus year (Earth days))","label":"Day minus year (Earth days)","prefix":null,"suffix":"days","section":"Comparison","hidden":false,"hero":true,"slider":null,"value":18.3,"display":"18.3"},{"text":"ratio day to year = round(rotation days / orbital days, 3) // @label(Rotation ÷ orbit)","label":"Rotation ÷ orbit","prefix":null,"suffix":null,"section":"Comparison","hidden":false,"hero":false,"slider":null,"value":1.081,"display":"1.081"},{"text":"# How Many \"Years\" in One \"Day\"","label":null,"prefix":null,"suffix":null,"section":"How Many \"Years\" in One \"Day\"","hero":false,"slider":null,"value":null,"display":null},{"text":"years per day = round(rotation days / orbital days, 3) // @label(Years per rotation)","label":"Years per rotation","prefix":null,"suffix":null,"section":"How Many \"Years\" in One \"Day\"","hidden":false,"hero":false,"slider":null,"value":1.081,"display":"1.081"},{"text":"# Reference: Earth","label":null,"prefix":null,"suffix":null,"section":"Reference: Earth","hero":false,"slider":null,"value":null,"display":null},{"text":"earth rotation hours = 23.93 // hr @label(Earth sidereal day) @suffix(hr)","label":"Earth sidereal day","prefix":null,"suffix":"hr","section":"Reference: Earth","hidden":false,"hero":false,"slider":null,"value":23.93,"display":"23.93"},{"text":"earth orbit days = 365.25 // days @label(Earth orbit (days))","label":"Earth orbit (days)","prefix":null,"suffix":"days","section":"Reference: Earth","hidden":false,"hero":false,"slider":null,"value":365.25,"display":"365.25"}]},{"id":"planetary-surface-gravity","title":"Planetary Surface Gravity","description":"Calculate surface gravity of a planet from its mass and radius.","category":"science","icon":"globe","tags":["planetary","gravity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"planetary_mass_kilograms = 5.97e24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5.97e+24,"display":"5.97e24"},{"text":"planetary_radius_meters = 6371000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371000,"display":"6,371,000"},{"text":"gravitational_constant = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"surface_gravity = (gravitational_constant * planetary_mass_kilograms) / planetary_radius_meters^2 // m/s^2 @hero","label":null,"prefix":null,"suffix":"m/s^2","section":null,"hidden":false,"hero":true,"slider":null,"value":9.816243509027343,"display":"9.816"}]},{"id":"plant-population-density","title":"Plant Population Density","description":"Calculate total plants needed for a field or garden bed.","category":"everyday","icon":"sprout","tags":["garden"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"field_width_meters = 20 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"field_length_meters = 50 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"row_spacing_meters = 0.5 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"plant_spacing_in_row_meters = 0.3 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"total_plants = (field_width_meters / row_spacing_meters) * (field_length_meters / plant_spacing_in_row_meters) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":6666.666666666666,"display":"6,666.67"}]},{"id":"plant-watering-frequency-estimator","title":"Plant Watering Frequency Estimator","description":"Estimate days between waterings based on temperature and humidity.","category":"health","icon":"leaf","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"container_size_liters = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"ambient_temperature_celsius = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"humidity_percentage = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"base_watering_interval_days = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"temperature_factor = (ambient_temperature_celsius - 20) * 0.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"humidity_factor = (60 - humidity_percentage) * 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"estimated_watering_interval_days = base_watering_interval_days - temperature_factor - humidity_factor","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"plastic-bottle-waste-reduction","title":"Plastic Bottle Waste Reduction","description":"Calculate weight of plastic waste avoided by using reusables.","category":"everyday","icon":"cup-soda","tags":["eco","waste"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"bottles_per_week = 7 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"bottle_weight_grams = 15 // grams","label":null,"prefix":null,"suffix":"grams","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"weeks_per_year = 52 // weeks","label":null,"prefix":null,"suffix":"weeks","section":null,"hidden":false,"hero":false,"slider":null,"value":52,"display":"52"},{"text":"annual_plastic_waste_avoided_kg = bottles_per_week * bottle_weight_grams * weeks_per_year / 1000 // kg @hero","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":true,"slider":null,"value":5.46,"display":"5.46"}]},{"id":"podcast-hosting-cost-growth","title":"Podcast Hosting Cost Growth","description":"Project monthly podcast hosting cost growth from storage increases.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"initial_monthly_hosting_cost = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"monthly_storage_increase_gigabytes = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"cost_per_extra_gigabyte = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"months_of_growth = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"projected_monthly_cost_after_growth = initial_monthly_hosting_cost + (monthly_storage_increase_gigabytes * months_of_growth * cost_per_extra_gigabyte)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":140,"display":"140"}]},{"id":"point-break-even-mortgage","title":"Point Break Even Mortgage","description":"Calculate months to break even when buying mortgage discount points.","category":"finance","icon":"home","tags":["mortgage","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Points Analysis","label":null,"prefix":null,"suffix":null,"section":"Points Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = 400000 // 50k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Points Analysis","hidden":false,"hero":false,"slider":{"min":50000,"max":1000000,"step":5000},"value":400000,"display":"$400,000.00"},{"text":"interest rate without points = 7.0 // %","label":null,"prefix":null,"suffix":"%","section":"Points Analysis","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"interest rate with points = 6.75 // %","label":null,"prefix":null,"suffix":"%","section":"Points Analysis","hidden":false,"hero":false,"slider":null,"value":6.75,"display":"6.75"},{"text":"number of points = 1 // 0..4 by 0.25","label":null,"prefix":null,"suffix":null,"section":"Points Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.25},"value":1,"display":"1"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_cost_of_points = loan amount * (number of points / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":4000,"display":"$4,000.00"},{"text":"$_monthly_payment_no_points = loan amount * (7.0/1200 * (1+7.0/1200)^360) / ((1+7.0/1200)^360 - 1)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2661.2099807167297,"display":"$2,661.21"},{"text":"$_monthly_payment_with_points = loan amount * (6.75/1200 * (1+6.75/1200)^360) / ((1+6.75/1200)^360 - 1)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2594.392386272862,"display":"$2,594.39"},{"text":"$_monthly_savings = monthly_payment_no_points - monthly_payment_with_points","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":66.8175944438676,"display":"$66.82"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"break even months = cost_of_points / monthly_savings // @hero months","label":null,"prefix":null,"suffix":"months","section":"Result","hidden":false,"hero":true,"slider":null,"value":59.864471825012146,"display":"59.86"},{"text":"break even years = break even months / 12","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":4.9887059854176785,"display":"4.989"},{"text":"$total savings over 30 years = (monthly_savings * 360) - cost_of_points","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":20054.333999792336,"display":"$20,054.33"}]},{"id":"point-distance-2d","title":"Point Distance 2d","description":"Calculate Euclidean distance between two 2D points.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-24T04:21:27.454Z"},"rows":[{"text":"# Point 1","label":null,"prefix":null,"suffix":null,"section":"Point 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