How we calculate

Fraction, exponent and logarithm engine

The fraction, exponent and log calculators.

Formulas

• Fractions use exact BigInt arithmetic and are reduced by the greatest common divisor, so no rounding enters the result. Mixed number = whole + numerator / denominator.
• Power = base^exponent; a negative exponent is the reciprocal of the positive power. Logarithm of x in base b = ln(x) / ln(b) (change of base).

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Chemistry engine

The chemistry calculator: molar mass, moles and grams, molarity and dilution.

Formulas

• Molar mass = sum of (standard atomic weight × atom count) over the parsed formula, including parentheses and hydrates. Moles = grams ÷ molar mass; molarity = moles ÷ liters; dilution C1·V1 = C2·V2.

Sources

• IUPAC CIAAW abridged standard atomic weights (2021). Elements with no standard weight use the mass number of the longest-lived isotope.

Update frequency: Reviewed when IUPAC revises standard atomic weights or the calculator is changed.

Birthday engine

The birthday calculator: next birthday, days until it, weekday born, days lived and zodiac sign.

Formulas

• Age uses calendar-date arithmetic (years, then months, then days). Days lived is the calendar-day difference between the birth date and the as-of date.
• A Feb 29 birthday falls on March 1 in non-leap years. Zodiac signs use the commonly published fixed Western date ranges.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Time zone engine

The time zone converter, which reads UTC offsets from the IANA time zone database built into the runtime.

Formulas

• Local wall time is resolved to a UTC instant using the source zone offset at that date; the target time is that instant shown in the target zone.
• A local time skipped by a daylight saving change is rejected; a repeated local time uses its first occurrence.

Sources

• IANA Time Zone Database, via the JavaScript Intl API.

Update frequency: Follows the time zone data shipped with the runtime; reviewed when the calculator is changed.

Military time engine

The military time converter between 12-hour and 24-hour time.

Formulas

• 12:00 AM is 0000, 12:00 PM is 1200; 1:00 PM to 11:59 PM add 12 hours. 2400 is accepted as the end of the day and equals 0000 of the next day.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Parlay engine

The parlay calculator, which does arithmetic on odds you enter and uses no market data.

Formulas

• American +A becomes decimal 1 + A/100; -A becomes 1 + 100/A. Combined decimal odds are the product of the legs; a pushed leg counts as 1.
• Payout = stake × combined decimal; profit = payout − stake; implied probability = 1 ÷ combined decimal.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Date engine

Age, date, date difference, day counter, weeks between dates, hours, minutes to hours, add time and countdown calculators, the business days calculator, and the N-days-from-today and days-until pages. Also the Time Duration Calculator (exact elapsed time between two dates and times), the Date To Date Calculator (one span in days, weeks, months and years) and the Time Calculator (hh:mm:ss addition and subtraction).

Formulas

• Hours and add-time use wall-clock arithmetic with no daylight-saving adjustment. The countdown resolves a chosen IANA time zone through Intl; a time skipped by a clock change moves forward by the gap and a repeated time uses its first occurrence.
• Dates are UTC calendar dates; a time zone never shifts a result.
• A span is whole years, then whole months, then remaining days.
• Adding months clamps to the last day of a shorter month (January 31 + 1 month = February 28 or 29).
• Business days exclude Saturdays and Sundays and any holidays you enter.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Currency conversion engine

The Currency Converter (user-supplied rate, margin and flat fee, minor-unit rounding from Intl). No exchange rates are built in.

Formulas

• Received = (amount - flat fee) x rate x (1 - margin / 100). To receive a target: send = target / (rate x (1 - margin / 100)) + flat fee, rounded up to the minor unit.
• Minor-unit digits (JPY 0, USD 2, KWD 3) come from the browser Intl data, not from a table in the site.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Birth chart engine

The Birth Chart Calculator (tropical signs, Ascendant, Midheaven and whole-sign houses; 1800 to 2050).

Formulas

• Sun and Moon: Meeus, Astronomical Algorithms, chapters 25 and 47 (truncated). Planets: JPL Keplerian elements for approximate positions, Table 1 (1800 to 2050).
• Ascendant and Midheaven from local sidereal time (Meeus chapters 12 and 14); whole-sign houses counted from the Ascendant sign.
• Accuracy is a few hundredths of a degree for the Sun and Moon and about arcminutes for planets; it is an entertainment tool, not an ephemeris.

Sources

• E.M. Standish and J.G. Williams, Keplerian Elements for Approximate Positions of the Major Planets, JPL Solar System Dynamics (ssd.jpl.nasa.gov/planets/approx_pos.html).
• Jean Meeus, Astronomical Algorithms, 2nd ed.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Palworld breeding engine

The Palworld Breeding Calculator (child of two parents, and every parent pair for a target Pal).

Formulas

• Child = the Pal whose breeding rank is closest to floor((rankA + rankB + 1) / 2), with same-species and unique-combination overrides.

Sources

• PalCalc datamine (github.com/tylercamp/palcalc), db v28, commit 08fe1eea, fetched 2026-11-04.

Update frequency: Reviewed when a game update changes breeding data.

Seasonal countdown engine

The "how many days until" pages for US holidays.

Formulas

• Each date comes from its calendar rule, for example Thanksgiving is the 4th Thursday of November.
• The next event on or after today is chosen; today counts as 0 days.

Sources

• US federal holiday rules, as described in the engine source comments.

Update frequency: Dates are computed from rules, so there is no yearly data refresh; the event list and rules are reviewed when pages are added.

Percentage engine

Percentage calculators and the "X out of Y" score pages.

Formulas

• Percentage of a whole: part ÷ whole × 100.
• Percentage change: (new − old) ÷ |old| × 100.
• Results are rounded for display only; the underlying value is not rounded.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Grade engine

Grade, weighted grade, test grade and final grade calculators.

Formulas

• Weighted grade = sum(score × weight) ÷ sum(weight).
• Score needed on the final = (target − current × (1 − w)) ÷ w, with w the final’s weight as a fraction.
• Standard letter scale: 90 is an A, 80 a B, 70 a C, 60 a D.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

GPA engine

The GPA calculator (semester, weighted and cumulative).

Formulas

• GPA = sum(grade points × credits) ÷ sum(credits) on the 4.0 scale.
• Weighted GPA adds 0.5 for honors and 1.0 for AP courses; schools differ, so this is a common convention.

Sources

• The engine describes the credit-weighted GPA as the standard US college and high-school method; no document is cited.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Statistics engine

Average, weighted average, median, mode, standard deviation, variance, z-score, and the Z-Score and Probability calculators (normal distribution, tail probabilities, binomial trials).

Formulas

• Mean = sum ÷ count. The median of an even-sized set is the average of the two middle values.
• Sample and population variance and standard deviation are both available and labelled.
• Weighted average = sum(weight × value) ÷ sum(weights); weights cannot be negative and must not all be 0.
• Quartiles are the medians of the lower and upper halves of the sorted data (the middle value is left out when the count is odd); IQR = Q3 − Q1; outliers lie beyond Q1 − 1.5 × IQR or Q3 + 1.5 × IQR.
• Normal distribution: Φ(z) = erfc(−z ÷ √2) ÷ 2 computed by a series and a continued fraction (accurate to about 1e-12), and the inverse by Acklam’s algorithm plus one Halley step; two-tailed p = 2 × (1 − Φ(|z|)). Binomial probabilities use a log-factorial sum for stability.
• Probability rules: P(A and B) = P(A) × P(B) for independent events, P(A or B) = P(A) + P(B) − P(A and B), P(A | B) = P(A and B) ÷ P(B), and at least one success in n trials = 1 − (1 − p)^n.
• Standard error of the mean = sample standard deviation ÷ √n; coefficient of variation = standard deviation ÷ |mean|, undefined when the mean is 0.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Arithmetic engine

The basic, simple, scientific and math calculators, the Roman Numerals Converter and the Square Root Calculator.

Formulas

• A hand-written expression parser; input is never executed as code.
• Roman numerals use standard subtractive notation for 1 to 3999; input is accepted only if it is the canonical numeral for its value (IIII, VX and IC are rejected).
• Square root: the value y with y² = x; a radical is simplified by pulling pairs of equal primes out of the square root (√72 = 6√2); a negative input gives an imaginary result (√−16 = 4i). Cube roots allow negative inputs.
• The % operator divides by 100. Results are cleaned to 12 significant digits to hide floating-point noise.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Number theory and ratio engine

Greatest common factor, least common multiple, the ratio calculator, the Factor Calculator and the Prime Factorization Calculator.

Formulas

• GCF and LCM come from prime factorization by trial division, for whole numbers of 1 or more.
• Factors come from the prime factorization: the number of factors is the product of (exponent + 1) and their sum is the product of (1 + p + … + p^e).
• A ratio is simplified by its common factor; a proportion a : b = c : d is solved for the one missing term.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Permutation and combination engine

The permutation and combination calculators.

Formulas

• Permutations P(n, r) = n! ÷ (n − r)!; with repetition n^r.
• Combinations C(n, r) = n! ÷ (r! (n − r)!); with repetition C(n + r − 1, r).
• Results are exact BigInt integers for n and r up to 1,000, never rounded floating-point values.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Quadratic engine

The quadratic formula calculator.

Formulas

• Roots of ax² + bx + c = 0 are (−b ± √(b² − 4ac)) ÷ 2a. A negative discriminant gives a complex pair.
• Real roots use the stable form q = −(b + sign(b)·√D) ÷ 2, roots q ÷ a and c ÷ q, so a large b does not cancel the small root.
• With a = 0 the equation is linear: x = −c ÷ b.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Simple interest engine

The interest calculator (simple interest, compared with the compound growth engine).

Formulas

• Simple interest I = P × r × t and final amount A = P + I, with the rate r as an annual decimal and t in years; days are converted at 365 days a year and months at 12 months a year.
• The comparison page uses the compound-growth engine for the same principal, rate and time, so the only difference shown is compounding.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Sample size engine

The sample size, margin of error and confidence interval calculators.

Formulas

• Proportion: n0 = z² × p(1 − p) ÷ e², with p = 0.5 as the worst case when the true share is unknown. Mean: n0 = (z × σ ÷ e)².
• z is the two-sided normal quantile for the chosen confidence level, from the inverse normal function. Finite population correction: n = n0 ÷ (1 + (n0 − 1) ÷ N). The answer is always rounded up.

Sources

• Cochran, W. G., Sampling Techniques (New York: John Wiley & Sons; first published 1953). Formulas for proportions and means. Edition, chapter and page are not cited because they were not checked.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Algebra engine

The algebra calculator: one linear equation, two linear equations and the quadratic formula.

Formulas

• Linear ax + b = cx + d: x = (d − b) ÷ (a − c); no solution when a = c and b ≠ d, every x when a = c and b = d. Inputs are held as exact fractions, so 0.1x + 0.2 = 0.3 gives exactly x = 1.
• Two linear equations are solved with Cramer’s rule; a zero determinant means no solution (parallel lines) or infinitely many (the same line). Quadratics reuse the quadratic engine.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Numerical integration engine

The integral calculator (numerical rules; it reuses the arithmetic parser).

Formulas

• Composite rules on n equal subintervals of width h = (b − a) ÷ n: trapezoid, midpoint and Simpson’s 1/3 rule (n even). The error estimate for Simpson compares n and 2n subintervals: |S₂ₙ − Sₙ| ÷ 15.
• The result is a numerical approximation, not an antiderivative. Improper integrals are not supported, and a function value that is not finite stops the calculation.

Sources

• Burden, R. L. and Faires, J. D., Numerical Analysis (Brooks/Cole, later Cengage Learning; later editions add A. M. Burden). Composite Newton–Cotes formulas. Edition, section and page are not cited because they were not checked.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Function plotting engine

The graphing calculator (reuses the arithmetic parser).

Formulas

• Samples y = f(x) across the x range; undefined values and jumps that do not shrink under bisection break the curve.
• Degree-2 fit: a = (f(1) + f(−1)) ÷ 2 − f(0), b = (f(1) − f(−1)) ÷ 2, c = f(0), checked at three more points. Vertex x = −b ÷ 2a, D = b² − 4ac, roots (−b ± √D) ÷ 2a.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Matrix engine

The matrix calculator (up to 4 × 4).

Formulas

• Sum, difference, product (row by column), scalar multiple, transpose and trace. The determinant and rank of whole-number matrices use exact integer elimination (Bareiss), so a determinant of 0 is exact; decimal matrices use elimination with partial pivoting and a 1e-12 relative tolerance.
• The inverse uses Gauss–Jordan elimination and is reported as singular when the determinant is 0.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Symbolic derivative engine

The derivative calculator (symbolic differentiation with the rules applied, slope and tangent line at a point). Also the Calculus Calculator, which dispatches to the derivative and integral engines.

Formulas

• Rules applied: constant, power (d/dx xⁿ = n·xⁿ⁻¹), sum, product ((uv)′ = u′v + uv′), quotient ((u/v)′ = (u′v − uv′) ÷ v²) and chain (f(g(x))′ = f′(g(x))·g′(x)), with the standard derivatives of sin, cos, tan, eⁿ, ln and sqrt.
• The slope at x = a is f′(a); the tangent line is y = f(a) + f′(a)(x − a). Results are checked against a central difference in the tests.

Sources

• Standard single-variable calculus differentiation rules. A specific textbook edition and page were not checked.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Geometry engine

Slope, midpoint, square footage, square yard, circumference, volume and Pythagorean theorem calculators, plus the trigonometry (sin/cos/tan, inverses, right-triangle solver), geometry (2D shape area and perimeter), area (shape areas in six units), perimeter and triangle (SSS, SAS, ASA) solver and distance (2D, 3D and great-circle) calculators.

Formulas

• Slope = rise ÷ run between two points; a vertical line has no slope.
• Midpoint = ((x1 + x2) ÷ 2, (y1 + y2) ÷ 2); a missing endpoint is 2 × midpoint − known endpoint.
• Area of rectangles, triangles and circles is summed and shown in several units.
• Circle: circumference = 2πr = πd and area = πr², solved back from whichever one value you know (r = C ÷ 2π, r = √(A ÷ π)). Square yards = area in square feet ÷ 9, with 1 sq yd = 0.83612736 m².
• Right triangle: c = √(a² + b²) and a = √(c² − b²); area = ab ÷ 2; angle A = atan2(a, b); altitude to the hypotenuse = ab ÷ c.
• Unit definitions are exact: 1 in = 1/12 ft, 1 yd = 3 ft, 1 ft = 0.3048 m.
• Distance: √(Δx² + Δy² + Δz²) in 2D/3D; haversine great-circle distance on a sphere of mean radius 6,371.0088 km, with 1 mi = 1.609344 km and 1 nmi = 1.852 km exact.
• Volume of cubes, cylinders, cones, spheres and other common solids from their dimensions.

Sources

• Exact definitions of the foot and yard in meters.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Paycheck engine

The take-home pay and paycheck calculators and the state paycheck pages.

Formulas

• Per-paycheck stub: Section 125 health premiums reduce FICA wages, federal taxable income and the state base; 401(k) reduces federal and state only.
• Annual estimate of federal income tax from the bracket table after the standard deduction.
• Payroll (FICA) tax: Social Security and Medicare on gross pay, plus Additional Medicare above its threshold.
• State income tax on the state paycheck pages: a flat rate, or graduated bands, applied to wages above the state’s standard deduction or exemption for a single filer; a rule that holds only up to some wage refuses higher wages instead of guessing.
• The annual state pages estimate the year’s liability spread over pay periods; they are not employer withholding calculations.
• Additional 2026 state and municipal scenarios use the cited employer formulas, statutory local wage rates and employee contribution caps. Whole-dollar per-check rounding is applied where prescribed; continuing older formulas retain their real effective dates. Pay-period and W-4 comparisons use the IRS frequency and Step 2/4(c) methods.
• The California, New York City and Philadelphia pages model withholding for one biweekly paycheck: IRS Publication 15-T Worksheet 1A (single, standard schedule), New York State and City Method II, California Method B plus SDI, and the Philadelphia wage tax. Conditions a table does not cover are refused, not guessed.

Sources

• IRS Revenue Procedure 2025-32, section 4.01: 2026 income tax rate tables (taxable income brackets).
• IRS announcement IR-2025-103 (October 9, 2025): 2026 standard deduction amounts.
• IRS Publication 15 (2026): Social Security wage base $184,500, 6.2% Social Security and 1.45% Medicare employee rates, 0.9% Additional Medicare Tax withholding on wages above $200,000.
• Figures last verified on 2026-11-02.
• State flat rates and allowances: Tax Foundation, State Individual Income Tax Rates and Brackets, 2026 (a secondary source).
• New York rates: NYS-50-T-NYS (1/26), Withholding Tax Tables and Methods, New York State Department of Taxation and Finance.
• Withholding methods, read 2026-11-07: IRS Publication 15-T (2026), Federal Income Tax Withholding Methods; NYS-50-T-NYS (1/26), Withholding Tax Tables and Methods, New York State Department of Taxation and Finance; NYS-50-T-NYC (1/26), New York City Withholding Tax Tables and Methods, New York State Department of Taxation and Finance; California Withholding Schedules for 2026, Method B, Employment Development Department; City of Philadelphia, Wage tax for employers.

Update frequency: Tax figures are for tax year 2026. The maintenance calendar schedules an update each January once the IRS figures are published.

VA combined rating engine

The VA disability calculator (combined rating only, no payment amounts).

Formulas

• Ratings are combined largest first: each rating applies to the efficiency left after the previous ones, rounded to a whole number at each step.
• The final combined rating is rounded to the nearest 10, with 5 rounding up.
• Bilateral factor: ratings for paired limbs are combined first, 10% of that value is added, and the result counts as one rating.

Sources

• 38 CFR 4.25 (combined ratings table) and 38 CFR 4.26 (bilateral factor), ecfr.gov.
• The stepwise whole-number rounding is our reading of the VA combined ratings table; the VA decides your actual rating.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Salary and work-time engine

Salary, time card, time clock, work hours, overtime, timesheet, profit margin, margin and ROI calculators.

Formulas

• Every pay period converts through the annual amount (52 weeks a year unless the schedule says otherwise).
• Overtime defaults to hours above 40 a week at 1.5 times the rate.
• Profit margin is on revenue and markup is on cost; price for a target margin = cost ÷ (1 − margin).
• The markup calculator solves the selling price (cost × (1 + markup)), the markup (price ÷ cost − 1) or the cost (price ÷ (1 + markup)), and shows the matching margin = markup ÷ (1 + markup).
• The margin calculator solves revenue, cost and profit from any two known values: cost and margin (revenue = cost ÷ (1 − margin)), revenue and margin (cost = revenue × (1 − margin)), cost and markup (revenue = cost × (1 + markup)), or profit and margin (revenue = profit ÷ margin).
• Money is rounded to cents, half away from zero.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Loan engine

The loan payment calculator, the Mortgage Calculator (principal, interest, tax, insurance, HOA, PMI) and the Amortization Calculator (monthly and yearly schedules, extra payments), plus the Car Payment and Car Lease calculators, Mortgage Payoff (extra payments, extra needed for a target term), VA Loan (funding fee, financed loan, P&I), Down Payment, Closing Cost and Home Affordability, plus the Auto Loan and Personal Loan calculators (financed amount with tax and fees; net proceeds after an origination fee and the effective APR on them), plus the APR Calculator (APR with points and fees by solving the rate that equates the payments to the net amount financed), plus the Refinance Calculator (payment before and after, break-even months, interest difference, optional cash-out) and the Rent vs Buy Calculator (yearly cumulative net cost of renting and buying with a break-even year), plus the FHA Loan Calculator (loan payment with a financed 1.75% upfront premium and annual MIP from the HUD table), plus the Home Loan Calculator (the same loan compared over 15, 20 and 30 years with payoff months).

Formulas

• Fixed-rate payment = P × r ÷ (1 − (1 + r)^−n), with r the yearly rate ÷ 12 and n the number of monthly payments; at 0% it is P ÷ n.
• Each month: interest = balance × r, and the rest of the payment reduces the balance. An optional extra payment goes entirely to principal and the last payment is trimmed to end at exactly 0.
• Car lease: depreciation = (adjusted cap cost − residual) ÷ term; rent charge = (adjusted cap cost + residual) × money factor; money factor = APR ÷ 2400.
• Home affordability: housing limit = min(income × front %, income × back % − debts); loan = (budget − t × down) ÷ (k + t), with t the property-tax rate and k the payment factor per dollar; price = loan + down. Cash to close = down payment + closing costs − seller credit.
• Results show the payment unrounded in the maths and in dollars and cents on screen; fees, insurance, taxes and day-count conventions are not included.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Roth IRA engine

The Roth IRA calculator, plus the Compound Interest, Savings and CD calculators (compound amount, annuity future value, APY, months to a savings goal, CD maturity), plus the Investment Calculator (growth with monthly contributions and a yearly table), the Inflation and Annuity calculators (future cost = amount × (1+r)^years; annuity PV/FV with ordinary or due timing), plus the Retirement Calculator (yearly projection with growing contributions and a withdrawal-rate income), plus the 401(k) Calculator (employer match, 2026 IRS deferral limits and a yearly projection). Also the RMD Calculator (IRS Uniform Lifetime divisors and required beginning age). Also the Social Security Calculator (PIA from the 2026 bend points $1,286 and $7,749, full retirement age by birth year, early and delayed claiming adjustments).

Formulas

• Growth: each year balance = previous balance × (1 + return) + contribution, with contributions at the end of the year. The return is the number you enter, not a forecast.
• 2026 limit: $7,500, plus $1,100 from age 50. Income phase-out (MAGI): $153,000 to $168,000 single or head of household, $242,000 to $252,000 married filing jointly, $0 to $10,000 married filing separately and living with the spouse.
• Compound and savings: balance after n periods = P × (1 + r/n)^(n×t), plus regular deposits as the future value of an annuity; APY = (1 + r/n)^n − 1; a CD pays P × (1 + r/n)^(n×t) at maturity. The early-withdrawal penalty is a user-entered assumption.
• Mortgage: principal and interest use the loan formula above; tax, insurance and HOA are added monthly; PMI is a flat yearly percent of the loan while the down payment is under 20%.
• Social Security PIA = 90% of AIME up to $1,286 + 32% up to $7,749 + 15% above, rounded down to the dime. Early claiming: −5/9 of 1% a month for the first 36 months, −5/12 of 1% beyond; delayed: +2/3 of 1% a month to age 70.
• Inside the range: limit × (top − MAGI) ÷ (top − bottom), rounded up to the next $10, minimum $200 (the Publication 590-A worksheet rule).

Sources

• IRS news release, “401(k) limit increases to $24,500 for 2026, IRA limit increases to $7,500” (irs.gov), opened on 2026-11-03 for the limits and ranges. The rounding rule is from IRS Publication 590-A and was not re-opened.
• SSA, “Primary Insurance Amount formula” (ssa.gov/oact/COLA/piaformula.html), for the 2026 bend points; the full retirement age table and claiming adjustments follow SSA rules and were not re-opened.

Update frequency: The limits and ranges are for tax year 2026. The maintenance calendar schedules an update each autumn once the IRS announces the next year’s figures.

Sales tax and discount engine

The sales tax, discount and tip calculators. The tip calculator works in whole cents and gives the first few people the odd cent when a bill does not split evenly, and the budget calculator (income minus expenses with a 50/30/20 comparison). Also the Income Tax Calculator (2026 US federal brackets and standard deduction).

Formulas

• Sales tax = price × rate ÷ 100; total = price + tax. Reverse: price = total ÷ (1 + rate ÷ 100).
• Discounts apply one after another: sale = price × (1 − d1) × (1 − d2), so two 20% discounts give 36% off.
• Percent off = (original − sale) ÷ original × 100. Tax rates are entered by you; none are looked up.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Health and fitness engine

BMI, BMR, TDEE, body fat, calorie, calorie deficit, macro, heart rate, pace, sleep, pregnancy, cycle, dog age, maintenance calorie, height (predicted adult height) and BAC estimate calculators.

Formulas

• Calories: Mifflin-St Jeor basal rate × an activity factor from 1.2 to 1.9, with weekly goals at about 3,500 kcal per pound. The activity factors and the 3,500 figure are rules of thumb with no checked source.
• Maintenance calories: Mifflin-St Jeor, revised Harris-Benedict or Katch-McArdle resting rate × an activity factor, shown with a ±10% range. The Harris-Benedict coefficients, Katch-McArdle constants and activity factors are unverified rules of thumb.
• BAC estimate: Widmark, BAC% = grams of alcohol ÷ (body weight in g × r) × 100 − β × hours. r (about 0.68 men, 0.55 women) and β (0.015 per hour) are literature averages, so the result is a rough range and not a driving guide.
• Calorie deficit: daily target = maintenance calories − (weight to lose × 3,500 kcal per lb ÷ days available). The 3,500 figure is a rule of thumb that overstates long-term loss.
• Macros: grams = calories × share ÷ 4 for protein and carbohydrate, ÷ 9 for fat (Atwater factors). The four splits are examples, not guideline values.
• Protein: 0.8 g per kg (general), 1.2 to 1.6 g per kg (active) or 1.6 to 2.2 g per kg (strength); only the strength range has a checked source.
• BMI = weight in kg ÷ height in m squared, with the adult category cut-offs published by the CDC: under 18.5, 18.5 to under 25, 25 to under 30, 30 and over.
• Ideal weight: Devine, Robinson, Miller and Hamwi height-based formulas, as commonly published. Only the Robinson paper was opened, and the page uses its rounded coefficients, which differ slightly from the paper.
• Body surface area: Mosteller (square root of height in cm × weight in kg ÷ 3600) and Du Bois (0.007184 × weight^0.425 × height^0.725).
• Water: 33 ml per kg, plus 350 ml per 30 minutes of exercise, plus 10% in hot weather. A rule of thumb with no checked source.
• One-rep max: the average of seven repetition-based equations (Epley, Brzycki, Lander, Lombardi, O’Conner, Mayhew, Wathan). Only the Brzycki form was checked against a published article; the original publications of the other six were not located, so Epley and the rest are unverified.
• Heart rate: maximum from Fox (220 − age) or Tanaka (208 − 0.7 × age); zones as a percent of maximum, or of heart rate reserve (Karvonen) when a resting rate is entered. The zone bands have no checked source.
• Pace: time ÷ distance, with 1 mile = 1.609344 km exactly.
• Sleep: bedtimes or wake times in whole 90-minute cycles plus 15 minutes to fall asleep. The 90 minutes approximates published cycle lengths (70 to 120 minutes) and the 15 minutes is an assumption.
• IVF: due date = transfer + (266 - embryo age): +263 for a day-3 embryo, +261 for a day-5 blastocyst. Ultrasound: scan date + (280 - gestational age in days). Term stages use the 37w, 39w, 41w and 42w boundaries.
• Due date = last menstrual period + 280 days (40 weeks), adjusted by the difference from a 28-day cycle, or conception + 266 days. Trimesters begin at weeks 14 and 28; sources label them slightly differently, so treat them as approximate.
• Ovulation and period dates: ovulation 14 days before the next period by default, with a fertile window of the 5 days before it plus ovulation day. Cycle length is repeated from your last period; real cycles vary.
• Dog age: 15 human years for year one, 9 more for year two, then 5 per year (a rule of thumb for a medium dog).

Sources

• Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr 1990;51(2):241-247
• Hall KD, Sacks G, Chandramohan D, et al. Quantification of the effect of energy imbalance on bodyweight. Lancet 2011;378(9793):826-837
• Tanner JM, Goldstein H, Whitehouse RH. Standards for children’s height at ages 2-9 years allowing for height of parents. Arch Dis Child 1970;45(244):755-762
• Deurenberg P, Weststrate JA, Seidell JC. Body mass index as a measure of body fatness: age- and sex-specific prediction formulas. Br J Nutr 1991;65(2):105-114
• Roza AM, Shizgal HM. The Harris Benedict equation reevaluated: resting energy requirements and the body cell mass. Am J Clin Nutr 1984;40(1):168-182
• National Institute on Alcohol Abuse and Alcoholism (NIAAA), What Is A Standard Drink? (web page, checked November 4, 2026)
• National Highway Traffic Safety Administration (NHTSA), Drunk Driving (web page; the page itself returned HTTP 403 to our automated check on November 4, 2026)
• Utah Highway Safety Office, 0.05 BAC Law (web page, checked November 4, 2026)
• Electronic Code of Federal Regulations, 49 CFR 382.201 Alcohol concentration (search result summary, November 4, 2026)
• Posey D, Mozayani A. The estimation of blood alcohol concentration: Widmark revisited. Forensic Sci Med Pathol 2007;3(1):33-39 (bibliographic record confirmed; the paper itself is paywalled and was not opened)
• Food and Agriculture Organization of the United Nations, Chapter 3: Calculation of the Energy Content of Foods - Energy Conversion Factors (section 3.5.1, the Atwater general factor system; web page, checked November 2, 2026)
• Morton RW, Murphy KT, McKellar SR, et al. A systematic review, meta-analysis and meta-regression of the effect of protein supplementation on resistance training-induced gains in muscle mass and strength in healthy adults. Br J Sports Med 2018;52(6):376-384
• Centers for Disease Control and Prevention, Adult BMI Categories (page dated March 19, 2024)
• Robinson JD, Lupkiewicz SM, Palenik L, Lopez LM, Ariet M. Determination of ideal body weight for drug dosage calculations. Am J Hosp Pharm 1983;40(6):1016-1019
• Pai MP, Paloucek FP. The origin of the "ideal" body weight equations. Ann Pharmacother 2000;34(9):1066-1069
• Verbraecken J, Van de Heyning P, De Backer W, Van Gaal L. Body surface area in normal-weight, overweight, and obese adults. A comparison study. Metabolism 2006;55(4):515-524
• Mosteller RD. Simplified calculation of body-surface area. N Engl J Med 1987;317(17):1098
• Flint B, Das JM, Hall CA. Body Surface Area. In: StatPearls (NCBI Bookshelf NBK559005), last updated February 6, 2025
• Du Bois D, Du Bois EF. A formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 1916;17:863-871 (reprinted in Nutrition 1989;5(5):303-311)
• National Academies of Sciences, Engineering, and Medicine, Dietary Reference Intakes for Water, Potassium, Sodium, Chloride, and Sulfate (news release of February 11, 2004)
• LeSuer DA, McCormick JH, Mayhew JL, et al. The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. J Strength Cond Res 1997;11(4):211-213
• Abdul-Hameed U, Rangra P, Shareef MY, Hussain ME. Reliability of 1-repetition maximum estimation for upper and lower body muscular strength measurement in untrained middle aged type 2 diabetic patients. Asian J Sports Med 2012
• Brzycki M. Strength testing: predicting a one-rep max from reps-to-fatigue. J Phys Educ Recreat Dance 1993;64(1):88-90
• Tanaka H, Monahan KD, Seals DR. Age-predicted maximal heart rate revisited. J Am Coll Cardiol 2001;37(1):153-156
• Rugbumrung M, Rukbumrung T, Impanya S, Thurayot A. Effects of aerobic exercise on physical fitness in obesity using Fox vs. Tanaka’s maximum heart rate and percentage vs. Karvonen methods. Int J Exerc Sci 2025;18(8):695-711
• Karvonen MJ, Kentala E, Mustala O. The effects of training on heart rate: a longitudinal study. Ann Med Exp Biol Fenn 1957;35(3):307-315
• National Institute of Standards and Technology, NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically (web page, checked November 2, 2026)
• Hirshkowitz M, Whiton K, Albert SM, et al. National Sleep Foundation’s sleep time duration recommendations: methodology and results summary. Sleep Health 2015;1(1):40-43
• Institute of Medicine, Sleep Disorders and Sleep Deprivation: An Unmet Public Health Problem, chapter 2 "Sleep Physiology" (National Academies Press, 2006)
• NICHD (National Institutes of Health), About Pregnancy (web page, checked November 2, 2026)
• American College of Obstetricians and Gynecologists, Committee Opinion No. 700: Methods for Estimating the Due Date, Obstetrics & Gynecology 2017;129(5):e150-e154
• American College of Obstetricians and Gynecologists, Committee Opinion No. 579: Definition of Term Pregnancy, Obstetrics & Gynecology 2013;122(5):1139-1140
• Wilcox AJ, Weinberg CR, Baird DD. Timing of sexual intercourse in relation to ovulation. N Engl J Med 1995;333(23):1517-1521
• Wilcox AJ, Dunson D, Baird DD. The timing of the "fertile window" in the menstrual cycle: day specific estimates from a prospective study. BMJ 2000;321(7271):1259-1262
• Fehring RJ, Schneider M, Raviele K. Variability in the phases of the menstrual cycle. J Obstet Gynecol Neonatal Nurs 2006;35(3):376-384
• American College of Obstetricians and Gynecologists, Committee Opinion No. 651: Menstruation in Girls and Adolescents: Using the Menstrual Cycle as a Vital Sign, Obstetrics & Gynecology 2015;126(6):e143-e146
• Each health page lists these under "Sources" with what each one supports and which inputs have no checked source. Links last checked on 2026-11-02. Dog age has no published source.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed. Results are estimates, not medical advice.

Auto and travel engine

Fuel cost, miles per gallon, tire size, vehicle cost and mileage reimbursement calculators, plus the Gas, Mileage, EV Charging Cost and Towing Capacity calculators.

Formulas

• Fuel needed = distance ÷ miles per gallon; cost = fuel × price per gallon.
• Miles per gallon = miles driven ÷ gallons used; L/100 km and MPG are reciprocal.
• Tire size codes (such as 225/45R17) are parsed into width, sidewall and diameter to compare speedometer error.
• Ownership cost = price − resale value + fuel, insurance and upkeep.
• Trip gas = distance ÷ MPG (L/100 km converted via 1 mile = 1.609344 km, 1 US gal = 3.785411784 L); mileage = ending odometer − starting odometer.
• EV charging: wall energy = battery kWh × (end% − start%) ÷ (1 − loss%); cost = wall kWh × price per kWh.
• Towing (an estimate from ratings you enter, not a specification): max trailer = lowest of (manufacturer tow rating, GCWR − loaded vehicle weight, payload ÷ tongue %, hitch rating); 1 lb = 0.45359237 kg. No outside source: all ratings are user-entered.
• Mileage reimbursement = miles × rate per mile, rounded half-up to the cent. 2026 IRS standard rates: business 72.5 ¢ to June 30 and 76 ¢ from July 1; medical 20.5 ¢ then 23.5 ¢; charitable 14 ¢. Parking and tolls are added separately.

Sources

• IRS standard mileage rates (https://www.irs.gov/tax-professionals/standard-mileage-rates): Notice 2026-10 and the July 1, 2026 revision. The other auto formulas have no outside source.

Update frequency: The IRS can change the rates mid-year, as it did in 2026: the rates are rechecked each January and whenever the IRS announces a change.

Physics engine

The physics calculator (basic mechanics in SI units).

Formulas

• Speed v = d ÷ t; force F = m × a; momentum p = m × v; work W = F × d; power P = W ÷ t.
• Kinetic energy KE = ½ × m × v²; gravitational potential energy PE = m × g × h with standard gravity g = 9.80665 m/s².
• Each relation is rearranged to solve for any one unknown; inputs are magnitudes above 0 in SI units.

Sources

• Standard acceleration of gravity, 9.80665 m/s², as adopted by the 3rd CGPM in 1901.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Number base engine

The binary converter and the Hex Converter.

Formulas

• A digit string in base b equals the sum of digit × b^position, counted from 0 at the right.
• Converting a whole number to base b divides repeatedly by b and reads the remainders from last to first.
• Whole numbers of any size are handled exactly (BigInt); a minus sign is kept as a sign, not two’s complement.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Kitchen conversion engine

The grams to cups, cups to tablespoons, ML to cups, cooking measurement converter and ounces to cups calculators.

Formulas

• Volume only: 1 US cup = 16 US tablespoons = 48 teaspoons = 8 US fluid ounces = 236.5882365 mL; a metric kitchen cup is 250 mL, tablespoon 15 mL, teaspoon 5 mL.
• Grams = cups × grams per cup for the ingredient; tablespoons and teaspoons are exact fractions of a cup.
• 1 oz = 28.349523125 g (1 lb = 0.45359237 kg); weight to cups = grams / grams per cup.

Sources

• King Arthur Baking, Ingredient Weight Chart (https://www.kingarthurbaking.com/learn/ingredient-weight-chart), checked 2026-10-20.

Update frequency: Ingredient weights are rechecked against the chart when ingredients are added or the chart changes.

Temperature conversion engine

The temperature converter, the Celsius to Fahrenheit Converter and the Fahrenheit to Celsius Converter.

Formulas

• Fahrenheit = Celsius × 9/5 + 32; Celsius = (Fahrenheit − 32) × 5/9; Kelvin = Celsius + 273.15.
• Values below absolute zero (−273.15 °C) are rejected. Results are rounded for display only.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Length conversion engine

The length converter, inches to cm, cm to inches, feet to meters, meters to feet, quarts to gallons, liters to gallons, millimeters to inches, miles to kilometers and km to miles calculators, plus the gallons to liters and metric conversion (SI prefixes, nano to giga) calculators, the speed converter (mph, km/h, m/s, knots, ft/s held as m/s) and volume converter (US, imperial, metric and cubic units held as liters). Also the Unit Converter, which dispatches to the length, mass, volume, temperature, speed and area engines.

Formulas

• Miles and kilometers: 1 mi = 1.609344 km, 1 yd = 0.9144 m, 1 ft = 0.3048 m and 1 nautical mile = 1,852 m (exact definitions). Fractions of an inch are rounded half up to the chosen denominator and reduced.
• Every length is held in millimeters: 1 cm = 10 mm, 1 m = 1,000 mm, 1 in = 25.4 mm and 1 ft = 304.8 mm (exact definitions).
• Speed is held in m/s: 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s, 1 knot = 1852/3600 m/s and 1 ft/s = 0.3048 m/s (exact definitions).
• Volume is held in liters: 1 US gal = 3.785411784 L, 1 imperial gal = 4.54609 L, 1 US fl oz = 29.5735295625 mL and 1 ft³ = 28.316846592 L (exact definitions).
• A conversion multiplies by the source factor and divides by the target factor. Results are rounded for display only.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Home project engine

The concrete, paint, gravel, tile, fence, roofing, brick, deck, sod and mulch calculators, the flooring, drywall, board feet, paver and wallpaper calculators, the asphalt and siding calculators and the BTU cooling estimate.

Formulas

• BTU/h = ENERGY STAR room air conditioner chart value for the floor-area band (for example 8,000 for 300 to 350 sq ft) × sun (0.9, 1, 1.1) × ceiling ÷ 8 × (1 + climate %) + 600 × (people − 2) + 4,000 for a kitchen; 12,000 BTU/h = 1 ton; 1 BTU/h = 0.29307107 W. A rule of thumb, not a Manual J load calculation.
• Concrete volume = length × width × thickness, converted to meters (1 ft = 0.3048 m, 1 in = 0.0254 m); 1 yd³ = 0.764554857984 m³ = 27 ft³. The order total adds the waste percentage.
• Paint = (wall length × height − doors − windows) × coats ÷ coverage; coverage is the figure you enter (350 sq ft per gallon or 10 m² per liter by default, rules of thumb to check against the can). The result is rounded up to a whole gallon or liter.
• Gravel = length × width × depth, converted to cubic yards (27 ft³ each), then × (1 + waste); tons = cubic yards × bulk density in tons per cubic yard, which is a typical value you should confirm with your supplier.
• Tile = area ÷ ((tile length + joint) × (tile width + joint)), rounded up, then × (1 + waste) rounded up; boxes = tiles ÷ tiles per box, rounded up.
• Roofing = (length + 2 × overhang) × (width + 2 × overhang) × √(1 + (rise ÷ 12)²); one square is 100 sq ft; squares with waste are rounded up, then × bundles per square. A plan-area estimate that leaves out hips, valleys, ridge caps and underlayment.
• Brick: bricks = net wall area ÷ ((brick length + joint) × (brick height + joint)) × wythes, rounded up, then × (1 + waste) rounded up; mortar = envelope volume minus brick volume per brick, bed and head joints only; bags only from a user-entered yield. Brick sizes, joints and waste are assumptions you can change.
• Deck: rows = ⌈(joist side + gap) ÷ (board width + gap)⌉; boards = rows × ⌈board run ÷ board length⌉, then × (1 + waste); joists = ⌈board run ÷ spacing⌉ + 1; fasteners = rows × joists × 2. A material estimate, not a structural design.
• Sod: net area = area − excluded; buy = net × (1 + waste); rolls = ⌈buy ÷ coverage per roll⌉. Mulch: volume = length × width × depth; total = volume × (1 + settling); bags = ⌈total ÷ bag size⌉. Coverage, bag size, waste and settling are values you enter.
• Fence = sections ⌈run ÷ post spacing⌉; posts = sections + 1 for an open run (or sections for a closed loop) plus one extra per gate; rails = sections × rails per section; pickets = ⌈run ÷ (picket width + gap)⌉ plus waste.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Random number and dice engine

The random number generator, the dice roller, the coin flip, the password generator and the wheel spinner. The wheel picks its winner with the same unbiased draw before any animation runs; the animation never decides the result.

Formulas

• Each draw is a 32-bit value from the Web Crypto API, mapped to the range by rejection sampling: draws at or above floor(2^32 ÷ range) × range are discarded, so every value is equally likely.
• Numbers without repeats use a partial Fisher-Yates shuffle. A die is a draw from 1 to its number of sides; the total is the sum. Average of one die = (sides + 1) ÷ 2.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Snow day points model

The snow day calculator, an input-based rule of thumb. It makes no weather request.

Formulas

• Score = min(100, round((snowfall + ice + cold + snow on ground + timing + district history points) × road multiplier + district-threshold bonus)). The weights are published on the page.
• The weights are a rule of thumb chosen by the site, not calibrated against real closure data. It is not an official school closure prediction.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Dynasty trade engine

The dynasty trade calculator, which uses values you enter and no market data.

Formulas

• Each side is sorted from most to least valuable; adjusted value = value × (1 − d)^rank, with rank 0 for the best asset. A side total is the sum of its adjusted values.
• Difference % = |A − B| ÷ the larger side × 100. The valuations are your own and subjective; no player values or statistics are looked up.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Weight conversion engine

The pounds to kilograms, kg to lbs and weight converter calculators.

Formulas

• 1 lb = 0.45359237 kg exactly (international avoirdupois pound); 1 lb = 16 oz = 453.59237 g; 1 stone = 14 lb. Results are rounded for display only.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

Love score engine

The love calculator (entertainment only).

Formulas

• Both names are lowercased and reduced to letters, then sorted so the order does not matter. Letter counts of the combined string are combined by adding neighboring pairs and keeping the last digit until two digits remain: the score, 0 to 99. It is a folk game with no scientific basis.

Update frequency: Pure calculation: no external data. Reviewed when the calculator is changed.

ACT score engine

The ACT score calculator.

Formulas

• Composite = (English + Math + Reading) / 3, rounded to the nearest whole number (0.5 and above rounds up), 1 to 36.
• The pre-September-2025 four-section rule is offered as a labelled mode. No raw-to-scale table is used because conversions differ per test form.

Sources

• ACT, Understanding Your ACT Scores (act.org), checked 2026-11-04.

Update frequency: Reviewed if ACT changes the Composite rule.

SAT score engine

The SAT score calculator.

Formulas

• Total = Reading and Writing section score + Math section score, each 200 to 800, so 400 to 1600.
• No raw-to-scaled table is used because the digital SAT does not publish one that fits every test taker.

Sources

• College Board, SAT Suite score report help (satsuite.collegeboard.org).

Update frequency: Reviewed if the College Board changes the score scale.