How We Calculate | CalcArcade

This page explains how the calculators on CalcArcade are built and checked. Each calculator page also has its own “How we calculate it” and “Assumptions and limits” sections.

Formulas

Loans and mortgages: the standard fixed-payment amortization formula, M = P × r ÷ (1 − (1 + r)⁻ⁿ), with a month-by-month schedule for payoff and extra-payment results.
Compound interest: A = P(1 + r/n)^nt, extended with end-of-month contributions.
BMI: weight in kilograms divided by height in meters squared (703 × pounds ÷ inches² in US units), with adult categories as published by the U.S. Centers for Disease Control and Prevention.
Dates: calculated in UTC calendar days, so daylight saving time never changes a result, with leap years handled explicitly.
Unit conversions: exact definitions, for example 1 US gallon = 3.785411784 liters.
Currency: daily reference exchange rates from Frankfurter (frankfurter.dev), which collects rates published by central banks and other official sources. The rates are saved in the page when the site is built and their date is shown with every result, so using the converter sends nothing to any other site. Any pair is converted through the US dollar, and you can type your own rate instead.

US tax figures

Every US tax figure (brackets, standard deductions, Social Security and Medicare limits, retirement limits, state rates) is kept in one dated file. It is for tax year 2026 and was last updated October 29, 2026. Sources:

IRS Rev. Proc. 2025-32 (2026 inflation adjustments): federal brackets, standard deduction, aged/blind addition, capital gains 0%/15% thresholds.
IRS Notice 2025-67 and IRS news release (2026 retirement limits): 401(k), catch-up and IRA limits.
IRS Rev. Proc. 2025-19 (2026 HSA limits): HSA contribution limits.
SSA contribution and benefit base: Social Security wage base.
SSA primary insurance amount formula: bend points and 90/32/15 factors.
IRS Topic 560 Additional Medicare Tax, Form 8959 and Form 8960: additional Medicare and net investment income tax thresholds (set by law, not indexed).
IRS Schedule SE instructions: self-employment tax: 92.35% factor, 12.4% and 2.9%, $400 minimum.
Tax Foundation: State Individual Income Tax Rates and Brackets, 2026: state income tax type and rates, and the full bracket tables, standard deductions and exemptions in data/tax/us-2026-state-brackets.json (secondary source).
Tax Foundation: State and Local Sales Tax Rates, midyear 2026: state sales tax rate and average local rate (secondary source; local averages as of Jan 1, 2026).
HUD: FHA 2026 loan limits (news release HUD No. 25-145): FHA one-unit loan limit floor $541,287 and ceiling $1,249,125.
VA: funding fee and loan closing costs: VA funding fee rates for purchase loans.
SSA: retirement age and benefit reductions and delayed credits: full retirement age by birth year, early claiming reductions, delayed retirement credits (statutory).
HUD Mortgagee Letter 2023-05: FHA annual mortgage insurance premium rates: FHA annual premium table by term, base loan amount and loan-to-value, and its duration.
IRS Notice 2025-67: Roth and traditional IRA income limits for 2026: Roth IRA and traditional IRA deduction phase-out ranges.
20 CFR 404.304(f): benefits are rounded down to the next lower dollar: rounding of Social Security monthly benefits.
Each state revenue department page listed on the state entry (income.source): flat-rate states checked one by one on 2026-10-29: AZ CO GA IL IN IA KY LA MI MS NC PA UT (ID and OH partly).
IRS: new and enhanced deductions for individuals (Tax Tip 2026-12) and IRM 21.6.4: senior deduction amount ($6,000), its phase-out thresholds ($75,000 / $150,000) and the maximums of the tips ($25,000), overtime ($12,500 / $25,000) and car-loan-interest ($10,000) deductions.
Congressional Research Service: Federal Individual Income Tax Brackets, Standard Deduction, and Other Parameters: the 6% phase-out rate of the senior deduction.

The tax calculators are estimates. They do not replace tax software or a tax professional, and they do not model every credit, deduction or special rule.

Testing

Each calculation is covered by automated tests. They check published reference values (for example a $300,000 loan at 6% over 30 years has a payment of $1,798.65), edge cases such as zero-interest loans, leap days and impossible inputs, and confirm that US and metric BMI inputs agree. The worked example on each page is produced by running the same calculation code, so it cannot drift out of date.

Estimates and changing data

Some results depend on tax rules, rates or published health formulas that change over time or only approximate real life. Where a calculator uses them, its page names the source, shows the date the figures apply to, and says who the result is for. If we cannot keep a figure current, we do not publish that calculator.

Health and body estimates

Health results are estimates for general information. They are not medical advice, a diagnosis or a treatment plan, and they cannot replace talking to a doctor or dietitian. A health calculator on this site uses one of these published formulas, and says which on its page:

BMI: weight ÷ height² (see above), with adult categories from the U.S. Centers for Disease Control and Prevention.
Resting energy (BMR): Mifflin-St Jeor (Mifflin MD and others, American Journal of Clinical Nutrition, 1990): men 10 × weight (kg) + 6.25 × height (cm) − 5 × age + 5, women the same with − 161 in place of + 5. Revised Harris-Benedict (Roza and Shizgal, 1984): men 88.362 + 13.397 × kg + 4.799 × cm − 5.677 × age, women 447.593 + 9.247 × kg + 3.098 × cm − 4.330 × age. Katch-McArdle: 370 + 21.6 × lean body mass (kg).
Daily calories (TDEE): BMR × an activity factor of 1.2, 1.375, 1.55, 1.725 or 1.9. Targets are 250 or 500 calories a day above or below.
Ideal body weight: Devine (1974), Robinson (1983), Miller (1983) and Hamwi (1964), each a base weight at 5 feet plus a set amount per inch above it, and the healthy range from BMI 18.5 to 24.9.
Body fat (US Navy circumference method), measurements in inches: men: 86.010 × log10(waist − neck) − 70.041 × log10(height) + 36.76. Women: 163.205 × log10(waist + hip − neck) − 97.684 × log10(height) − 78.387. Source: Hodgdon JA and Beckett MB, Naval Health Research Center, 1984. The category scale is the common American Council on Exercise one.
Heart rate zones: maximum heart rate 208 − 0.7 × age (Tanaka, Monahan and Seals, 2001) or 220 − age, zones as a percent of the maximum, or the Karvonen method with a resting rate: resting + (maximum − resting) × intensity.
Calories burned: MET × weight (kg) × hours, with MET values from the 2011 Compendium of Physical Activities (Ainsworth and others).
One rep max: Epley w × (1 + reps ÷ 30), Brzycki w × 36 ÷ (37 − reps) and Lombardi w × reps^0.10.
Body surface area: Mosteller √(height (cm) × weight (kg) ÷ 3600), Du Bois 0.007184 × W^0.425 × H^0.725 and Haycock 0.024265 × W^0.5378 × H^0.3964.
Waist-to-hip ratio: thresholds from the World Health Organization expert consultation on waist circumference and waist-hip ratio, 2008.
Macros: 4 calories per gram of carbohydrate and protein, 9 per gram of fat.
Due date (Naegele's rule): 280 days from the first day of the last period, moved by the difference between your cycle length and 28 days.

Review and updates

Pages show the date they were last reviewed. When we change a formula or assumption we update the page and its date. If you find an error, please tell us.

This site was last built on October 31, 2026.