How our calculators work

Every result is computed by small, tested functions in your browser. We keep full precision internally and round only when we display a number, so long chains of math don’t drift. Each calculator page shows its formula and a worked example generated by the same code that produces your result. Dates are handled as calendar dates, independent of your time zone.

• Mortgage Calculator

  M = P × [ r(1+r)^n ] / [ (1+r)^n − 1 ]

  Sources: Freddie Mac — Primary Mortgage Market Survey (weekly average mortgage rates); CFPB — What is private mortgage insurance?; CFPB — What is an escrow or impound account?

• Refinance Calculator

  Savings = M_current − M_new
  Break-even (months) = Closing costs ÷ Savings

  Sources: Freddie Mac — Primary Mortgage Market Survey (weekly average mortgage rates); CFPB — What fees or charges are paid when closing on a mortgage and who pays them?

• Life Insurance Calculator

  need = Debt + Income × years + Mortgage + Education + final expenses
  coverage = max(0, need − existing coverage − savings)

  Sources: NAIC — Life Insurance (consumer guide: how much coverage do you need?); NerdWallet — How much life insurance do I need? (industry needs-based method: DIME — Debt, Income, Mortgage, Education)

• Retirement Calculator

  B(m) = B(m−1) × (1 + i) + (you + match) / 12,  i = (1 + r)^(1/12) − 1
  match = salary × min(you %, limit %) × match %
  4% rule income = 0.04 × balance

  Sources: Cooley, Hubbard & Walz (1998), “Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable”, AAII Journal (the Trinity study); AAII — Cooley, Hubbard & Walz (1998), “Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable” (PDF); IRS — 401(k) and profit-sharing plan contribution limits

• Personal Loan Calculator

  M = P × [ r(1+r)^n ] / [ (1+r)^n − 1 ]

  Sources: CFPB — What is the difference between a loan interest rate and the APR?; CFPB Regulation Z, Appendix J to Part 1026 — Annual Percentage Rate Computations for Closed-End Credit

• Auto Loan Calculator

  Tax = (Price − Trade-in) × tax rate
  Financed = Price + Tax − Down − Trade-in
  M = Financed × [ r(1+r)^n ] / [ (1+r)^n − 1 ]

  Sources: CFPB — Auto loans; FTC — Financing or leasing a car; CFPB — What is the difference between a loan interest rate and the APR?

• Debt Payoff Calculator

  n = −log(1 − (r × B) / M) / log(1 + r)

  Sources: CFPB — How to reduce your debt; Federal Reserve — Consumer Credit (G.19), including credit card interest rates

• Compound Interest Calculator

  i = (1 + r/k)^(k/12) − 1   (monthly rate)
  FV = P(1 + i)^(12t) + PMT × [ ((1 + i)^(12t) − 1) / i ]

  Sources: U.S. SEC, Investor.gov — Compound Interest Calculator

• Income Tax Calculator 2026

  taxable = gross − pre-tax − max(standard, itemized)
  tax = Σ rate × income within each bracket
  effective = tax ÷ gross

  Sources: IRS Rev. Proc. 2025-32 (inflation adjustments for tax year 2026)

• Paycheck Calculator

  net = gross − federal − FICA − state − pre_tax
  FICA = 6.2% Social Security + 1.45% Medicare

  Sources: IRS Rev. Proc. 2025-32 (inflation adjustments for tax year 2026); IRS Topic 751 — Social Security and Medicare withholding (2026 wage base $184,500); Tax Foundation, State Individual Income Tax Rates and Brackets, 2026

• Sales Tax Calculator

  tax   = price × (rate ÷ 100)
  total = price + tax
  price = total ÷ (1 + rate ÷ 100)

  Sources: Tax Foundation, State and Local Sales Tax Rates, Midyear 2026 (rates as of July 1, 2026)

• Inflation Calculator

  value_end = amount x (CPI_end / CPI_start)

  Sources: U.S. Bureau of Labor Statistics, CPI-U (CUUR0000SA0); 2026 is an estimate

• Calorie / TDEE Calculator

  BMR = 10×kg + 6.25×cm − 5×age + 5
  TDEE = BMR × activity factor

  Sources: Mifflin MD, St Jeor ST et al. (1990), Am J Clin Nutr 51(2):241–247

• BMI Calculator

  BMI = 703 × weight(lb) ÷ height(in)²

  Sources: CDC — Adult BMI categories

• Square Footage Calculator

  area  = length × width
  total = area × rooms
  cost  = total × price per sq ft

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; NIST Handbook 44 (2026), Appendix C — General Tables of Units of Measurement

• Fuel Cost Calculator

  gallons = miles ÷ MPG
  cost = gallons × price_per_gallon

  Sources: U.S. Energy Information Administration — Gasoline and Diesel Fuel Update (weekly average pump prices); U.S. DOE & EPA — FuelEconomy.gov (official MPG ratings); U.S. DOE & EPA — Driving More Efficiently (the 15–30% highway and 10–40% city penalties for aggressive driving)

• Tip Calculator

  tip = bill × tip%
  total = bill + tip
  per_person = total ÷ people

  Sources: IRS — Tip Recordkeeping and Reporting

• Age Calculator

  age = target_date − birth_date
  (broken into years, months, days)

  Sources: U.S. Naval Observatory — Leap Years

• Date Duration Calculator

  duration = end_date − start_date
  business_days = total − weekends

  Sources: U.S. Naval Observatory — Leap Years

• Percentage Calculator

  result = (percent ÷ 100) × base

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B

• GPA Calculator

  GPA = Σ(grade points × credits) ÷ Σ credits
  A=4.0  A-=3.7  B+=3.3  B=3.0  B-=2.7 …

  Sources: College Board, BigFuture — How to Calculate Your GPA on a 4.0 Scale

• Length Converter

  result = value × factor(from) ÷ factor(to)
  base unit: meter · 1 in = 0.0254 m · 1 ft = 0.3048 m · 1 mi = 1,609.344 m · 1 nmi = 1,852 m

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; NIST Handbook 44 (2026), Appendix C — General Tables of Units of Measurement

• Volume Converter

  base unit: cubic meter · 1 L = 0.001 m³
  1 US gal = 231 in³ = 3.785411784 L · qt = gal/4 · pt = gal/8 · cup = gal/16
  fl oz = gal/128 · tbsp = fl oz/2 · tsp = tbsp/3 · 1 UK gal = 4.54609 L

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; NIST Handbook 44 (2026), Appendix C — General Tables of Units of Measurement

• Weight Converter

  base unit: kilogram · 1 lb = 0.45359237 kg (exact)
  1 oz = lb/16 = 28.349523125 g · 1 st = 14 lb · 1 t = 1,000 kg

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; NIST Handbook 44 (2026), Appendix C — General Tables of Units of Measurement

• Temperature Converter

  K = °C + 273.15
  °F = °C × 9/5 + 32
  °C = (°F − 32) × 5/9

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; BIPM — The International System of Units (SI Brochure, 9th edition)

• Area Converter

  base unit: square meter · 1 in² = 6.4516 cm² · 1 ft² = 144 in² = 0.09290304 m² · 1 yd² = 9 ft²
  1 acre = 43,560 ft² = 4,046.8564224 m² · 1 mi² = 640 acres · 1 ha = 10,000 m²

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; NIST Handbook 44 (2026), Appendix C — General Tables of Units of Measurement

• Angle Converter

  180° = π rad = 200 gon · 1 turn = 360°
  rad = deg × π/180 · deg = rad × 180/π · 1° = 60′ = 3,600″

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; BIPM — The International System of Units (SI Brochure, 9th edition)

• Speed Converter

  base unit: meter per second
  1 km/h = 1/3.6 m/s · 1 mph = 0.44704 m/s · 1 kn = 1,852 m/h

  Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), Appendix B; NIST Handbook 44 (2026), Appendix C — General Tables of Units of Measurement

Brackets and standard deductions come from Internal Revenue Service Rev. Proc. 2025-32 (inflation adjustments for tax year 2026). Taxable income = gross pay − pre-tax 401(k) − other pre-tax deductions − the standard deduction. The income tax calculator uses the same tables and subtracts itemized deductions instead when they are larger; it covers ordinary income only, with no credits, AMT, NIIT or capital-gains rates.

FICA: Social Security 6.2% on wages up to the $184,500 wage base; Medicare 1.45% on all wages, plus 0.9% Additional Medicare Tax that employers withhold on wages over $200,000 (IRS Topic 751). 401(k) deferrals are capped at the 2026 limit of $24,500 and don’t reduce FICA wages; other pre-tax deductions are treated as Section 125 (they reduce federal, FICA and state wages). We model W-4 withholding as annual tax spread evenly across paychecks, without credits.

State brackets, standard deductions and personal exemptions for all 50 states and DC come from the Tax Foundation, State Individual Income Tax Rates and Brackets, 2026 (rates as of January 1, 2026). Joint filers use the joint schedule; single, separate and head-of-household filers use the single schedule. Personal-exemption credits are subtracted from tax. Local and city income taxes, most phase-outs and other credits are not modeled. State-specific notes:

• Alabama's standard deduction shrinks as income rises and Alabama also lets filers deduct federal income tax paid. This simplified estimate applies neither.
• Arkansas's withholding formula subtracts a fixed adjustment that tapers off above $94,700 of taxable income. This estimate keeps the full adjustment, so it understates Arkansas tax by up to about $290 on high incomes.
• Connecticut's personal exemption phases out above $30,000 (single) / $48,000 (joint); applied here. Connecticut also recaptures part of its lowest rate and allows personal credits at lower incomes, neither of which this simplified estimate applies.
• Indiana county income taxes are not included.
• Maine adds a 2% surcharge on taxable income over $1,000,000 ($1,500,000 filing jointly), applied here.
• Maryland counties add a local income tax (not included).
• Michigan city income taxes are not included.
• New Hampshire does not tax wages.
• New York City and Yonkers local taxes are not included.
• Ohio municipal income taxes are not included. Ohio's personal exemption also shrinks as income rises, and this estimate uses the largest amount, so it understates Ohio tax slightly above $40,000 of income.
• Oregon lets filers subtract federal income tax paid, up to $8,250, which this simplified estimate does not apply, so it overstates Oregon tax.
• Pennsylvania does not exclude 401(k) contributions from state wages.
• South Carolina decoupled from the federal standard deduction for 2026, so its taxable income now starts from federal adjusted gross income rather than federal taxable income.
• Utah's taxpayer tax credit stands in place of a standard deduction: it is 6% of your federal deduction and exemptions, cut by 1.3% of income above a filing-status threshold, so it is still worth roughly $230 at $75,000 of income and only runs out near $92,500. Utah had not published the 2026 thresholds when this page was reviewed, so the estimate leaves the credit out and overstates Utah tax for most filers.
• Vermont had not published its 2026 brackets or standard deduction when this page was reviewed, so those use the most recent confirmed amounts; the personal exemption is the 2026 figure.
• Washington taxes only capital gains, not wages. Two payroll premiums are withheld from Washington paychecks and are not deducted here: Paid Family and Medical Leave at 1.13% of wages (employees pay 71.43% of it) and WA Cares at 0.58%, paid entirely by the employee — together about $1,040 a year on a $75,000 salary.
• Wisconsin's standard deduction phases out as income rises — it is gone by about $136,000 — and this estimate applies the full amount, so it understates Wisconsin tax at middle and higher incomes.

State rates and population-weighted average local rates come from the Tax Foundation, State and Local Sales Tax Rates, Midyear 2026 (rates as of July 1, 2026).

• Local rates are population-weighted averages; your city or county rate may differ.
• California, Utah and Virginia statewide mandatory local add-ons are included in the state rate.
• Missouri, Minnesota, New Jersey and New Mexico use their exact statutory state rates (the source table rounds to two decimals).
• New Jersey's published average local rate (−0.02%) is shown as 0%.

We use the U.S. Bureau of Labor Statistics Consumer Price Index for All Urban Consumers (CPI-U), U.S. city average, all items, 1982–84=100 (series CUUR0000SA0), annual averages from 1913 through 2025. The 2026 value (331.655) is an estimate: the average of Jan–Aug 2026 monthly CPI-U values. The official 2026 annual average will replace it once BLS publishes it in January 2027.

4calcs is published by the 4calcs team. Formulas come from standard, published methods and every data table from an official or widely cited primary source — the IRS, the Social Security Administration, the Bureau of Labor Statistics, the Tax Foundation, the CDC and NIST — which each calculator page lists under “Sources”.

Every calculator is a small, pure function covered by automated tests that compare its output with reference values worked out independently. The worked example on each page is generated by the same code that produces your result, so the explanation can’t drift from the math.

Tax tables are updated every year when the IRS publishes its inflation adjustments and when the Tax Foundation updates its state tables; CPI data is updated when BLS publishes each annual average. Each page shows the date its content or data was last updated. Advertising and partners never influence a result, and any partner link is clearly labeled.

Found a mistake? Tell us the calculator and the numbers you entered through the contact form. We check every report, fix confirmed errors and update the page’s “Last updated” date. The full process — how calculators are maintained and how guides are reviewed — is in our editorial policy.