Methodology: how our calculators work

Our principles

1. Standard formulas only. We do not invent math. Every calculator uses the same formulas that banks, actuaries, and standards bodies use.
2. Assumptions are visible. If a calculator assumes a fixed rate, compounds monthly, or ignores taxes, that assumption is documented below and surfaced on the tool itself where it matters.
3. Nothing is hidden. All calculations run client-side. You can open the browser developer tools and inspect the code. Nothing is sent to a server.
4. Precision is disclosed. Results are typically rounded to 2 decimal places for currency and 4 decimal places for unit conversions, unless stated otherwise.

Mortgage and refinance

Tools: Mortgage Calculator, Refinance Calculator, Auto Loan Calculator.

Monthly payment uses the standard amortizing-loan formula:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

where
  M = monthly payment
  P = principal (loan amount)
  r = monthly interest rate (annual rate / 12)
  n = total number of monthly payments (years * 12)

Assumptions: fixed annual rate for the full term, monthly compounding, equal payments. Does not include property taxes, insurance, HOA fees, or PMI unless explicitly added as inputs. Refinance break-even is calculated as closing costs divided by monthly payment savings.

Sources: Consumer Financial Protection Bureau (CFPB) amortization guidance, Federal Reserve loan formula reference.

Loan and EMI

Tools: Loan Calculator, EMI Calculator, Interest Calculator.

EMI uses the same amortizing formula as the mortgage tool. The interest calculator supports both simple interest (I = P * r * t) and compound interest (see below).

Compound interest and investment return

Tools: Compound Interest Calculator, Investment Return Calculator, ROI Calculator.

Future value with recurring contributions:

FV = P * (1 + r/n)^(n*t) + PMT * (((1 + r/n)^(n*t) - 1) / (r/n))

where
  FV  = future value
  P   = initial principal
  PMT = periodic contribution
  r   = annual interest rate (decimal)
  n   = compounding periods per year
  t   = time in years

Assumptions: constant rate of return, contributions made at the end of each period, no fees or taxes unless explicitly modeled. Real investment returns vary year to year. Our tools show the compounded result assuming a flat rate, which is useful for comparison but is not a forecast.

ROI formula: ROI = (Gain - Cost) / Cost.

Retirement and 401(k)

Tools: Retirement Calculator, 401(k) Calculator.

Both tools project future balance using the compound interest formula above, adding the annual employee contribution and any employer match as recurring deposits. For the 401(k) calculator, employer match is modeled as a percent of salary capped at the employer match limit.

Assumptions: annual contribution limits are not enforced (you are responsible for entering realistic numbers), salary growth is optional, returns compound annually, no taxes are withheld at retirement. The result is a pre-tax balance estimate.

Sources: IRS 401(k) contribution limit tables (for informational context only), standard time-value-of-money formulas.

Savings goal

Tool: Savings Goal Calculator.

Solves the future value formula above for the required monthly contribution given a target balance, time horizon, and assumed rate of return.

Income tax

Tool: Income Tax Calculator.

Applies published marginal tax brackets for the selected jurisdiction and filing status. Standard deduction is applied by default unless itemized deductions are entered. State taxes, city taxes, FICA, Medicare, and capital gains are not modeled unless the tool specifically says so.

Assumptions: single tax year, no tax credits beyond those explicitly modeled, no special situations (self-employment, AMT, estate, trust).

Tax rules change every year and vary by jurisdiction. Confirm with a qualified tax professional before filing.

BMI and body composition

Tools: BMI Calculator, Body Fat Calculator, Calorie Calculator, Macro Calculator.

BMI uses the WHO formula:

BMI = weight_kg / (height_m)^2

Body fat percentage uses the U.S. Navy method (circumference measurements) by default. Calorie needs use the Mifflin-St Jeor equation for basal metabolic rate, multiplied by an activity factor. Macro splits follow standard fitness-industry ratios (for example, 40/30/30 balanced).

Assumptions: BMI is a screening tool, not a diagnosis. It does not account for muscle mass, bone density, or fat distribution. Use it as a starting point, not a verdict.

Unit conversion

Tools: all converters, plus 324 dedicated pairs at /tools/convert/<pair>.

All unit conversions multiply the input by the internationally standardized conversion factor for that unit pair. Source factors come from SI definitions, NIST, and ISO standards. Temperature conversions use the exact arithmetic conversions (not multiplicative factors) between Celsius, Fahrenheit, and Kelvin.

Digital storage conversions default to binary prefixes (1 KB = 1024 bytes), which matches what operating systems display. SI decimal prefixes (1 KB = 1000 bytes), which matches what hard drive manufacturers advertise, are available for comparison.

Known limits

• We do not model inflation unless a tool explicitly lets you enter an inflation rate.
• Rates are assumed fixed for the full term unless the tool supports a variable-rate input.
• Taxes are only modeled by tools that explicitly say so.
• Currency is cosmetic. Math works the same regardless of currency symbol.
• Calculations assume modern browser JavaScript number precision (IEEE 754 doubles). Very large or very precise values may lose precision in the last few digits.

Report an issue

Spotted a bug in a calculation, disagreement with a formula, or outdated tax rule? Email sushi@freetoolpark.com or reach us via the contact page. Accuracy issues get priority.