Formula reference
The math behind the calculators.
This page explains the common formulas used by the calculators so visitors can check the inputs, compare scenarios, and understand estimate limits.
Last updated: August 27, 2026
Why formulas are shown
Calculator results are easier to trust when the method is visible. The goal is not to turn every visitor into a finance or math expert. The goal is to show enough of the calculation that a person can spot a wrong input, understand why two estimates differ, and know when a final number needs to come from a lender, dealer, tax office, or official source.
The formulas below are simplified planning formulas. They are useful for comparisons, but they do not replace contracts, formal disclosures, tax notices, or professional advice.
Loan and mortgage payment formula
The standard fixed-payment loan formula estimates the monthly principal and interest payment for a loan with a fixed rate and fixed term.
Monthly payment = P x [r(1 + r)^n] / [(1 + r)^n - 1]
P is the amount borrowed, r is the monthly interest rate, and n is the number of monthly payments.
For a mortgage estimate, principal and interest are only part of the monthly number. Property tax, homeowners insurance, mortgage insurance, and HOA dues can be added as monthly amounts to make a fuller house payment estimate.
For a car payment estimate, the amount borrowed may include vehicle price, sales tax, fees, and any add-ons, minus down payment and trade-in credit. The calculator result can be close for comparison, but a dealer or lender quote may change after credit approval, exact taxes, registration, and optional products.
Loan payoff method
A payoff estimate works month by month. The calculator adds interest for the month, subtracts the scheduled payment and any extra payment, then repeats until the balance reaches zero.
New balance = old balance + monthly interest - monthly payment
Monthly interest is usually estimated as current balance x annual rate / 12.
This makes it possible to compare a current payment against an accelerated payment. The difference can show estimated months saved and estimated interest saved. If the payment is too small to cover monthly interest, the balance may not go down.
Fuel cost formula
A fuel cost estimate starts with miles and MPG. It then multiplies gallons needed by the price per gallon.
Gallons needed = miles / MPG
Fuel cost = gallons needed x price per gallon
Real fuel use changes with speed, hills, idling, tires, cargo, temperature, and traffic. A fuel calculator is most useful for comparing trip budgets or splitting an estimated cost between passengers.
Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X percent of Y? | Y x X / 100 | 20% of 80 = 16 |
| What percent is X of Y? | X / Y x 100 | 15 of 60 = 25% |
| What is the percentage change? | (new - old) / old x 100 | 50 to 60 = 20% increase |
Tip and bill split formulas
A tip calculator usually multiplies the bill by the tip percentage, adds the tip to the bill, and divides by the number of people if the bill is being split evenly.
Tip amount = bill x tip percent / 100
Total = bill + tip amount
Per person = total / number of people
Local tax, service charges, coupons, and group policies can change what people decide to tip on. The calculator keeps the math clear and lets the user decide which bill amount to enter.
Unit conversion method
Most unit conversions multiply or divide by a fixed conversion factor. For example, miles to kilometers multiplies by 1.609344, pounds to kilograms multiplies by 0.45359237, and gallons to liters multiplies by 3.785411784. Temperature conversion uses a formula because Fahrenheit and Celsius have different zero points.