Mortgage Calculator

Background.

A mortgage calculator answers the single question that decides whether a house is actually affordable: what will the loan cost you, every month, for as long as it takes to pay it off? Plug in the amount you intend to borrow, the rate your lender has quoted, and the length of the term, and the calculator runs the same fully-amortizing equation that banks have used for more than a century. The output is your fixed principal-and-interest payment, the cumulative interest you will hand the lender across the life of the loan, and the grand total that will leave your account between now and the day the deed is yours free and clear.

The math itself is not a secret. It is a closed-form formula derived from the geometric series — the loan balance has to reach zero in exactly n payments, so each payment must be sized to retire a slice of principal large enough to do that while also covering the interest that accrues on the remaining balance every month.

What the formula does not tell you, but what this page does, is what to do with the answer.

A monthly payment that fits inside your budget today still has to fit inside it through job changes, rate shocks on the rest of your debt, and the surprise costs that come with owning a roof. The 28/36 rule used by most underwriters — housing costs under 28% of gross monthly income, total debt service under 36% — is a useful guardrail but not a substitute for thinking carefully about the next thirty years of your cash flow.

The other thing the formula does not tell you is what dominates the early years of the loan: interest. On a brand-new 30-year mortgage at today's rates, more than two-thirds of your first payment goes to the lender as interest, and only a fraction goes to actually reducing what you owe. That ratio slowly inverts as the balance shrinks, but the shape of the curve is steep enough that most homeowners who sell or refinance inside the first decade barely dent their principal.

This calculator gives you the three headline numbers, and the explainer below walks through how to read them, how a 15-year compares to a 30-year, how extra principal payments compress the schedule, and where the IRS still permits an interest deduction in 2026.

What is mortgage calculator?

A mortgage is a long-term loan secured by real estate, repaid in equal monthly installments under an amortization schedule. Each installment is split between two components. The interest portion compensates the lender for the time value of the money still outstanding and is calculated each month against the remaining principal balance. The principal portion is the actual reduction in what you owe. Because interest is charged on the unpaid balance, early payments are mostly interest and late payments are mostly principal — the split tilts steadily across the life of the loan. A fixed-rate mortgage locks the interest rate for the full term, so the monthly payment never changes; an adjustable-rate mortgage (ARM) fixes the rate only for an initial period, after which it resets against an index plus a margin. This calculator computes the fixed monthly payment for a fully amortizing fixed-rate loan, which is the most common structure in the United States. It does not model interest-only loans, balloon mortgages, or the variable-rate phase of an ARM.

How to use this calculator.

1. 01Enter the loan amount — the agreed purchase price minus your down payment. Do not include closing costs you will pay out of pocket; do include any closing costs you are rolling into the loan.
2. 02Enter the annual interest rate the lender quoted on the loan estimate. If you have the APR, prefer that — it includes lender fees and gives a more honest cost comparison across offers.
3. 03Choose a term. 30 years gives the lowest monthly payment but the highest lifetime interest; 15 years roughly cuts total interest in half but raises the monthly payment by 40–50%.
4. 04Read the three results. Monthly payment is what you owe every month for principal and interest. Total interest is what the loan costs you in interest alone. Total paid is the cumulative sum of every payment over the full term.
5. 05Compare scenarios. Change one input at a time and re-read the outputs to see how sensitive each is — small rate moves shift the monthly payment less than you would expect, while term length shifts total interest dramatically.

The formula.

The monthly payment is computed with the standard amortizing-loan formula M = P × [r(1+r)^n] / [(1+r)^n − 1]. P is the loan principal in dollars. r is the periodic (monthly) interest rate, calculated as the annual rate divided by 100 and then by 12. n is the total number of monthly payments, equal to the term in years multiplied by 12. The (1+r)^n term captures how the principal would grow if no payments were made; the bracketed fraction is the constant that, multiplied by the principal, produces the unique monthly payment that drives the balance to exactly zero on payment n. For the rare zero-interest case (r = 0), the formula reduces to M = P / n. After computing M, total paid is M × n and total interest is total paid minus P. The arithmetic in this calculator uses arbitrary-precision decimal math to avoid the floating-point rounding errors that affect spreadsheets and many web calculators on long terms.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Federal Reserve — Consumer Handbook on Adjustable-Rate Mortgages
2. [2]IRS Publication 936 (2025) — Home Mortgage Interest Deduction
3. [3]Consumer Financial Protection Bureau — Owning a Home
4. [4]Freddie Mac — Primary Mortgage Market Survey (weekly mortgage rate series)
5. [5]Federal Housing Finance Agency — Conforming Loan Limits
6. [6]Consumer Financial Protection Bureau — Loan Estimate and APR disclosure rules under TILA-RESPA