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Finance formula

How to calculate mortgage payment

The fixed mortgage payment formula estimates principal and interest for a standard amortizing home loan.

See the formulaOpen calculator
Direct answer
Formula
M = P * r * (1 + r)^n / ((1 + r)^n - 1)

Use the table below to match each symbol with the right input. Keep units consistent before you start.

Mortgage payment formula
Start here when you only need the equation and variable names.
Formula
M = P * r * (1 + r)^n / ((1 + r)^n - 1)

The fixed mortgage payment formula estimates principal and interest for a standard amortizing home loan.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
MMonthly principal and interestLoan payment before escrow items.currency per month
PLoan amountMortgage principal after down payment.currency
rMonthly interest rateAnnual rate divided by 12.Depends on inputs
nPayment countLoan term in months.months
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Good for fixed-rate mortgages before you add taxes, insurance, HOA dues, or mortgage insurance.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1Subtract down payment from home price to get the loan amount.
  2. 2Convert APR to a monthly decimal rate.
  3. 3Convert the loan term to months.
  4. 4Use the amortization formula for principal and interest.
Examples
These sample numbers show the order of operations and units.
Thirty-year mortgage
P
$320,000
APR
6.5%
n
360 months
  1. 1.r = 0.065 / 12 = 0.0054167
  2. 2.M = 320000 * r * (1 + r)^360 / ((1 + r)^360 - 1)
  3. 3.M = 2022.62
Result
Principal and interest are about $2,022.62 per month.
Fifteen-year mortgage
P
$180,000
APR
5.75%
n
180 months
  1. 1.r = 0.0575 / 12 = 0.0047917
  2. 2.M = 180000 * r * (1 + r)^180 / ((1 + r)^180 - 1)
  3. 3.M = 1494.74
Result
Principal and interest are about $1,494.74 per month.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Using an annual rate where the mortgage payment formula needs a monthly or period rate.
  • Entering 8 instead of 0.08 when the formula calls for a decimal rate.
  • Comparing results across different time periods without converting them first.
  • Rounding each step instead of rounding the final answer.
Open the Mortgage Calculator
Open the calculator for the answer without rewriting the formula.

Enter your values in the related calculator, then compare the output with the hand method above.

Open Mortgage Calculator
FAQs
Short answers for common formula questions.
Can I calculate Mortgage payment by hand?

Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.

Why does my Mortgage payment result differ from another calculator?

Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.

When is the Mortgage Calculator better than hand math?

Open the Mortgage Calculator to check several scenarios or skip the hand arithmetic.