Interest Rate Calculator
This free interest rate calculator solves for the annual interest rate (APR) from a loan amount, monthly payment, and term, the reverse of a typical loan calculator. Useful for checking what rate a stated payment actually works out to. Nothing you enter is sent anywhere or stored.
How to Use It
- Enter the loan amount, the monthly payment, and the loan term in months.
- The solved interest rate, total amount paid, and total interest update instantly.
- Useful for checking what rate a dealer or lender's stated payment actually works out to.
How It Works
Every other loan calculator on this site takes a rate and computes a payment. This one runs that process backward: it searches for the rate that turns your entered loan amount and term into the payment you actually entered. Because the amortization formula can't be algebraically solved for the rate directly, the search works by trying a rate, checking whether the payment it produces is too high or too low, and repeatedly narrowing the range in half until the computed payment matches yours to within a small fraction of a cent.
Formula
monthly payment = loan amount × [r(1 + r)^n] ÷ [(1 + r)^n − 1], solved for r by bisection since there is no algebraic inverse for r
A worked example: a $25,000 loan amount, a $483.32 monthly payment, and a 60 month term solve to exactly 6.00% APR, the same rate a $25,000 loan at 6% for 60 months would produce as its payment in the first place. Total paid over the full term comes to $28,999.20, of which $3,999.20 is interest.
Everything runs client-side in your browser. Nothing you enter is sent anywhere or stored.
Frequently Asked Questions
Why does this need to search for the answer instead of just calculating it directly?
The formula that turns a loan amount, rate, and term into a monthly payment has the interest rate sitting inside an exponent on both sides of the equation, so there is no way to rearrange it into a plug-and-solve formula for the rate itself. Instead, this tool tries a rate, checks the payment that rate would produce, and narrows in on the right answer step by step (a method called bisection) until the computed payment matches what you entered, accurate to a small fraction of a percent.
How is this different from the Loan, Mortgage, and Auto Loan Calculators?
Those three all solve the same direction: given a rate, they compute the payment. This tool runs in reverse, given a payment (from a real offer, a loan document, or an old statement), it solves for the rate that produces it. If you already know your rate and want the payment, one of those three is the more direct tool.
Why is a payment right at "loan amount divided by term" treated as valid?
That exact payment is what a 0% interest loan requires: paying back only the principal, in equal installments, with nothing extra. Zero percent is a real rate, promotional financing offers it fairly often, so this tool accepts that boundary case and correctly reports 0.00% rather than treating it as an error.
Why does a payment below "loan amount divided by term" produce an error?
A payment that low would pay off the loan on its own before term's end even with no interest at all, which means the math would need a negative interest rate to make the numbers balance over the full term. Negative-rate consumer loans are not a real thing, so this is treated as a mistyped payment or term rather than a valid, if unusual, answer.
Why is the search capped at 100% APR?
No realistic consumer loan approaches anywhere near 100% APR. A payment that would require a rate above that is far more likely to be a data entry mistake (an extra digit, the wrong field), so this tool reports a clear error naming that bound instead of returning a technically-computed but practically meaningless triple-digit rate.
Is the rate this shows the same as the APR on my actual loan paperwork?
Not necessarily. This solves for a rate based purely on the loan amount, payment, and term you enter, the pure amortization math. A real loan's disclosed APR can also fold in origination fees and other costs that raise the effective rate above the interest rate alone, and this calculator has no way to know about fees it was never told about.