APR to APY Calculator

APR — annual percentage rate — is a nominal rate. It is the periodic rate multiplied by the number of periods in a year, and it deliberately ignores compounding. A 1% monthly rate is quoted as a 12% APR whether or not that 1% is charged on interest that already accrued. APY — annual percentage yield — is the effective rate. It answers a different question: after a full year of compounding at that rate, what did a dollar actually become? The conversion is APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods per year. When interest compounds more than once a year, APY is always the larger of the two for the same nominal rate. That is not marketing; it is what the arithmetic produces. The gap is the value of interest earning interest inside the year.

The split is regulatory, not accidental. Consumer credit disclosure in the United States runs through the Truth in Lending Act, implemented by Regulation Z — that is the framework requiring lenders to disclose a cost-of-credit figure as an APR, in a standard form, so offers can be compared. Deposit accounts run through the Truth in Savings Act, implemented by Regulation DD, which is why banks quote savings and CD returns as an APY. The practical consequence is that the borrowing side of the market speaks in the smaller number and the saving side speaks in the larger one. Neither is dishonest. But when you carry a rate across that boundary in your head, you are comparing two different measurements and the comparison will be wrong.

The largest jump is from annual compounding to any frequent compounding. After that, adding frequency delivers steadily less. Run a 5% APR through the table on this page and you get exactly 5% APY compounded annually, about 5.12% compounded monthly, and about 5.13% compounded daily. The step from annual to monthly is worth twelve basis points; the step from monthly to daily is worth about one. Continuous compounding, the mathematical ceiling, barely improves on daily. The gap widens with the rate, though, and that is where it stops being trivial. At the rates typical of revolving credit rather than deposits, the same conversion moves the effective figure by multiple percentage points, not fractions of one. High-rate debt that compounds frequently costs meaningfully more than its stated APR suggests.

The rule is to compare like with like: APY against APY for savings accounts, money market accounts and CDs; APR against APR for loans and credit cards. When two products state different types, convert one of them — this calculator runs either direction. One caveat matters more than the compounding math itself. A loan's disclosed APR is not purely a compounding figure: it is a cost-of-credit measure that can fold in certain fees and charges, which is why a mortgage's APR is typically higher than its note rate. This calculator converts the rate. It does not know what fees a particular lender rolled into a particular disclosure, and the rules on which charges belong in an APR are detailed. So use the conversion to compare rate structures, and read the written disclosure — the Loan Estimate, the credit card agreement, the deposit account terms — for the fees. Terms vary by institution and by product.

The math assumes a rate that stays put and compounding that behaves as stated. Several common products break one of those assumptions. Variable rates move. Most credit cards and many deposit accounts carry rates tied to an index, so today's APY is a snapshot rather than a promise, and the account terms will say how and when it can change. A quoted yield can also be promotional, reverting to a different rate after an introductory window. Taxes and inflation sit outside the calculation entirely. Interest earned in a taxable account is generally taxable income, so the after-tax yield is lower than the APY, and inflation erodes purchasing power regardless of what the account pays. Finally, for credit cards, when interest is charged at all depends on the grace period and the balance: a balance paid in full by the due date each cycle may avoid interest on purchases altogether, in which case the APR-to-APY conversion is describing a cost you are not incurring.