APR & APY Calculator
Convert between APR and APY for any compounding frequency, including continuous compounding.
APR The plain annual rate, usually attached to loans. It's essentially the same number as the headline interest rate, before any effect of compounding.
APY The actual annual return on a deposit, with compounding folded in. Banks have to publish savings products in APY so customers can compare them apples-to-apples.
APR & APY Converter
Step-by-step formula
Popular APR → APY combinations
Quick reference for common rates across compounding frequencies. All numbers are computed live in your browser.
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APR vs APY: what's the difference
APR and APY both express annual interest rates, but they answer different questions. APR — annual percentage rate — is the nominal yearly rate, calculated as the periodic rate multiplied by the number of periods in a year. APY — annual percentage yield — is the effective rate, the actual percentage your balance grows by over one year once compounding is taken into account.
If interest is credited only once per year, APR and APY are identical. As soon as interest compounds more frequently than annually — quarterly, monthly, daily, or continuously — APY climbs above APR, because each new interest payment starts earning interest of its own. The more often compounding happens, the larger the gap. Put plainly, the difference between APY and APR is compounding — and because the interest rate is just another name for the nominal APR, the difference between APY and interest rate is the very same thing.
For loans, lenders are required to advertise APR (and U.S. law adds origination fees to the loan APR, so the legal definition is slightly broader than the math-only one shown here). For deposits, banks have to publish APY so consumers can compare savings products fairly. When you compare an interest rate from one product with an APY from another, you're not really comparing like with like — convert one to the other first. That's why questions like APY vs interest rate — or annual percentage yield vs interest rate — really come down to how much compounding adds on top of the headline rate.
How to convert APR to APY
To calculate annual percentage yield, you convert APR to APY: when interest compounds n times per year, raise (1 + APR / n) to the n-th power and subtract 1. The result is the APY as a decimal — multiply by 100 to get a percent.
Example: a 6% APR compounded monthly works out to an APY of about 6.168%. The same 6% APR compounded daily gives roughly 6.183%. Compounded once a year, it stays at exactly 6%. The continuous-compounding limit — the theoretical ceiling as n grows arbitrarily large — is eAPR − 1, which for 6% APR is about 6.184%.
The calculator above performs this conversion both ways, so it works as an annual percentage yield calculator (sometimes called an APY yield calculator) in one direction and an APY to APR calculator in the other. Switch to the "APY → APR" tab if you already know the published yield on a savings account and want to back out the underlying nominal rate.
APR, APY and interest rate explained
Most people use "interest rate" loosely to mean whatever annual percentage is printed on a quote. In strict finance terminology, the interest rate is the nominal annual rate — the same thing as APR in the math-only sense used on this page. The difference is mostly regulatory: the term "APR" comes with consumer-protection rules around loans, while "interest rate" is a more generic label.
APY is a different idea. It tells you what fraction of your starting balance you'll actually earn in a year, given how often interest compounds. Two products can show the same interest rate but very different APYs, and the one with more frequent compounding will always win on APY.
For credit cards, the difference between the published APR and the effective APY can be substantial. A card with a 24% APR billed monthly carries an effective APY closer to 26.8% — money you don't see on the marketing material but absolutely feel on the statement.
One important caveat about loan APR: the legal definition under the U.S. Truth in Lending Act bundles origination fees, broker fees, and other finance charges into the rate, so the APR a lender quotes can exceed the pure nominal interest rate. This calculator works with the math-only APR — the periodic rate × number of periods — and does not model fees.
APR to APY formula
Periodic compounding (n times per year):
APY = (1 + APR / n)n − 1
Continuous compounding (the theoretical limit as n → ∞):
APY = eAPR − 1
To go in the other direction, solve for APR:
APR = n × ((1 + APY)1/n − 1) (periodic)
APR = ln(1 + APY) (continuous)
The same formulas are sometimes called the effective annual rate conversion, which makes this an effective annual rate calculator as well. APY and effective annual rate (EAR) are the same number — different names, same math.