APR & APY Calculator

Convert between APR and APY

This APR to APY calculator converts a nominal annual rate (APR) into the effective annual yield (APY), or works backwards from APY to APR. Choose how often interest compounds and the result appears instantly, to four decimal places.

How to use it

1. Pick a mode: APR → APY or APY → APR.
2. Enter the rate as a percentage, for example 5.
3. Choose the compounding frequency: annually, semi-annually, quarterly, monthly, bi-weekly (26), weekly (52), daily (365) or continuous.
4. Read the converted rate.

APR to APY formula

APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods per year. For continuous compounding, APY = e^APR − 1.

Example: 5% APR compounded monthly = (1 + 0.05 ÷ 12)^12 − 1 = 5.1162% APY.

APY to APR formula

APR = n × ((1 + APY)^(1/n) − 1), or ln(1 + APY) for continuous compounding.

Example: 5% APY with monthly compounding = 12 × (1.05^(1/12) − 1) = 4.8889% APR.

5% APR at each compounding frequency

Compounding	APY
Annually	5.0000%
Semi-annually	5.0625%
Quarterly	5.0945%
Monthly	5.1162%
Daily	5.1267%
Continuous	5.1271%

The more often interest compounds, the higher the APY, but the gains shrink quickly after monthly compounding.

Frequently asked questions

What is the difference between APR and APY?

APR is the simple yearly rate before compounding. APY includes the effect of earning interest on interest, so it is always equal to or higher than APR when interest compounds more than once a year.

Which rate should I compare?

Compare savings accounts by APY, because it shows what you actually earn in a year. When comparing loans, make sure both offers use the same measure.

Does this include fees?

No. It is a pure rate conversion. Loan APRs quoted by lenders may also include fees, which this calculator does not model.