How do you convert APR to APY?

APY = (1 + APR ÷ n)n − 1, where n is the number of compounding periods per year and APR is written as a decimal.

What is 5% APR as APY?

With monthly compounding, 5.1162%. With daily compounding, 5.1267%. With annual compounding, exactly 5%.

Why is APY higher than APR?

APY includes interest earned on interest during the year; APR does not.

Is APY the same as EAR?

Yes, both are the effective annual rate. APY is the term used by banks for deposit accounts.

APR to APY Formula and Calculator

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APR to APY Calculator

APR, the annual percentage rate, is a nominal rate: it is the periodic rate multiplied by the number of periods in a year. APY, the annual percentage yield, is what that rate really produces over a year once interest is compounded. Banks advertise savings accounts by APY because it is the higher and more meaningful number; lenders often quote APR.

Formula

APY = (1 + APRn)ⁿ − 1

Where

APY: annual percentage yield (effective annual rate)
APR: annual percentage rate (nominal), as a decimal
n: compounding periods per year

Calculator

APR (%)

Compounding

Result and step-by-step solution

APY

5.1162%

On 10,000.00 for a year this APR earns 511.62 instead of 500.00 simple interest.

Periodic rate
APRn = 0.0512 = 0.00416667
Compound over the year
(1 + 0.00416667)¹² = 1.0511619
Subtract 1
APY = 5.1162%

How to use the formula

To convert, divide the APR by the number of compounding periods n, compound for one year and subtract 1: APY = (1 + APR ÷ n)ⁿ − 1. A 5% APR compounded monthly gives an APY of 5.1162%; compounded daily it is 5.1267%; continuously it is 5.1271%. The calculator shows the periodic rate and growth factor so you can reproduce the result by hand.

The page also shows what the difference means in money: on 10,000 for a year, a 5% APR compounded monthly earns 511.62 rather than 500. For the reverse conversion use the APY to APR calculator. Note that in lending, APR may also include fees, which this formula does not add.

Frequently asked questions

How do you convert APR to APY?: APY = (1 + APR ÷ n)ⁿ − 1, where n is the number of compounding periods per year and APR is written as a decimal.
What is 5% APR as APY?: With monthly compounding, 5.1162%. With daily compounding, 5.1267%. With annual compounding, exactly 5%.
Why is APY higher than APR?: APY includes interest earned on interest during the year; APR does not.
Is APY the same as EAR?: Yes, both are the effective annual rate. APY is the term used by banks for deposit accounts.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.