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APR to APY calculator

What a rate earns once compounding is counted, and back.

Reviewed by Victor Yuki Matusita on . First published .

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Turn
%

APY

5.13%

A rate of 5% compounded daily earns 5.13% a year.

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Every compounding

How to use the APR to APY calculator

  1. Choose whether to turn an APR into an APY or the other way round.
  2. Type the rate and pick how often it compounds.
  3. Read the result, and the table with every compounding.

How APR and APY are related

The formula

APY = (1 + APR ÷ n)^n − 1, where n is the number of times a year the rate compounds.

Going back, APR = n × ((1 + APY)^(1 ÷ n) − 1). Both are shown as percents with two decimals.

Assumptions

  • The rate is a nominal yearly rate, compounded the number of times a year you choose; daily compounding uses 365 days.
  • The money stays in for a whole year with nothing added or taken out.
  • The result is rounded to two decimals, half up, as Regulation DD asks for the APY.

Worked example

This is the example the calculator opens with, worked out by the same engine you use above.

You enter
TurnAPR into APY
Rate5%
Compoundingdaily
You get
APY5.13%
yearly5.00%
twice a year5.06%
quarterly5.09%
monthly5.12%
daily5.13%

A rate of 5% compounded daily earns 5.13% a year.

Sources

Educational tool

This calculator is an educational tool, not financial advice. The account disclosure states the APY that applies to you.

Questions about APR and APY

What is the difference between APR and APY?

The APR is the yearly rate before compounding. The APY is what the money earns in a year once interest is added on interest, so it is never lower than the APR.

Why do savings accounts show the APY?

Regulation DD asks banks to state the annual percentage yield on deposit accounts, so accounts that compound differently can be compared.

Is a loan APR the same thing?

A loan APR also counts fees and is worked out by another rule, Regulation Z. This calculator only turns a nominal rate into its yearly yield and back.

Why do the CFPB examples match this calculator?

The examples of Regulation DD, Appendix A, with rates compounded daily give the same APY to two decimals: 5.25% daily is 5.39%, for instance.

Privacy

Your numbers stay on your device. The calculator runs in your browser, so nothing you type is sent anywhere, and the link you copy keeps the numbers after the #, a part of the address your browser never sends.