APY to APR Calculator

Convert an APY to an APR, or an APR to an APY, for any compounding period. The APY to APR calculator shows the rate per period and how far apart the two are.

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Estimate only. Not financial advice.

How to use the APY to APR Calculator

  1. Choose APY to APR or APR to APY.
  2. Enter the Rate and pick how often interest is compounded.
  3. Press Calculate. The converted rate appears with the rate per period and the gap between the two.

How it works

APY = (1 + APR ÷ n)^n − 1
APR = n × ((1 + APY)^(1 ÷ n) − 1)
continuous: APY = e^APR − 1, APR = ln(1 + APY)
  • n: compounding periods per year (12 for monthly, 365 for daily)

Examples

  • 5% APR compounded monthly = 5.1162% APY.
  • 5% APY compounded monthly = 4.8889% APR.
  • 5% APR compounded daily = 5.1267% APY, and continuously 5.1271%.

Which number should I compare?

Banks advertise savings with APY because it is the bigger number and includes compounding. Loans are advertised with APR. To compare a savings account with a loan, or two accounts that compound differently, convert both to APY.

Limitations

  • Fees are not included. For loan fees, use the APR calculator.
  • Assumes the rate stays the same for the whole year.

Frequently asked questions

What is the difference between APY and APR?

APR is the simple yearly rate. APY includes the effect of compounding within the year, so it is always equal or higher.

When are APY and APR the same?

When interest is compounded once a year.

Is 5% APY the same as 5% APR?

No. With monthly compounding, 5% APY equals a 4.8889% APR.

Often used together with the APY to APR Calculator.