How do you convert APY to APR?

APR = n × [(1 + APY)1/n − 1], where n is the number of compounding periods per year.

What is the periodic interest rate from an APY?

(1 + APY)1/n − 1. For monthly compounding use n = 12.

Is the APR always lower than the APY?

Yes, whenever interest compounds more than once a year. With annual compounding they are equal.

APY to APR Formula and Calculator

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APY to APR Calculator

If you know the annual percentage yield of an account and how often it compounds, you can recover the nominal APR that produces it. This is useful when comparing a savings account quoted by APY with a bond or loan quoted by nominal rate, or when you need the periodic rate for a spreadsheet: the periodic rate is simply APR ÷ n.

Formula

APR = n × [(1 + APY)^1/n − 1] continuous: APR = ln(1 + APY)

Where

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

Calculator

APY (%)

Compounding

Result and step-by-step solution

APR

Compounded monthly, this nominal rate produces an APY of 5.1162%.

Take the n-th root of the growth factor
(1 + 0.051162)^1/12 = 1.0041666748
Periodic rate
1.0041666748 − 1 = 0.0041666748
Multiply by n
APR = 12 × 0.0041666748 = 5%

How to use the formula

The formula reverses the APY conversion. Take the n-th root of the annual growth factor (1 + APY) to get the growth per period, subtract 1 to get the periodic rate, and multiply by n. For continuous compounding the answer is the natural logarithm ln(1 + APY). The calculator shows each of these numbers to ten decimal places so rounding is visible.

The default example converts an APY of 5.1162% with monthly compounding back to an APR of 5.0000%, the round trip of the APR to APY calculator. The same formula is behind Excel’s NOMINAL function: NOMINAL(5.3543%, 4) returns 5.25%, and so does this page.

Frequently asked questions

How do you convert APY to APR?: APR = n × [(1 + APY)^1/n − 1], where n is the number of compounding periods per year.
What is the periodic interest rate from an APY?: (1 + APY)^1/n − 1. For monthly compounding use n = 12.
Is the APR always lower than the APY?: Yes, whenever interest compounds more than once a year. With annual compounding they are equal.
What is the continuous compounding version?: APR = ln(1 + APY).

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