APR to APY Converter

Convert between APR and APY with different compounding frequencies. Compare daily, monthly, quarterly compounding effects on your interest rates.

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What is APR to APY Converter?

This tool converts between Annual Percentage Rate (APR) and Annual Percentage Yield (APY). APR is the simple interest rate without compounding, while APY reflects the actual return including compound interest effects. The difference depends on how often interest is compounded.

In DeFi and crypto lending, APY is commonly used to express yield because most protocols compound interest automatically. Understanding the difference helps you accurately compare investment opportunities.

Conversion Formulas

Conversion	Formula	Description
APR → APY	APY = (1 + APR/n)^n - 1	n = compounding periods per year
APY → APR	APR = n × ((1 + APY)^(1/n) - 1)	n = compounding periods per year
APR → APY (Continuous)	APY = e^APR - 1	e = Euler's number (2.71828...)
APY → APR (Continuous)	APR = ln(1 + APY)	ln = natural logarithm

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the nominal interest rate without accounting for compounding. APY (Annual Percentage Yield) is the effective rate that includes the effect of compound interest. APY is always equal to or greater than APR. For example, 12% APR compounded monthly equals 12.68% APY.

Why does compounding frequency matter?

The more frequently interest is compounded, the higher the effective yield. Daily compounding produces a higher APY than monthly compounding for the same APR. This is because each compounding period adds interest to the principal, and subsequent periods earn interest on that accumulated interest.

How is APR/APY used in DeFi?

DeFi protocols display yields as APR or APY. Lending platforms like Aave and Compound typically show APY since interest accrues per block. Staking protocols may show APR. When comparing DeFi yields, always check whether the rate is APR or APY and the compounding frequency to make accurate comparisons.

What is continuous compounding?

Continuous compounding is the theoretical limit of compounding frequency, where interest is compounded an infinite number of times per year. It uses the mathematical constant e (Euler's number). In practice, it approximates very frequent compounding like per-block compounding in DeFi.

Example Conversions

5% APR compounded monthly = 5.116% APY
10% APR compounded daily = 10.516% APY
12% APY with monthly compounding = 11.386% APR
5% APR with continuous compounding = 5.127% APY