APR to APY Converter
Convert Annual Percentage Rate (APR) to Annual Percentage Yield (APY)
About This Tool
Enter an APR and the compounding frequency, and read back the equivalent APY. The math is APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year.
Reach for it when comparing a DeFi protocol that quotes APR (per-period rate, no compounding) against one that quotes APY (with compounding baked in). The two numbers diverge fast at high rates — a 100% APR compounded daily is over 171% APY.
Goes the other way too: enter the APY you want and the compounding cadence, and the calculator solves for the APR a quote needs to advertise to deliver that yield.
The formula is a textbook compound interest derivation: APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. The reverse direction — solving APR for a given APY — is APR = n · ((1 + APY)^(1/n) − 1). Pick which one you want and the tool fills in the rest. Continuous compounding (the limit as n → infinity) gives APY = e^APR − 1, which is the floor for "I'm compounding as fast as possible" calculations.
Worked example. A DeFi pool advertises 100% APR with daily compounding (n=365). APY = (1 + 1.0/365)^365 − 1 = 1.7146 − 1 = 1.7146, or 171.46% APY. Same protocol with hourly compounding (n=8760)? APY = (1 + 1.0/8760)^8760 − 1 = 1.7180 − 1 = 171.80%. Continuous compounding ceiling is e^1 − 1 = 171.83%. The marginal gain from compounding more often than daily is about 0.4 percentage points at this rate — visible but small. At 5% APR, the daily-vs-continuous gap is 0.001 percentage points, effectively nothing. Compounding cadence matters most at high rates.
Where DeFi quotes get sneaky: protocols sometimes advertise APY assuming auto-compounding that you have to enable yourself, then quote a base APR for the no-claim case. Read which one is the headline number. A 100% APY headline with "auto-compounded daily" footnote means the underlying APR is 69.3% — that's the rate the protocol actually pays, with the rest coming from your own compound action. If you forget to claim and re-stake, you only get the 69.3%.
The tool also handles the reverse problem common in CeFi marketing: a savings account quotes 5.00% APY. What APR is that? At monthly compounding (n=12), APR = 12 · ((1.05)^(1/12) − 1) = 4.889%. The advertised 5.00% APY is the marketing number; the underlying APR is what's actually getting paid into your account each month. Banks know this; consumers usually don't.
The about text and FAQ on this page were drafted with AI assistance and reviewed by a member of the Coherence Daddy team before publishing. See our Content Policy for editorial standards.