APR to APY Converter
APR is a simple annual rate; APY is the effective yield once interest compounds within the year. Because interest earns interest, APY is always at least as high as APR, and the gap widens with more frequent compounding. This converter takes an APR and a compounding frequency, then returns the periodic APY, the continuous-compounding APY, and the exact difference between APY and APR, so you can compare savings products, lending rates, or DeFi yields on a common annual basis.
APR to APY formula
r = APR / 100, n = periods per year
APY = ((1 + r / n) ^ n - 1) * 100
Continuous APY = (e ^ r - 1) * 100
Difference = APY - APR
When the compounding frequency is 1, APY equals APR. As the frequency rises, APY approaches the continuous-compounding limit, which is the highest possible APY for that APR.
Using the result
- Use 365 for daily, 12 for monthly, 4 for quarterly, 2 for semiannual, 1 for annual compounding.
- The continuous figure is a benchmark ceiling, rarely paid in practice but useful for comparison.
- Always compare offers on APY, not APR, when compounding frequencies differ.
- DeFi yields and many savings accounts compound daily, so 365 is a frequent choice.
- The difference column shows exactly how much compounding adds for your chosen frequency.
APR to APY: frequently asked questions
What is the difference between APR and APY?
APR (annual percentage rate) is the simple annual interest rate without compounding. APY (annual percentage yield) is the effective rate after compounding within the year. Because interest earns interest, APY is always equal to or higher than APR, and the difference grows with more frequent compounding.
How do you convert APR to APY?
APY equals one plus the APR divided by the number of compounding periods, raised to the power of the number of periods, minus one. For continuous compounding, APY equals e raised to the APR, minus one. This tool computes both the periodic and the continuous result from the APR you enter.
What compounding frequency should I use?
Match the frequency to how often interest is added: 365 for daily, 12 for monthly, 4 for quarterly, 2 for semiannual, and 1 for annual (where APY equals APR). DeFi protocols and many savings products compound daily, so 365 is a common choice for crypto yields.
What is continuous compounding?
Continuous compounding is the theoretical limit of compounding infinitely often. Its APY is e raised to the APR minus one, where e is Euler's number (about 2.71828). It is the highest possible APY for a given APR and is used as a benchmark and in some financial models.
Why does APY matter when comparing offers?
Two products can advertise the same APR but pay different amounts if they compound at different frequencies. APY puts them on a common annual basis, so comparing APYs (or computing them from APR) shows which offer actually pays more over a year. Regulators often require APY disclosure for this reason.
Official sources
- U.S. SEC Investor.gov: Compound interest and APY.
- U.S. Federal Reserve: Regulation DD and APY disclosure.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.