APY and APR measure the same underlying interest rate from two different angles. APR (Annual Percentage Rate) is the nominal rate before compounding — the number a lender advertises. APY (Annual Percentage Yield) is what you actually earn or pay after compounding is applied at whatever frequency the product specifies. When someone says a savings account earns "5%" monthly compounding, the APY is slightly above 5% and the difference compounds silently into your balance.
Enter a rate in either direction and choose a compounding frequency. Load Sample starts with 5% APR at monthly compounding, which yields an APY of 5.1162%. Pressing Load Sample again cycles through a DeFi staking yield (8% APY daily compounding), a credit card APR (12% monthly), and two others. The Swap button appears once a result is shown: it moves the result into the input and flips the direction, so you can verify a round-trip conversion without retyping.
Getting Your First Conversion
- Select the direction: APR to APY or APY to APR.
- Choose the compounding frequency — Monthly is the most common for savings and loans; Daily is typical for DeFi protocols; Continuous is a mathematical limit used in options pricing.
- Type the rate as a percentage — enter 5 for 5%, not 0.05.
- The result, formula, and a full frequency comparison table appear immediately. Click Copy next to the result to grab the percentage string, or copy the formula line for a spreadsheet or document.
- Press Swap to feed the result back as input in the opposite direction, useful for verifying a round-trip.
The Two Formulas, Side by Side
- APR to APY: APY = (1 + APR divided by n)^n minus 1, where n is the number of compounding periods per year. For continuous compounding, APY = e^APR minus 1.
- APY to APR: APR = n times ((1 + APY)^(1 divided by n) minus 1). For continuous compounding, APR = ln(1 + APY).
- Both results show up to 4 decimal places with trailing zeros stripped, so 5.1162% displays as-is but 5.0000% displays as 5.
- The comparison table at the bottom shows what the converted rate would be at every frequency, so you can see how much the compounding interval matters.
Accuracy Limits
- All arithmetic uses JavaScript's 64-bit double precision. For typical financial rates under a few hundred percent, the result is accurate to 10 or more significant digits, well beyond the 4 displayed.
- Very high APY values close to or above 100% combined with low compounding frequencies (annual, n=1) produce large but valid APR values. The formula shows "—" only when the result is not a finite real number.
- Continuous compounding (e^r) is a mathematical limit, not an achievable real-world product. It is included because many DeFi protocols use it in their yield formulae and it is the standard assumption in Black-Scholes options pricing.