APY ↔ APR Calculator
Convert between APR (nominal annual rate) and APY (effective annual yield) at any compounding frequency — both directions.
Result
- APR (nominal)5.00000%
- APY (effective)5.11619%
- APY − APR (bps)11.62 bp
- Compounding frequencyMonthly (12/yr)
- APY at continuous comp.Upper bound for the same APR; the spread vs finite-compounding shrinks as n→∞.5.12711%
- $10,000 grows to (1 yr)A 1-year future-value sanity check using the computed APY.$10,511.62
Step-by-step
- APY = (1 + APR/n)^n − 1 = (1 + 0.05000/12)^12 − 1 = 0.051162.
- Spread = APY − APR = 0.001162 = 11.62 basis points.
How to use this calculator
- Pick direction — APR → APY (most common) or APY → APR (rare; back-solve nominal from effective).
- Enter the rate in percent (5.0 for 5%, not 0.05).
- Choose the compounding frequency from the dropdown. For US savings accounts, "Daily" is the legal-compounding standard; for credit cards, "Monthly".
- Read the converted rate plus the spread in basis points.
About this calculator
APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are NOT the same. APR is the nominal annual rate quoted on most credit products; APY is the effective annual rate after compounding. The conversion is APY = (1 + APR/n)^n − 1 where n is the number of compounding periods per year. For continuous compounding, APY = e^APR − 1. The two differ more as n grows — at 1×/yr they're identical; at daily compounding (n=365) the APY exceeds APR by about 0.13% on a 5% APR. US Regulation DD (Truth in Savings) mandates banks disclose APY for deposit accounts; Regulation Z (Truth in Lending) mandates APR for credit. Knowing both lets you compare a savings account quoting APY against a CD quoting APR-with-monthly-compounding without doing the math in your head.