APR to APY Calculator
Convert between APR (annual percentage rate) and APY (annual percentage yield) for any compounding frequency
Last updated: 2026-07-18
APR (Annual Percentage Rate) is a nominal annual rate -- it doesn't account for compounding within the year. APY (Annual Percentage Yield) is the effective annual rate you actually earn or pay once compounding is factored in, so it's always equal to or higher than the APR for the same nominal rate. Banks are required to advertise savings and CD rates as APY and loan rates as APR, which can make two accounts or offers look harder to compare than they should be -- this calculator converts between the two for any compounding frequency.
APR to APY Conversion Formula
O(1)n = number of compounding periods per year (12 for monthly, 365 for daily, etc.)
Continuous compounding is the limit as n approaches infinity
Both rates are entered and returned as percentages. The higher the compounding frequency n, the closer APY gets to the continuous-compounding limit for a given APR -- the difference is usually small (a few hundredths of a percent between monthly and daily compounding) but grows with the rate itself. To go the other direction (APY to APR), the formula is inverted: APR = n × ((1 + APY)^(1/n) − 1), or APR = ln(1 + APY) for continuous compounding.
Use Cases
Comparing Savings Accounts
Convert a monthly-compounding CD's APR into APY to compare it against an account already quoted in APY.
Comparing Loan Offers
See the effective annual cost of a loan whose rate compounds more often than once a year.
Verifying Advertised Rates
Check that a bank's advertised APY matches its stated nominal rate and compounding schedule.
Modeling Continuous Compounding
See the theoretical upper bound on yield for a given nominal rate as compounding frequency increases without limit.
Frequently Asked Questions
Why is APY always higher than APR (for a positive rate)?
APY includes the effect of earning interest on interest already paid during the year, which APR (a simple nominal rate) does not account for -- so compounding always pushes the effective rate above the nominal one whenever the rate is positive.
Do APR and APY ever match?
Yes -- if compounding happens only once a year (n = 1), APY equals APR exactly, since there's no intra-year compounding to add extra yield.
Which one should I look at when comparing savings accounts?
APY, since it already reflects the actual compounding schedule and lets you compare accounts with different compounding frequencies on equal footing.
Which one should I look at when comparing loans?
For consumer loans, APR is the legally required disclosure and (unlike the APR/APY relationship for savings) is a nominal rate rather than compounded, so it already reflects fees plus interest -- see our APR calculator for how fees factor in separately.
What does "continuous compounding" mean in practice?
It's the mathematical limit of compounding infinitely often (every instant) rather than a real-world payment schedule -- some financial models use it as a simplifying assumption, but very few real accounts actually compound continuously.
References
Ad Space (AdSense)