APR to APY Calculator
APR and APY describe the same rate from two angles, and confusing them leads to unfair comparisons. APR is the nominal annual rate before compounding; APY is the effective rate after compounding is taken into account, so APY is always at least as high as APR. This APR to APY calculator converts a nominal rate into its effective yield for any compounding frequency, and shows the reverse conversion to prove the two are exact inverses. Use it to compare savings accounts quoted in APY against loans quoted in APR, or to see how much more frequent compounding actually adds.
Calculate
Default result: 6.1678
APR to APY Calculator · Result
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Effective annual yield (APY %)
6 × 12
- Back to APR (% — confirms the inverse)
- 6.0000
This calculator provides estimates for general informational purposes only and is not financial, investment, tax, or legal advice. Results are projections based on the figures you enter and the stated assumptions, and actual outcomes will differ. Consult a qualified financial professional before making borrowing, saving, or investment decisions.
Reviewed by the calculators.dev team · Last updated 2026-06-24
Formula reviewed against Inch Calculator APR to APY — effective-annual-rate conversion reference
How to calculate
Enter the nominal APR and how many times a year interest compounds. The calculator applies the effective-rate formula: divide the APR by the compounding frequency, add one, raise it to the number of periods, and subtract one. For 6% compounded monthly, the APY is about 6.1678%. The second line converts that APY back to an APR to confirm the round-trip returns your original 6%, demonstrating the conversion is exact.
APY = (1 + APR/n)^n − 1, where APR is the nominal rate as a decimal and n is the number of compounding periods per year. The inverse is APR = n · ((1 + APY)^(1/n) − 1). More frequent compounding (larger n) raises the APY for the same APR; with annual compounding (n = 1), APR and APY are equal.
Example calculation
A 6% nominal APR compounded monthly is equivalent to an effective annual yield of about 6.1678%. The APY is higher than the APR because interest is added 12 times a year and each addition earns interest of its own. Converting the 6.1678% APY back to a nominal rate returns 6.0000%, confirming the two are exact inverses.
- apyPercent
- 6.1678%
- aprRoundTripPercent
- 6.0000%
Assumptions
- The APR is a pure interest rate; lender APRs that bundle in fees will not convert cleanly to a yield.
- The compounding frequency is constant over the year.
- Rates are entered and shown as annual percentages, not decimals.
Common mistakes
- Comparing a savings APY directly against a loan APR without converting them to the same basis.
- Assuming APR and APY are the same — they only match when interest compounds once a year.
- Entering the rate as a decimal (0.06) instead of a percentage (6).
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal annual rate before compounding. APY is the effective rate after compounding, so it reflects interest earning interest. For the same stated rate, APY is higher whenever interest compounds more than once a year.
Why is APY higher than APR?
Because interest is added during the year and then earns interest itself. At 6% compounded monthly, those twelve additions push the effective yield to about 6.1678%.
When are APR and APY equal?
When interest compounds exactly once a year (n = 1). With any more frequent compounding, the APY exceeds the APR.
Should I compare accounts by APR or APY?
Compare like with like. APY is the better measure of what you actually earn or pay over a year, so convert everything to APY (or everything to APR) before comparing.