APY vs. APR Calculator
Convert a nominal APR to an effective APY, or find the nominal APR that produces a given APY, at a chosen compounding frequency. APR and APY are related but not interchangeable — labels and formulas keep the distinction explicit.
Your results will appear here
Enter your assumptions and calculate to see the estimated result and supporting details.
How this calculator works
Choose APR → APY or APY → APR. Enter the rate and compounding frequency (daily, monthly, quarterly, or annually).
Results show the converted rate, periodic rate, and an educational illustration of growth on $1,000 over one year.
Formula / methodology
APY = (1 + APR/n)^n − 1 APR = n × ((1 + APY)^(1/n) − 1)
- n is compounding periods per year: daily 365, monthly 12, quarterly 4, annually 1.
- With annual compounding (n = 1), APR equals APY.
- For positive APR and n > 1, APY is greater than APR.
- Continuous compounding is not included in this phase.
Worked example
A 12% APR compounded monthly is about 12.6825% APY.
A 5% APR compounded daily is about 5.1267% APY.
With annual compounding, 5% APR and 5% APY are identical.
Important assumptions
- APR is nominal; APY is effective annual.
- Supported frequencies: daily (365), monthly (12), quarterly (4), annually (1).
- The $1,000 illustration is educational only and is not transmitted or stored.
Common questions
More frequent compounding within the year produces a higher effective annual yield for the same nominal APR.
Yes. Converting APR → APY → APR (and the reverse) reproduces the original rate within floating-point tolerance.
Yes. 0% APR and 0% APY convert to each other.