What this APY to APR calculator does
This tool converts an APY (Annual Percentage Yield) into a matching APR (Annual Percentage Rate) for a given compounding schedule. APY includes the effect of compounding, while APR is the nominal annual rate before the compounding effect is applied.
If you know APY from a savings product and want the nominal annual rate that produced it, this calculator helps you back it out quickly. It’s also useful for comparing rates quoted in different formats.
APY vs APR: quick explanation
APY (Annual Percentage Yield)
APY shows your effective annual return after compounding. Because compounding earns interest on interest, APY is typically higher than APR for the same base rate when compounding occurs more than once per year.
APR (Annual Percentage Rate)
APR is the nominal yearly rate. It does not by itself tell you the effective yearly growth unless you also know how often compounding happens.
Formula used by the calculator
The conversion from APY to APR uses:
APR = n × ((1 + APY)1/n − 1)
- APY must be converted to decimal first (for example, 5% = 0.05).
- n is compounding periods per year (12 monthly, 365 daily, etc.).
- The calculator returns APR as a percent.
Example
Suppose APY is 5.00% with monthly compounding (n = 12). The equivalent APR is approximately 4.8889%. If the same APY uses daily compounding, the equivalent APR changes slightly. That’s why compounding frequency matters whenever converting or comparing rates.
How to use this calculator
- Enter the APY value in percent.
- Select compounding frequency (or choose custom).
- Choose how many decimal places you want in the output.
- Click Calculate APR.
Common mistakes to avoid
- Entering APY as a decimal (0.05) instead of percent (5.00).
- Ignoring compounding frequency during comparison shopping.
- Comparing borrowing APR and savings APY directly without conversion.
- Rounding too aggressively when accuracy matters.
When this conversion is useful
Use APY-to-APR conversion for:
- Comparing high-yield savings accounts that publish APY while internal calculations use nominal rates.
- Building spreadsheets for personal finance or forecasting.
- Checking whether a quoted APY seems consistent with stated compounding.
- Translating rate formats for clearer apples-to-apples comparison.
Frequently asked questions
Is APR always lower than APY?
For positive rates with more than annual compounding, yes—APR will be lower than APY. If compounding is annual (n=1), APY and APR are equal.
Can APY be negative?
It can, in rare cases. The calculator supports negative APY values above -100%. APY less than or equal to -100% is mathematically invalid for this formula.
Does this include fees?
No. This is a pure mathematical conversion between nominal and effective rates. Product fees, taxes, and account rules are not included.
Bottom line
APY tells you what you effectively earn over a year; APR tells you the nominal annual rate. With the right compounding frequency, you can convert between them and compare offers with much more confidence.