APR to APY Calculator: Convert Annual Rates

This free APR to APY calculator converts an annual percentage rate (APR) into an annual percentage yield (APY) for a stated compounding schedule. Enter the APR and the number of compounding periods per year to see the equivalent APY, plus the difference between the two rates.

Formula

For a nominal APR compounded at a regular frequency, the effective annual yield is: APY = 100 × [(1 + APR / (100 × m))^m − 1].

• APR is the stated nominal annual rate, entered as a percentage.
• m is the number of compounding periods in one year, such as 12 for monthly or 4 for quarterly compounding.
• APY is the resulting effective annual rate, expressed as a percentage after compounding.
• APY minus APR is the difference in percentage points; it is not the percentage increase relative to APR.

The calculation assumes the same rate applies during every compounding period and that interest remains in the account or balance to compound. It converts a nominal rate into an annual effective rate; it does not account for fees, changing rates, deposits, withdrawals, or a particular financial product’s terms.

Worked Example

Using the calculator’s default APR of 5% and 12 compounding periods per year:

1. Find the periodic rate: 5 ÷ (100 × 12) = 0.0041666667, or about 0.4166667% per month.
2. Add 1: 1 + 0.0041666667 = 1.0041666667.
3. Raise that value to the 12th power: (1.0041666667)¹² ≈ 1.0511618979.
4. Subtract 1 and convert to a percentage: (1.0511618979 − 1) × 100 ≈ 5.1162% APY.
5. Subtract APR: 5.1162% − 5% = 0.1162 percentage points.

With results rounded to four decimal places, the calculator displays APY: 5.1162% and APY minus APR: 0.1162 percentage points.

What APR and APY Mean

APR and APY describe annual rates in different ways. APR is generally a nominal annual rate: it states a yearly rate without expressing the full effect of earning or owing interest on previously accumulated interest. APY expresses the effective annual yield after compounding. For a positive rate compounded more than once a year, APY is higher than APR when all other assumptions are equal.

The distinction matters when comparing figures that use different conventions. For example, a rate that compounds monthly accumulates interest twelve times in a year, while a rate compounded annually accumulates it once. The calculator translates the stated APR under the selected schedule; it cannot establish whether a particular product’s advertised rate is defined that way. Check the product disclosure for its stated yield, compounding schedule, and applicable fees.

How to Use the Calculator

• Enter the nominal APR as a percentage, not as a decimal. For example, enter 5 for 5%, not 0.05.
• Enter the number of compounding periods in a year: 12 for monthly, 4 for quarterly, 2 for semiannual, or 1 for annual compounding.
• Read the first result as the effective annual percentage yield under those assumptions.
• Use the second result to see the APY–APR gap in percentage points. A result of 0.1162 means the APY is 0.1162 percentage points above the APR.

The calculator accepts frequencies from 1 to 365 periods per year as a mathematical input range. Use the schedule actually specified for the rate rather than selecting a frequency merely because it produces a preferred result. If the rate compounds daily, the exact convention for counting days can matter; this calculator treats the year as having the stated number of equal periods.

Common Mistakes and Limits

• Mixing percentage and decimal formats: Entering 0.05 means 0.05%, not 5%, in this calculator.
• Using the wrong frequency: Monthly compounding means 12 periods, not 1. The frequency changes the calculated APY.
• Confusing percentage points with percent change: The displayed difference is a subtraction of rates. It is not the relative percent by which APY exceeds APR.
• Treating APY as a guaranteed return: The result is a mathematical equivalent for a fixed rate and specified schedule. A variable rate, fees, balance changes, or product-specific rules can lead to different actual earnings or costs.
• Comparing unlike rate disclosures: If a quoted figure already represents an effective yield, converting it as though it were nominal APR may misstate the comparison. Confirm what each quoted number represents.

At 0% APR, the formula returns 0% APY regardless of compounding frequency. Results are rounded to four decimal places, so a displayed value may differ slightly from a figure rounded or disclosed using another convention. The formula is not a loan payment calculator and does not calculate the total interest paid on a changing balance.

When This Conversion Is Useful

APR-to-APY conversion is useful when you need to understand how compounding changes a nominal annual rate into an effective annual rate. It can also help explain why two rates with the same nominal APR may produce different annual outcomes if they compound on different schedules. For a fair comparison, make sure both rates refer to the same kind of product, period, balance assumptions, and treatment of fees.

For borrowing, a quoted APR can include cost components beyond the interest rate depending on how that APR is defined, while this calculator’s formula only compounds the entered rate. It therefore should not be used to convert a loan’s disclosed APR into a complete borrowing cost or to infer a payment. For savings or investments, the result is likewise not a promise of earnings: actual results depend on the account terms, rate changes, cash flows, and any applicable charges.

Frequently Asked Questions

Is there a free APR to APY calculator?
Yes. This calculator is free to use. Enter the APR and compounding periods per year to calculate the equivalent effective annual yield.

How do I convert APR to APY?
Use APY = (1 + APR/m)^m − 1, with APR written as a decimal and m as periods per year. This page accepts APR as a percentage and converts it in the formula automatically.

Is APY always higher than APR?
For a positive nominal APR with more than one compounding period per year, APY is higher under this formula. With annual compounding, APY equals APR; at a zero rate, both are zero.

What compounding frequency should I enter?
Enter the schedule stated for the rate: 12 for monthly, 4 for quarterly, 2 for twice a year, or 1 for annually. If the disclosure uses a different convention, follow that disclosure rather than guessing.

Does this calculator include fees or changing rates?
No. It assumes a fixed nominal APR and regular compounding. It does not include fees, taxes, deposits, withdrawals, or rate changes, so check the applicable disclosure for complete product figures.

This result is an estimate from the stated inputs, and the lender’s disclosure gives the exact figures.

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in apr | APR | % | 5 | 0 | 100
in freq | Compounding periods per year | - | 12 | 1 | 365
out apy | Equivalent APY | % | 100 * ((1 + apr / (100 * freq)) ^ freq - 1) | 4
out diff | APY minus APR | percentage points | apy - apr | 4