APR to APY Calculator - Convert Nominal & Effective Rates

Use this APR to APY Calculator to convert between APR and APY locally. Enter a rate, choose compounding frequency, and see the effective interest rate, spread, and frequency comparison instantly.

Click for theater mode
Conversion Direction

All rate conversions run locally in your browser. Your rate and compounding frequency are not uploaded.

Results are standard APR/APY math only. Fees, penalties, leap-year day counts, and lender-specific rules are not included.

Converted Result

APR → APY
Input Rate (APR)
12%
Converted Rate (APY)
12.682503%
Spread
+0.682503%
Formula Used
APY = (1 + APR / n)^n - 1

Compounding Frequency Comparison

FrequencyPeriods / YearConverted ResultSpread
Annually112%0%
Semi-Annually212.36%+0.36%
Quarterly412.550881%+0.550881%
Monthly1212.682503%+0.682503%
Daily36512.747462%+0.747462%
Continuous∞12.749685%+0.749685%

How to Use

  1. Choose a conversion direction, such as APR → APY.
  2. Enter the known interest rate, such as 12.
  3. Select the compounding frequency, such as Monthly.
  4. Review the converted rate, spread, and formula note in the result panel.
  5. Click "Load example" to inspect 12% APR compounded monthly and compare Daily, Monthly, Quarterly, and other frequencies in the table.

Core Features

  • Two-Way APR/APY Conversion: Switch between APR to APY and APY to APR to compare nominal and effective annual rates.
  • Multiple Compounding Periods: Supports annually, semi-annually, quarterly, monthly, daily, and continuous compounding.
  • Frequency Comparison Table: Enter one rate and see how each compounding frequency changes the converted result and spread.
  • Instant Local Math: No submit button and no server upload; changing the rate, direction, or frequency updates the answer immediately.
  • Plain-English Rate Context: Explains APR, APY, nominal rates, and effective rates without burying the result in banking jargon.

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Calculation Logic

This tool uses the standard Effective Annual Rate formula. APR is usually a nominal annual rate, while APY includes the effect of compounding within the year.

APR to APY:

APY=(1+APRn)n−1 \text{APY}=\left(1+\frac{\text{APR}}{n}\right)^n-1

APY back to APR:

APR=n×((1+APY)1n−1) \text{APR}=n\times\left((1+\text{APY})^{\frac{1}{n}}-1\right)

Here nn is the number of compounding periods per year, so monthly compounding uses n=12n=12. Continuous compounding uses eAPR−1e^{\text{APR}}-1 and ln⁡(1+APY)\ln(1+\text{APY}).

Results use a standard mathematical model. They do not include credit card fees, loan origination fees, leap-year day counts, grace periods, penalty rates, or lender-specific billing rules.

FAQ

What is the difference between APR and APY?

APR (Annual Percentage Rate) is a nominal annual rate that usually does not show the full effect of compounding. APY (Annual Percentage Yield) is an effective annual rate that includes compounding over one year.

When is APR used versus APY?

Borrowing products such as credit cards and loans often show APR. Savings, deposits, and investing products often show APY. When comparing products, make sure the rates use the same basis.

Why is APY usually higher than APR?

When interest compounds more than once per year, earned interest can earn more interest. That makes APY higher than the matching nominal APR. With annual compounding, they are equal.

Can I convert APY back to APR?

Yes. Switch the direction to APY → APR, enter the known APY and compounding frequency, and the calculator will infer the matching nominal APR.

Are my rate inputs uploaded?

No. The APR/APY conversion runs in your browser, so your rate and compounding frequency are not sent to a server.

Why can credit card APR differ from the interest I actually pay?

Credit card cost can also depend on daily balances, payment timing, grace periods, penalty rates, annual fees, and other charges. This tool only converts the standard rate formulas.