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APR to APY Converter (and back)

Convert between APR (nominal rate) and APY (effective yield) for any compounding frequency — daily, monthly, quarterly, annually, or continuous.

Runs 100% in your browser — nothing is uploaded.
APY
6.1678%
At 6% APR, APY by compounding frequency:
FrequencyAPY
Annually6.0000%
Semi-annually6.0900%
Quarterly6.1364%
Monthly6.1678%
Daily6.1831%
Continuous6.1837%

APR is the nominal rate stated on the loan or account. APY is what you actually earn (or pay) once compounding is factored in. For a fair comparison between two products, always compare APYs.

How to use

  1. 1
    Pick a direction

    APR → APY (what a stated rate really earns) or APY → APR (what your quoted yield implies as a nominal rate).

  2. 2
    Enter the rate

    As a percentage, e.g. 6.5 for 6.5%.

  3. 3
    Pick a compounding frequency

    Daily, monthly, quarterly, semi-annually, annually, or continuously. Savings accounts usually compound daily; credit cards monthly.

  4. 4
    Read the converted rate

    Precision is 4+ decimal places — enough for any spreadsheet or contract math.

Examples

6% APR → monthly compounding
Input
APR: 6% · Compounding: monthly
Output
APY = 6.1678%
Standard credit-card rate. The 0.17% gap is what compounding adds over the stated rate.
5% APY → APR (daily)
Input
APY: 5% · Compounding: daily
Output
APR = 4.8790%
When a savings account advertises 5% APY, the underlying daily rate produces exactly that yield.
20% APR credit card → true annual cost
Input
APR: 20% · Compounding: monthly
Output
APY = 21.9391%
The reason carrying a credit card balance is more expensive than the sticker rate — nearly 2 full points more.
Continuous compounding limit
Input
APR: 6% · Compounding: continuous
Output
APY = 6.1837%
The mathematical ceiling. Daily compounding at 6.1831% is already within 0.001% of this — beyond daily, the difference vanishes.

Frequently asked

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the stated nominal rate without compounding. APY (Annual Percentage Yield) is what you actually earn or pay after compounding. At 6% APR compounded monthly, the APY is 6.17%.

Why does compounding frequency matter?

More frequent compounding means interest earns interest sooner. Daily compounding of 6% APR gives 6.183% APY; annual compounding gives exactly 6%. The gap grows quickly at higher rates.

What is continuous compounding?

The mathematical limit as compounding frequency approaches infinity. APY = e^APR − 1. At 6%, continuous compounding gives 6.184% APY — essentially the same as daily. Used in bond math and options pricing.

Which rate should a savings account advertise?

APY. It reflects what you actually earn in a year. US banks are legally required to disclose APY (Truth in Savings Act).

Which rate does a credit card show?

APR. Credit card statements show the nominal rate; the effective rate you pay is higher after monthly compounding of unpaid balances.

How do I convert APY back to APR?

For n compoundings per year: APR = n × ((1 + APY)^(1/n) − 1). This tool does both directions — pick "APY → APR" in the mode toggle.

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