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APY Calculator

Convert between nominal APR and effective APY at any compounding frequency, and see the same rate tabulated daily, monthly, quarterly and continuously.

5.0000%
Nominal rate (APR)
5.1162%
Effective rate (APY)
0.416667%
Rate per period
$511.62
Interest in one year

The same 5.0000% nominal rate at every compounding frequency

CompoundingAPYInterest in a yearBalance after a year
Daily (365)5.1267%$512.67$10,512.67
Weekly5.1246%$512.46$10,512.46
Monthly5.1162%$511.62$10,511.62
Quarterly5.0945%$509.45$10,509.45
Semi-annually5.0625%$506.25$10,506.25
Annually5.0000%$500.00$10,500.00
Continuously5.1271%$512.71$10,512.71

Two accounts can only be compared fairly on APY, because APY already includes the effect of compounding. A higher nominal rate compounded annually can lose to a lower one compounded daily.

APY = (1 + APR/n)n − 1 and APR = n((1 + APY)1/n − 1), with er − 1 and ln(1 + APY) for continuous compounding. Worked check: a 5% nominal rate is a 5.1162% APY compounded monthly, 5.0945% quarterly, 5.1267% daily and 5.1271% continuously — and converting 5.1162% APY back at monthly compounding returns exactly 5.0000%. Arithmetic only, not financial advice.

What is the APY Calculator?

The ByteTools APY Calculator converts in both directions between the nominal rate a bank advertises and the effective annual yield you actually earn.

  • Two-way conversion between nominal APR and effective APY
  • Daily, weekly, monthly, quarterly, semi-annual, annual and continuous compounding
  • Comparison table of the same nominal rate at every frequency
  • Rate per compounding period shown to six decimal places
  • One-click copy of the full conversion summary
  • Local, private and free — nothing leaves your browser

How to use the APY Calculator

  1. 1

    Choose whether you know the nominal rate (APR) or the effective rate (APY).

  2. 2

    Type the rate you have and pick the compounding frequency it applies to.

  3. 3

    Optionally enter a balance to see the interest in money rather than percentages.

  4. 4

    Read the converted rate and the rate per compounding period in the summary tiles.

  5. 5

    Scan the comparison table to see what the same nominal rate yields at every other frequency, and copy the summary if you need it.

About the APY Calculator

The ByteTools APY Calculator converts in both directions between the nominal rate a bank advertises and the effective annual yield you actually earn. APY = (1 + APR/n)^n − 1 going one way, APR = n((1 + APY)^(1/n) − 1) coming back, with the continuous forms e^r − 1 and ln(1 + APY) also supported.

The comparison table is the part most people come for: it takes your nominal rate and shows the APY it produces at daily, weekly, monthly, quarterly, semi-annual, annual and continuous compounding, side by side. Add a balance and it prices one year of interest at each frequency so the difference is in money rather than decimals.

It is for anyone comparing savings accounts, CDs or money market funds whose rates are quoted on different bases. Everything runs in your browser, no rates are fetched and nothing is uploaded. Arithmetic only, not financial advice.

Frequently asked questions

What is the difference between APR and APY?

APR is the nominal annual rate before compounding; APY is the effective rate after it. A 5% APR compounded monthly is a 5.1162% APY, so the account pays slightly more than the headline number suggests.

How do you convert APR to APY?

Use APY = (1 + APR/n)^n − 1, where n is the number of compounding periods a year. For 5% compounded quarterly that is (1 + 0.05/4)^4 − 1 = 5.0945%, and for continuous compounding it becomes e^0.05 − 1 = 5.1271%.

Which is better for savings, APR or APY?

Always compare on APY. It already includes the effect of compounding, so it is the only number that lets you rank two accounts fairly. A lower nominal rate compounded daily can beat a higher one compounded annually.

Does more frequent compounding make a big difference?

At normal savings rates the effect is real but small: on 5%, moving from annual to daily compounding lifts the yield from 5.0000% to 5.1267%. At high rates or over long horizons the gap widens considerably.

What is continuous compounding?

It is the mathematical limit of compounding infinitely often, calculated as e^r − 1. It sets the ceiling on what any compounding frequency can deliver — for a 5% nominal rate that ceiling is 5.1271%.

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