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APY Calculator: Convert APR to APY (Any Compounding)

Use this APY calculator to convert any nominal interest rate (APR) to its effective Annual Percentage Yield. Pick the compounding frequency to see exactly what your savings or CD will earn — works as a CD APY calculator too.

%
APY (effective)0.00%
Monthly equivalent rate0.000%
$10,000 grows to (1 yr)$10,000.00
APY − APR difference0.00%
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How this calculator works

APR (Annual Percentage Rate) is the simple, nominal interest rate. APY (Annual Percentage Yield) is the effective rate after compounding is applied. Since 1991, federal Truth-in-Savings rules require US banks to disclose the APY on deposit accounts so consumers can make a fair comparison.

The APR-to-APY conversion formula

Both directions of the conversion are governed by a single relationship between rate, compounding frequency, and effective yield:

APY = (1 + APR/n)n − 1
APR = n × ((1 + APY)1/n − 1)
n
Number of compounding periods per year
APR
Nominal annual rate (the headline number some banks quote)
APY
What you actually earn over a year of holding the balance

A 4.50% APR compounded monthly produces a 4.594% APY — small but meaningful. The wider the compounding (annual → daily), the bigger the gap.

How to calculate APY for a CD or savings account

For a certificate of deposit, the bank quotes APY directly — the math is already done. To verify their disclosure, plug the stated APR (sometimes called "interest rate") and the stated compounding frequency into the formula above. For a high-yield savings account where the rate can change, recompute monthly to track your true effective yield.

Why APY matters more than APR for savings

APR is what the money is doing on paper. APY is what the money actually earns once interest-on-interest is included. Two banks can quote the same APR but different APYs if their compounding frequencies differ. When comparing accounts, only compare APY against APY.

Source: APY definition and disclosure rules are codified in the US Truth-in-Savings Act, 12 CFR § 1030 (Regulation DD).

FAQ

How is APY calculated?
APY = (1 + APR/n)n − 1, where APR is the nominal annual rate and n is the number of compounding periods per year. For a 4.5% APR compounded monthly, APY = (1 + 0.045/12)12 − 1 = 4.594%. The more frequent the compounding, the higher the APY for the same APR.
How do I use a certificate of deposit (CD) APY calculator?
Set the direction to APR → APY, enter the bank's stated nominal rate, and pick the matching compounding frequency from the disclosure. Most US CDs compound daily or monthly. The result is the effective annual yield you'd earn if held the full term.
How do I convert APR to APY?
Use the formula APY = (1 + APR/n)n − 1, where n is the number of compounding periods per year. The calculator handles this automatically: enter the APR, pick the compounding frequency, and read the APY. The conversion always produces APY ≥ APR.
How do I convert APY back to APR?
Reverse the formula: APR = n × ((1 + APY)1/n − 1). The calculator handles this when you switch the direction to APY → APR. Useful when a bank quotes APY but you need the nominal rate to compare against another product.
Why do banks usually quote APY for savings but APR for loans?
Each makes the rate look better for the bank. Savings accounts: APY is HIGHER than APR after compounding, so banks advertise APY. Loans: APR is LOWER than the effective annual rate, so banks advertise APR. Always read the fine print to know which is quoted.
Is daily compounding really better than monthly?
Mathematically yes, but the difference is tiny. At 4.5% APR, monthly compounding gives 4.5940% APY; daily gives 4.6020% — a 0.008-percentage-point difference. On $10,000 over 1 year that's an extra $0.80. Don't change banks for compounding frequency; do change for the headline APY.
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