APR to APY Calculator

Convert between APR and APY across different compounding frequencies. See exactly how the math works.

APR & APY Converter

Enter an annual rate, choose how it is quoted, and instantly compare equivalent rates across compounding frequencies.

Annual interest rate

The quoted annual rate as a percentage (e.g. 5 for 5%).

Rate type

APR (nominal)

Stated rate before compounding — needs a frequency to calculate true yield.

APY (effective)

True annual yield — compounding is already factored in.

Compounding frequency

How often interest is compounded per year for the quoted APR.

Equivalent Rates

Your quoted rate of 5% matches "Monthly (12×/yr) APR" in the table below — the other rows show what it would be under different compounding rules.

Tap any row to see detailed conversion steps below.

For learning and comparison only. Always verify the exact terms in the official product disclosure before making financial decisions.

How the conversion works

Follow the math step by step for the selected result. Each formula updates automatically when you pick a different row.

5% APR (nominal)↓5.11619% Equivalent APY

Conversion inputs

Quoted rate5%

Rate typeAPR (nominal)

Source compoundingMonthly (12×/yr)

Normalized APY5.11619%

Target resultEquivalent APY (5.11619%)

Target compoundingN/A (effective rate)

1Step 1 — Convert the percentage to a decimal

r = \frac{5}{100} = 0.05

2Step 2 — Find the effective annual yield (APY)

APY = \left(1 + \frac{0.05}{12}\right)^{12} - 1 = 0.0511619

3Result

\boxed{APY = 0.0511619 \times 100 = 5.11619\%}

Understanding APR and APY

APR and APY both express interest on an annual basis, but they measure different things:

Term	Full name	What it tells you
APR	Annual Percentage Rate	The nominal (stated) rate before compounding is fully reflected.
APY	Annual Percentage Yield	The effective rate after compounding — what your balance actually earns (or costs) in one year.

Because APY already accounts for the compounding effect, it is the more transparent number for comparing savings products like CDs and high-yield savings accounts. APR remains common in loan quotes, credit-card disclosures, and investment specifications because it separates the base rate from the compounding rule, letting each party apply its own frequency.

The math behind APR ↔ APY

Discrete compounding ( $n$ times per year)

When interest compounds a fixed number of times each year — monthly ( $n = 12$ ), semimonthly ( $n = 24$ ), bi-weekly ( $n = 26$ ), weekly ( $n = 52$ ), daily ( $n = 365$ ), quarterly ( $n = 4$ ), or semiannually ( $n = 2$ ) — the two rates are related by a power formula:

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

To go the other way, solve for APR:

\text{APR} = n\left((1 + \text{APY})^{\,1/n} - 1\right)

Continuous compounding

When compounding happens infinitely often (the mathematical limit as $n \to \infty$ ), the exponential function takes over:

\text{APY} = e^{\text{APR}} - 1 \qquad \text{APR} = \ln(1 + \text{APY})

Why the frequency matters

The same nominal APR produces a higher APY when interest compounds more frequently. For example, 5% APR compounded daily yields a slightly higher APY than 5% APR compounded monthly — because each day's earned interest starts earning its own interest sooner.

Conversely, the same APY maps back to a lower APR as the compounding frequency increases, because more frequent compounding achieves the same effective yield from a smaller nominal rate.

How to use this calculator

Enter the annual rate as a percentage (e.g. 5 for 5%).
Select the rate type — APR if it is a nominal rate, or APY if it is already an effective rate.
Pick the compounding frequency (shown only for APR) that matches how the product or disclosure compounds interest.
Review the results table — the calculator shows the equivalent APY plus APRs for every common compounding convention so you can compare them at a glance.
Tap any result row to expand a step-by-step breakdown of the exact formulas used in the conversion.

When this converter is useful

Comparing deposit products: one bank advertises APY, another quotes APR — use this tool to put both on the same footing.
Checking a loan disclosure: translate a quoted APR into the effective annual cost for a given compounding schedule.
Understanding compounding impact: see exactly how much difference monthly vs. daily vs. continuous compounding makes on the same nominal rate.
Auditing yield assumptions: verify the numbers in a savings projection or CD calculator model.
Learning the formulas: the step-by-step section lets you trace each calculation so you can reproduce it independently.

> Disclaimer: This calculator is for educational and comparison purposes. Always refer to the official disclosure from your bank, lender, or financial institution before making any financial decision.