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APR to APY Converter | Convert APR to APY by compounding

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Convert between APR and APY (EAR) for any compounding frequency, including continuous compounding, with the formula shown. The true cost of a loan and the true return on a deposit — enter either rate and get the other.

Last updated: June 2026 · Free · No sign-up required

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About the Apr To Apy Converter

Every result on this page comes from a real formula — APY = (1 + APR/n)^n – 1; APR = n x ((1 + APY)^(1/n) – 1) — computed live in your browser the moment you press the button.

Scroll past the converter for a quick-reference table, a step-by-step methodology with a fully worked example, and answers to the questions people most often ask about apr to apy converter.

Quick reference

APY for a 6% APR by compounding frequency:

CompoundingPeriods/yrAPY
Annually16.000%
Quarterly46.136%
Monthly126.168%
Daily3656.183%

info Apr To Apy Converter

Free math calculator — enter your numbers and get an instant, accurate result.

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Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

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info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

APR vs APY:

TermWhat it represents
APRNominal annual rate, ignores intra-year compounding
APY / EAREffective rate including compounding
More frequent compoundingHigher APY for the same APR
Use APY to compareTrue earning/borrowing cost

lightbulb Worked example

Let's say you are using the Apr To Apy Converter. Converts apr to apy using APY = (1 + APR/n)^n - 1, instantly in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula APY = (1 + APR/n)^n - 1; APR = n x ((1 + APY)^(1/n) - 1) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: APY = (1 + APR/n)^n - 1; APR = n x ((1 + APY)^(1/n) - 1)

The Apr To Apy Converter is built on a well-established calculation method. It uses the formula APY = (1 + APR/n)^n - 1; APR = n x ((1 + APY)^(1/n) - 1) to turn your inputs into a reliable result. Converts apr to apy using APY = (1 + APR/n)^n - 1, instantly in your browser. The steps are shown on the page so you can follow the reasoning from input to output.

APR is the stated nominal rate, while APY (also called the effective annual rate) reflects how often interest compounds. The calculator converts between them for any frequency: as compounding gets more frequent, the APY rises above the APR. Always compare savings accounts and loans by APY/EAR, because it captures the true annual cost or yield.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What's the difference between APR and APY?
The Apr To Apy Converter is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Converts apr to apy using APY = (1 + APR/n)^n - 1, instantly in your browser. There is no limit on usage, and it works on any device.
How do I convert APR to APY?
Enter the required values into the input fields and press the calculate button. The tool applies the formula APY = (1 + APR/n)^n - 1; APR = n x ((1 + APY)^(1/n) - 1) and returns the result with a short explanation of each step, so you can check the working yourself.
Why is APY higher than APR?
APY includes the effect of compounding while APR does not. The formula APY = (1 + APR/n)^n − 1 shows that more frequent compounding (larger n) raises the effective yield above the nominal rate. A 5% APR compounded monthly gives an APY of about 5.12%, and compounded daily about 5.13%. The difference grows with the rate and frequency.
Which should I use to compare accounts?
Always compare APY for savings and deposit accounts, because it reflects the true annual return including compounding, and APR for loans, because that is the quoted cost basis. Comparing a loan's APR against a savings account's APY directly is apples to oranges. The converter lets you translate between the two so every comparison is on the same footing.
Are APY and EAR the same?
Yes — annual percentage yield (APY) and effective annual rate (EAR) are the same concept under different names: the true annual rate including compounding. Both use the formula (1 + r/n)^n − 1. Banks favor the term APY, while finance textbooks and consumer disclosures often use EAR. The converter outputs both so the naming never causes confusion.
Why is the APY always higher than the APR?
Because APR is the nominal rate while APY folds in compounding — APY = (1 + APR/n)ⁿ − 1, so interest earned starts earning its own interest. With monthly compounding, a 12% APR becomes about 12.68% APY. Only with annual compounding (n = 1) do the two match exactly.
How does compounding frequency change the result?
More frequent compounding pushes APY higher for the same APR: at 12% APR, monthly compounding gives ~12.68% while daily gives ~12.75%. The tool supports any frequency, including continuous compounding via e^(APR) − 1. Lenders quote APR and savers compare APY, which is exactly why both directions are convertible.
Which rate should I compare when choosing a savings account?
Compare APY — it is the effective annual yield after compounding, so the higher APY is the better deal regardless of the quoted APR or compounding schedule. Two accounts with the same APR can pay different amounts if one compounds monthly and the other quarterly. The converter lets you normalize any quote to APY.
Can I convert APY back to APR?
Yes — the inverse is APR = n × ((1 + APY)^(1/n) − 1), and the tool does both directions. Going backward is exact, not approximate: a 12.68% APY with monthly compounding returns precisely 12% APR. That is useful when a lender quotes an effective rate and you need the nominal one for comparison.

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