Finance · 5 min read
How to Calculate APY from APR
Effective yearly yield after compounding — APY = (1 + r/m)^m − 1
APY converts a nominal APR and a compounding frequency into an effective yearly rate. This tutorial walks through APY = (1 + r/m)^m − 1, a 5% APR / monthly worked example, and a playground that turns the frequency dial so you can see the effective-yield gap. Figures are illustrative; fees and taxes are omitted.
Written by the My Calculator Stack editorial team. About our methods
These figures are illustrative. Fees, taxes, and product-specific rules are omitted. Quoted APY on a real account can differ. This is not investment, tax, or financial advice.
1.What APR and APY are
APR here is the nominal annual rate r, stated without intra-year compounding. APY is the effective yearly yield after that rate is applied m times per year. At the same nominal r, more frequent compounding raises APY slightly. Banks often advertise APY so yields with different compounding schedules can be compared.
2.The formula
APY = (1 + r/m)^m − 1. r is the nominal APR as a decimal (5% → 0.05) and m is compounds per year. The period rate is r/m; raising (1 + r/m) to m compounds once across a year, then subtracting 1 leaves the effective annual rate. Multiply by 100 for a percent. The same equation powers the APY calculator on this site.
\[ \mathrm{APY} = \left(1+\frac{r}{m}\right)^{m} - 1 \]
3.Worked example
Take 5% APR compounded monthly (m = 12) — the same defaults as the APY calculator. Period rate r/m = 0.05/12. Then APY = (1 + 0.05/12)^12 − 1 ≈ 0.05116, or about 5.12%. Annual compounding (m = 1) leaves APY = APR. Daily compounding (m = 365) lifts the same 5% APR to about 5.13%.
\[ \mathrm{APY}=\left(1+\frac{0.05}{12}\right)^{12}-1\approx 0.0512 \]
4.Frequency dial and effective yield
Turn the compounding-frequency dial and move APR to see APY update. The bar stacks nominal APR against the extra yield from compounding. This is a teaching widget — no account fees, no continuous compounding toggle, no full calculator chrome. Open the APY calculator when you want the standalone tool.
Inline playground
Illustrative — fees and taxes omitted
Monthly · m = 12
Effective APY
5.12%
APR 5.00% · extra yield 0.12%
(1 + 0.05/12)^12 − 1 ≈ 5.12%
Illustrative only — nominal APR to APY, no account fees, no continuous compounding.
Open the full APY calculator →5.Open the full calculator
The APY calculator uses the same (1 + r/m)^m − 1 equation, the same 5% / monthly example, and the same limitation that fees and taxes are omitted. Browse other finance tools if you need future value, compound interest, or inflation next.
Try it yourself
Open the related calculator and put these formulas to work.