Calculate APY

APY = ((1 + nominal annual rate ÷ compounds per year)^compounds per year − 1) × 100.

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Nominal annual rate (%)

Compounds per year

Answer

…

APY = ((1 + nominal annual rate ÷ compounds per year)^compounds per year − 1) × 100.

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Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

Step-by-step calculation

Inputs are substituted below. Each line evaluates the next operation; intermediate values are displayed to 12 significant digits while the calculation uses full precision.

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Formula and assumptions

Assumes a fixed nominal rate and no fees or withdrawals. A quoted loan APR can include fees, so it is not always this nominal rate.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Calculate APY

APY = ((1 + nominal annual rate ÷ compounds per year)^compounds per year − 1) × 100.

Assumes a fixed nominal rate and no fees or withdrawals. A quoted loan APR can include fees, so it is not always this nominal rate.

Next: Present value calculator

A worked example

With nominal annual rate (%) = 5, compounds per year = 12, the annual percentage yield (%) is 5.1161897881733.

Next: Calculate CAGR

Before you use the result

Assumes a fixed nominal rate and no fees or withdrawals. A quoted loan APR can include fees, so it is not always this nominal rate.

Example results for nominal annual rate (%)

These examples use Compounds per year: 12. They are reference calculations, not recommended settings.

Nominal annual rate (%)	Annual percentage yield (%)
2.5	2.52884569833
5	5.11618978817
10	10.4713067441

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ToolOctopus. “Calculate APY.” Updated 2026-09-26. https://tooloctopus.com/apy-calculator.

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