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Math

Factorial Calculator

Calculate the exact factorial of a whole number from zero to 500.

Exact method explained belowEditable inputs
Calculation notebook
Calculation notebook

The formula and worked example below explain the calculation.

See the method

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Your result

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Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter whole number n.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

Input reference and sample values

Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.

InputFormat and unitsSample
Whole number nNumeric value. Zero or positive. Maximum: 500.10

Result for these sample inputs

3628800
Input
10

Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.

The method, explained

n! is the product of integers from 1 through n. By definition, 0! = 1. Results use arbitrary-precision integer arithmetic.

A WORKED EXAMPLE

5! = 5 × 4 × 3 × 2 × 1 = 120.

What to keep in mind

Only whole numbers from 0 to 500 are accepted. This does not extend factorials to non-integers through the gamma function.

Common questions

Why is zero factorial one?

The empty product is defined as one, making combinatorial identities consistent.

Are large results rounded?

No. The factorial is displayed as an exact integer; copy it to preserve every digit.

Methodology maintained by ClarityKit. How these tools are built and checked.