How this calculator works
Multiply all positive integers up to n. The empty product at n = 0 is defined as 1, which makes factorial identities and counting formulas work at their boundaries. Exact integer arithmetic avoids overflow and rounding. This tool uses the discrete factorial rather than extending it through the gamma function.
Formula
n! = 1 × 2 × ... × n for integer n >= 1; 0! = 1.
Worked example
5! = 1 × 2 × 3 × 4 × 5 = 120, with 3 decimal digits. Also 0! = 1, with 1 digit.
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Frequently asked questions
Why does zero factorial equal one?
There is one way to arrange no objects. Algebraically, the empty product is the multiplicative identity 1.
Can I enter 2.5?
No. Non-integer extensions use the gamma function and are outside this integer factorial tool.
Why is the answer text?
Large factorials exceed finite numeric ranges and safe integer precision. Text preserves every calculated digit.