The factorial of a non-negative integer n, written n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.

Why is 0! equal to 1?

By convention and mathematical consistency, 0! is defined as 1. This makes combinatorial formulas work correctly — for instance, there is exactly one way to arrange zero items.

What is the largest input this tool supports?

The tool uses JavaScript BigInt, so it can compute exact integer results up to very large values. Inputs above 10,000 may take a moment due to the size of the numbers involved.

Can I compute the factorial of a negative number or a decimal?

No — the standard factorial function is only defined for non-negative integers. For non-integer values, the Gamma function generalizes factorial, but that is beyond the scope of this tool.

How is this useful in probability?

Factorials appear in the formulas for permutations (n! / (n-r)!) and combinations (n! / (r!(n-r)!)), which count arrangements and selections in probability and statistics.

Factorial Calculator

Name: Factorial Calculator
Availability: InStock
Author: Nham Vu

Enter a non-negative integer to instantly compute its factorial with a full step-by-step expansion.

Enter a Non-Negative Integer

Value of n

Quick presets

Enter a value and press Calculate.

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Summary

Enter a non-negative integer to instantly compute its factorial with a full step-by-step expansion.

How it works

Type a non-negative integer into the input field.
The calculator immediately computes n! using BigInt arithmetic.
The step-by-step expansion is shown below the result.
Use the Copy button to copy the numeric result to your clipboard.
Click Reset to clear the input and start over.

Use cases

Check combinatorics homework — permutations and combinations both require n!.
Verify probability calculations that involve factorial terms.
Explore how quickly factorial values grow for large n.
Compute exact large factorials without floating-point rounding errors.
Teach or learn the definition of factorial step by step.
Quick reference when working through statistics or discrete math problems.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu