---
title: "Factorial Calculator — n! Exact Results up to n=5000"
description: "Calculate n! exactly for any integer up to 5000. Shows full digit count, double factorial n!!, and Stirling's approximation for large n. Free factorial calculator."
url: "https://worldcalculators.org/calculators/factorial/"
canonical: "https://worldcalculators.org/calculators/factorial/"
---

# Factorial Calculator

Calculate n! exactly for any integer up to 5000. Shows full digit count, double factorial n!!, and Stirling's approximation for large n. Free factorial calculator.

## Quick answer

n! = n × (n−1) × ... × 2 × 1. 0! = 1 (by definition). Key values: 5! = 120  ·  10! = 3,628,800  ·  20! ≈ 2.43×10¹⁸  ·  100! ≈ 9.33×10¹⁵⁷ (158 digits).

## Frequently Asked Questions

0! = 1 by definition. The mathematical justification: there is exactly one way to arrange 0 objects (the empty arrangement). Also, the formula nCr = n! / (r!(n−r)!) requires 0! = 1 to work when r = 0 or r = n.
100! = 9.332621544... × 10¹⁵⁷. It has 158 digits. The number of digits in n! can be estimated as ⌊log₁₀(n!)⌋ + 1, or via Stirling: approximately n·log₁₀(n/e) + ½·log₁₀(2πn).

Source: https://worldcalculators.org/calculators/factorial/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.