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Factorial Calculator

Find n factorial for any integer up to 20.

How it is calculated

The factorial of a non-negative whole number is the product of all whole numbers from 1 up to it: n! = n × (n−1) × … × 2 × 1, with 0! = 1 by definition. The tool multiplies the integers one by one in exact integer arithmetic. It accepts only whole numbers from 0 to 20, because 20! = 2,432,902,008,176,640,000 is the largest factorial that fits in a 64-bit integer; a decimal, a negative number or anything above 20 returns no result rather than an inexact one. Digits are grouped with the separator of the page language.

Worked example

For n = 10 the product is 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. Multiply in pairs: 10 × 9 = 90, 90 × 8 = 720, 720 × 7 = 5,040, 5,040 × 6 = 30,240, 30,240 × 5 = 151,200, 151,200 × 4 = 604,800, 604,800 × 3 = 1,814,400, and × 2 = 3,628,800. The tool returns 3,628,800. That is how many different orders 10 distinct items can be arranged in.

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Common mistakes

  • Entering a decimal such as 4.5. Factorial here is defined for whole numbers only, so there is no result.
  • Expecting 0! to be 0. By definition 0! = 1, which is what makes combination formulas work.
  • Typing a number above 20 and expecting a huge value. Beyond 20 the result no longer fits exactly, so the tool refuses it.
  • Confusing n! with n × 2 or n². Factorial grows far faster: 5! = 120, while 5² = 25.
  • Using n! when order does not matter. For choosing a group from n items you need combinations, which divide factorials by each other.

About this calculator

This tool computes n! (n factorial), the product of every whole number from 1 up to n — for example 5! = 5×4×3×2×1 = 120. It is capped at 20 because 20! is the largest factorial that fits in a 64-bit integer, which keeps every result exact.

Factorials show up constantly in combinatorics: counting how many ways a deck of cards can be arranged, how many ways a race can finish, or computing permutations and combinations for probability problems. Students, and anyone writing code that needs nCr or nPr, use this to check their work by hand.

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