Factorial Calculator

Compute n! for whole numbers, with exact results for large values.

What the Factorial Calculator does

The factorial of n is the product of every whole number from 1 to n. It counts the number of ways to arrange n distinct items, which makes it the backbone of permutations and combinations.

Formula

  • n! = n × (n−1) × (n−2) × … × 2 × 1
  • 0! = 1 by definition

Inputs explained

InputUnitRequiredNotes
nnumberYesAccepts 0 or more, up to 2000.

How to use it

  1. Enter n.
  2. Select Calculate.

Worked example

How many ways can 5 books be arranged on a shelf?

n
5

5! = 5 × 4 × 3 × 2 × 1 = 120 arrangements.

Frequently asked questions

Why is 0! equal to 1?

There is exactly one way to arrange nothing — the empty arrangement. Defining 0! as 1 also keeps the combination formula consistent.

Can I take the factorial of a decimal?

Not with this calculator. Fractional factorials require the gamma function, where n! = Γ(n+1).

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