Factorial Calculator: Calculate n! Factorials

Factorial Calculator

The factorial operation (denoted as n!) is fundamental to combinatorics, probability theory, and many areas of mathematics. It tells you how many ways you can arrange n distinct items in sequence.

What is a Factorial?

n! = n × (n-1) × (n-2) × ... × 2 × 1

For example:

• 5! = 5 × 4 × 3 × 2 × 1 = 120


• 3! = 3 × 2 × 1 = 6


• 0! = 1 (by definition)

Applications

Permutations: Arranging items in order. The number of ways to arrange 5 books on a shelf is 5! = 120.

Combinations: Selecting items from a group. Used in probability calculations.

Series Expansions: Taylor series and Maclaurin series use factorials extensively.

Factorial Growth: Factorials grow extremely fast. 10! = 3,628,800 while 20! = 2,432,902,008,176,640,000.

Important Properties

• 0! = 1 (by mathematical convention)


• 1! = 1


• Factorials are only defined for non-negative integers


• The maximum calculable factorial depends on the number system used (typically up to 170! for 64-bit systems)