Factorial Calculator

Free Online Factorial Calculator with Step-by-Step Solutions

Understanding Factorials

Definition & Properties

A factorial (n!) is the product of all positive integers up to n.

n! = n × (n-1) × (n-2) × ... × 2 × 1

Special Cases:

  • 0! = 1 (by definition)
  • 1! = 1
  • Negative numbers: undefined
  • Non-integers: calculated via Gamma function

Common Applications

  • Probability & Statistics
  • Combinations (nCr)
  • Permutations (nPr)
  • Sequence Analysis
  • Algorithm Complexity
  • Number Theory

Example Calculations

3! = 3 × 2 × 1 = 6
4! = 4 × 3 × 2 × 1 = 24
5! = 5 × 4 × 3 × 2 × 1 = 120