Factorial Calculator

Factorial Calculator - Multi-Tools

Factorial Calculator

Note: Maximum input is 170 due to JavaScript number limitations

Result

How to Use

  1. Enter a non-negative integer (0 to 170)
  2. Click "Calculate Factorial" to see the result
  3. The calculator will show the factorial value and calculation steps

What is a Factorial?

The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted by n! and calculated as:

n! = n × (n-1) × (n-2) × ... × 2 × 1

Example: 5! = 5 × 4 × 3 × 2 × 1 = 120

Special case: 0! = 1

Properties of Factorials

Property Description Example
Definition Product of all positive integers up to n 4! = 4 × 3 × 2 × 1 = 24
Zero Factorial 0! is defined as 1 0! = 1
Recursive Definition n! = n × (n-1)! 5! = 5 × 4!

Applications

  • Permutations and combinations
  • Probability calculations
  • Taylor series expansions
  • Combinatorial problems
  • Statistical analysis
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