Factorial Calculator

Calculate factorials (n!) with step-by-step solutions, factorial properties, and real-world applications

✓ Large number support ✓ Step-by-step breakdown ✓ Growth visualization

Calculate Factorial

!

Enter a non-negative integer (0 ≤ n ≤ 170)

Common Factorials

0! 1
1! 1
2! 2
3! 6
4! 24
5! 120
6! 720
7! 5,040
8! 40,320
10! 3,628,800

Factorial Properties

0! = 1 (by definition)
n! = n × (n-1)!
n! = n × (n-1) × ... × 2 × 1
Factorial grows very rapidly
Used in permutations & combinations

Applications

Permutations
Arranging n objects: n!
Combinations
C(n,r) = n!/(r!(n-r)!)
Probability
Calculating event probabilities
Series
Taylor series expansions
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Understanding Factorials

A factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

Definition

n! = n × (n-1) × (n-2) × ... × 2 × 1

Special Cases

  • 0! = 1 (by mathematical convention)
  • 1! = 1
  • Factorial is undefined for negative numbers

Real-World Applications

Combinatorics

Counting arrangements, permutations, and combinations in mathematics and computer science.

Probability Theory

Calculating probabilities in games, statistics, and risk analysis.

Computer Science

Algorithm analysis, recursive functions, and computational complexity.

Physics & Chemistry

Statistical mechanics, quantum mechanics, and molecular arrangements.