Factorial Calculator
Calculate factorials (n!) with detailed step-by-step solutions and explanations for any non-negative integer.
Enter Number
• Enter integers from 0 to 170
• Factorials grow very quickly!
Result
Enter a non-negative integer to calculate its factorial
Factorial Formula
n! = n × (n-1) × (n-2) × ... × 2 × 1
where n ≥ 0
Special case: 0! = 1
Examples
Small Factorials
0! = 1
1! = 1
2! = 2 × 1 = 2
3! = 3 × 2 × 1 = 6
4! = 4 × 3 × 2 × 1 = 24
5! = 5 × 4 × 3 × 2 × 1 = 120
Larger Factorials
6! = 720
7! = 5,040
8! = 40,320
9! = 362,880
10! = 3,628,800
15! ≈ 1.31 × 10¹²
Applications
Permutations
The number of ways to arrange n objects is n!
Combinations
Used in the formula C(n,r) = n! / (r!(n-r)!)
Probability
Calculating probabilities in various scenarios
Calculus
Taylor series expansions and other mathematical series
Frequently Asked Questions
A factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.