Factorial Calculator
The Factorial Calculator helps you quickly find the factorial of any non-negative integer. Factorials, denoted by an exclamation mark (n!), are fundamental in combinatorics, probability, and many areas of mathematics, representing the product of all positive integers less than or equal to n.
Enter a non-negative integer.
The Factorial Calculator helps you quickly find the factorial of any non-negative integer. Factorials, denoted by an exclamation mark (n!), are fundamental in combinatorics, probability, and many areas of mathematics, representing the product of all positive integers less than or equal to n.
n! = n × (n-1) × (n-2) ×. × 2 × 1 Special case: 0! = 1
To find 5!, you multiply all positive integers from 1 up to 5: 5! = 5 × 4 × 3 × 2 × 1 = 120
A factorial, denoted by n! (read as 'n factorial'), is the product of all positive integers less than or equal to n. For example, 4! = 4 × 3 × 2 × 1 = 24. The special case 0! is defined as 1.
The definition of 0! = 1 is crucial for mathematical consistency, especially in formulas for permutations and combinations. It allows these formulas to work correctly when n=0 or r=0, preventing division by zero and maintaining patterns in sequences.
Factorials are widely used in probability and combinatorics to count the number of ways things can be arranged or selected. For example, calculating the number of ways to arrange a deck of cards, the number of possible orders for a race, or the number of unique passwords of a certain length.
© 2025-2026 PromathTools. All rights reserved.
Built by KruskalCode – SaaS & Automation Experts
