Factorial (n!) is the product of all positive integers from 1 to n. 5! = 5×4×3×2×1 = 120. 0! = 1 by definition. Factorials grow extremely fast: 10! = 3,628,800, 20! ≈ 2.4×10¹⁸. Used in permutations, combinations, and probability.

Where are factorials used?

Factorials calculate: permutations (n! arrangements of n items), combinations (n!/(r!(n-r)!) ways to choose r from n), probability, Taylor series in calculus, and counting problems. "How many ways can 5 people line up?" = 5! = 120.

How do I calculate factorial of large numbers?

Large factorials exceed normal number storage. 100! has 158 digits. Use arbitrary-precision libraries or Stirling's approximation: n! ≈ √(2πn)(n/e)^n. Our calculator handles large factorials precisely using BigInt arithmetic.

What is double factorial?

Double factorial (n!!) multiplies every other number: 7!! = 7×5×3×1 = 105, 8!! = 8×6×4×2 = 384. Not the same as (n!)! which would be factorial of factorial. Used in certain physics and combinatorics formulas.

Why is 0! equal to 1?

0! = 1 by convention, and it makes formulas work correctly. The empty product (multiplying zero numbers) equals 1. Also, n! = n × (n-1)! implies 1! = 1 × 0!, so 0! = 1. Combinatorially, there is exactly 1 way to arrange 0 items: do nothing.

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Factorial Calculator

Factorial (n!) is the product of all positive integers up to n. 5! = 5×4×3×2×1 = 120. 0! = 1 by definition. Used in permutations (n! arrangements) and combinations. Factorials grow extremely fast: 10! = 3,628,800.

Calculate factorials, double factorials, permutations, and combinations. Supports large numbers with BigInt.

Enter n

Quick Reference

5!	= 120
10!	= 3,628,800
20!	= 2.43 × 10¹⁸
100!	≈ 9.33 × 10¹⁵⁷ (158 digits)

Formulas

n! = n × (n-1) × (n-2) × ... × 1
n!! = n × (n-2) × (n-4) × ...
P(n,r) = n! / (n-r)!
C(n,r) = n! / (r! × (n-r)!)

How to Use

Enter your value in the input field
Click the Calculate/Convert button
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Frequently Asked Questions

What is a factorial?: Factorial (n!) is the product of all positive integers from 1 to n. 5! = 5×4×3×2×1 = 120. 0! = 1 by definition. Factorials grow extremely fast: 10! = 3,628,800, 20! ≈ 2.4×10¹⁸. Used in permutations, combinations, and probability.
Where are factorials used?: Factorials calculate: permutations (n! arrangements of n items), combinations (n!/(r!(n-r)!) ways to choose r from n), probability, Taylor series in calculus, and counting problems. "How many ways can 5 people line up?" = 5! = 120.
How do I calculate factorial of large numbers?: Large factorials exceed normal number storage. 100! has 158 digits. Use arbitrary-precision libraries or Stirling's approximation: n! ≈ √(2πn)(n/e)^n. Our calculator handles large factorials precisely using BigInt arithmetic.
What is double factorial?: Double factorial (n!!) multiplies every other number: 7!! = 7×5×3×1 = 105, 8!! = 8×6×4×2 = 384. Not the same as (n!)! which would be factorial of factorial. Used in certain physics and combinatorics formulas.
Why is 0! equal to 1?: 0! = 1 by convention, and it makes formulas work correctly. The empty product (multiplying zero numbers) equals 1. Also, n! = n × (n-1)! implies 1! = 1 × 0!, so 0! = 1. Combinatorially, there is exactly 1 way to arrange 0 items: do nothing.