Factorial Calculator
Calculate factorial n! = n×(n-1)×...×2×1, subfactorial !n (derangements), and double factorial n!! with step-by-step solutions.
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Factorial Calculator - Calculate n! and More
Calculate factorials instantly with our comprehensive calculator. Find n! (factorial), !n (subfactorial/derangements), and n!! (double factorial) with detailed step-by-step solutions. Perfect for combinatorics and probability.
What is a Factorial?
A factorial n! is the product of all positive integers up to n. For example, 5! = 5×4×3×2×1 = 120. Factorials are fundamental in combinatorics, probability, and calculus. Special variations include subfactorial !n (number of derangements) and double factorial n!! (product of integers with same parity).
Factorial Formula
n! = n × (n-1) × (n-2) × ... × 2 × 1How to Use This Calculator
Factorial Calculator Applications
Permutations & Combinations
Essential for calculating P(n,r) and C(n,r) formulas.
Probability Theory
Calculate arrangements and selections in probability problems.
Taylor Series
Factorials appear in denominators of Taylor/Maclaurin expansions.
Derangement Problems
Use subfactorial for 'hat check' and similar problems.
Frequently Asked Questions
By definition, 0! = 1. This is not arbitrary - it's required for many mathematical formulas to work correctly, including the binomial coefficient formula C(n,0) = n!/0!n! = 1.