Calculate factorial n! = n×(n-1)×...×2×1, subfactorial !n (derangements), and double factorial n!! with step-by-step solutions.
You might also find these calculators useful
Calculate permutations P(n,r) with or without repetition
Calculate combinations C(n,r) with or without repetition
Calculate probability, permutations, and combinations
Calculate percentages, percentage change, 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.
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 × 1Essential for calculating P(n,r) and C(n,r) formulas.
Calculate arrangements and selections in probability problems.
Factorials appear in denominators of Taylor/Maclaurin expansions.
Use subfactorial for 'hat check' and similar problems.
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.