Calculate factorial n! = n×(n-1)×...×2×1, subfactorial !n (derangements), and double factorial n!! with step-by-step solutions.
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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
Essential 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.
Calculate standard factorial, subfactorial, and double factorial
Handles large numbers with proper formatting
Shows step-by-step calculations
Instant results for numbers up to 170
Perfect for probability and statistics
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.
The subfactorial !n counts derangements - permutations where no element appears in its original position. For example, !4 = 9 means there are 9 ways to rearrange 4 items so none stays in place.
Double factorial n!! is the product of all integers from n down to 1 with step 2. So 7!! = 7×5×3×1 = 105, and 6!! = 6×4×2 = 48. It's used in physics and combinatorics.
This calculator computes factorials up to 170!, which is about 7.26 x 10^306 - the largest value before the result exceeds the range of a standard 64-bit floating point number (roughly 1.8 x 10^308). For 171! and beyond the value is displayed in scientific notation once it passes 10^15.