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
Enter a non-negative integer
Select the factorial type (standard, subfactorial, or double)
View the result instantly
See the step-by-step calculation
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.
Why Use This Calculator
Three Factorial Types
Calculate standard factorial, subfactorial, and double factorial
Large Number Handling
Handles large numbers with proper formatting
Step-by-Step Work
Shows step-by-step calculations
Instant Results
Instant results for numbers up to 170
Probability Ready
Perfect for probability and statistics
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.
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.