Factorial Calculator
Calculate factorials, double factorials, and subfactorials with step-by-step solutions. Perfect for students, teachers, and professionals working with combinatorial mathematics.
Factorial Calculator
Calculate factorials, double factorials, and subfactorials with step-by-step solutions
Enter Values
Maximum value: 170 (for standard factorial)
About Factorials
• Standard: n! = n × (n-1) × (n-2) × ... × 2 × 1
• Double: n!! = n × (n-2) × (n-4) × ... (until 1 or 2)
• Subfactorial: !n = number of derangements
• Special: 0! = 1 (by definition)
Common Factorial Values
Factorial Applications
Understanding Factorials
Factorials are fundamental mathematical functions that represent the product of all positive integers from 1 to a given number. They appear extensively in combinatorics, probability theory, and many other areas of mathematics.
Our calculator supports three types of factorial calculations:
- Standard Factorial (n!): The product of all positive integers from 1 to n
- Double Factorial (n!!): The product of every other number from n down to 1 or 2
- Subfactorial (!n): The number of derangements (permutations with no fixed points)
Factorials grow extremely rapidly, which is why we limit calculations to reasonable values to maintain accuracy and performance.
How to Use This Calculator
Real-World Applications
Probability & Statistics
Factorials are essential for calculating permutations, combinations, and probability distributions in statistical analysis.
Combinatorics
Used to count the number of ways to arrange objects, solve counting problems, and analyze discrete structures.
Computer Science
Important for algorithm analysis, complexity theory, and understanding computational efficiency.