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Factorial Calculator
Calculate factorial (n!) of any number with detailed steps
Enter a number between 0 and 170
How Factorial Calculation Works
Factorial (n!) is the product of all positive integers less than or equal to n. It's a fundamental concept in mathematics, particularly in combinatorics and probability.
Enter any non-negative integer between 0 and 170
Click "Calculate Factorial" to compute the result
View the step-by-step multiplication process
Copy the result for use in other applications
Factorial Formula:
n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
0! = 1 (by mathematical definition)
1! = 1
Factorial grows very rapidly with larger numbers
Common Examples:
5! = 5 × 4 × 3 × 2 × 1 = 120
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
10! = 10 × 9 × ... × 2 × 1 = 3,628,800
0! = 1 (special case)
Real-World Applications:
Combinatorics: Counting permutations and combinations
Probability: Calculating probabilities in complex scenarios
Statistics: Arrangements and sampling methods
Computer Science: Algorithm analysis and complexity
Mathematics: Taylor series and mathematical analysis
Technical Notes:
Maximum input is 170 due to computational limits
Uses BigInt for precise large number calculations
Factorial growth is exponential (faster than exponential)
Results are displayed with proper formatting for large numbers