Factorial Calculator
Calculate the factorial of any non-negative integer. Perfect for mathematics, combinatorics, and probability calculations.
Calculate Factorial
Enter a non-negative integer (0-20):
What is a Factorial?
A factorial is the product of all positive integers less than or equal to a given number. It's denoted by an exclamation mark (!) after the number.
Factorial Formula
For any positive integer n:
n! = n × (n-1) × (n-2) × ... × 2 × 1
Special case:
0! = 1
Examples
| n | Calculation | Result |
|---|---|---|
| 0 | 0! = 1 | 1 |
| 1 | 1! = 1 | 1 |
| 3 | 3! = 3 × 2 × 1 | 6 |
| 5 | 5! = 5 × 4 × 3 × 2 × 1 | 120 |
| 10 | 10! = 10 × 9 × ... × 2 × 1 | 3,628,800 |
Applications of Factorials
- 🔢 Combinatorics: Counting arrangements and selections
- 🎲 Probability: Calculating odds and permutations
- 📊 Statistics: Distribution calculations
- 🔬 Mathematics: Series expansions and special functions
- 💻 Computer Science: Algorithm analysis and complexity
Limitation Note
⚠️ Note: Factorials grow extremely large very quickly. This calculator is limited to n ≤ 20 to prevent overflow. For larger factorials, specialized mathematical software is recommended.
Interesting Facts
- The factorial function grows faster than exponential functions
- Factorials are used in the famous birthday problem
- They appear in Taylor series expansions
- The number 1 appears in every factorial greater than 1