📐 Factorial Calculator
Calculate factorial n!
n!
Enter a non-negative integer (0-170)
How to Use This Calculator
Enter n
Type a non-negative integer (0, 1, 2, 3, ...).
Click Calculate
See the factorial result and additional information.
Formula
n! = n × (n-1) × (n-2) × ... × 2 × 1
Special cases: 0! = 1, 1! = 1
Example 1: Calculate 5!
5! = 5 × 4 × 3 × 2 × 1
5! = 120
Example 2: Calculate 7!
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
7! = 5,040
Example 3: Calculate 0!
0! = 1 (by definition)
About Factorial Calculator
The Factorial Calculator computes n! (n factorial), which is the product of all positive integers from 1 to n. Factorials grow very rapidly and are used extensively in combinatorics, probability, and permutation calculations.
When to Use This Calculator
- Combinatorics: Calculate permutations and combinations
- Probability: Count arrangements and orderings
- Statistics: Binomial coefficients and distributions
- Series: Taylor series and approximations
Why Use Our Calculator?
- ✅ Fast Calculation: Instant results
- ✅ Large Numbers: Handles up to 170!
- ✅ Multiple Formats: Standard and scientific notation
- ✅ Free Tool: No registration
Important Facts
- 0! = 1 (by definition)
- n! grows very fast: 10! = 3,628,800, 20! ≈ 2.43 × 10¹⁸
- Factorials are only defined for non-negative integers
- Used in permutation formula: P(n,k) = n!/(n-k)!
Frequently Asked Questions
Why is 0! = 1?
By definition, 0! = 1. This makes formulas work consistently and ensures n!/n = (n-1)!.
What is the largest factorial I can calculate?
This calculator handles up to 170! accurately. Larger values exceed JavaScript's number limits.
Can I calculate factorial for negative numbers?
No, factorial is only defined for non-negative integers. For negative numbers or decimals, use the Gamma function.