Factorial Calculator
Compute n! exactly with full big-integer digits for any n up to 5000.
Factorial Calculator
Compute n! exactly with full big-integer digits for any n up to 5000.
How to use the Factorial Calculator
- Enter a non-negative whole number.
- Click Calculate.
Formula
n! = n × (n−1) × (n−2) × ... × 2 × 1
0! = 1 (by convention)
Example
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
Step-by-step calculation
- Multiply sequentially: 1×2=2, ×3=6, ×4=24, ×5=120, ×6=720, ×7=5040, ×8=40320, ×9=362880, ×10=3628800.
- Result: 3,628,800.
Real-world uses
- Permutation and combination calculations.
- Probability theory.
- Series expansion coefficients.
Common mistakes
- Entering negative numbers (factorial is not defined for negatives).
- Confusing n! with n × 2 (factorial is not doubling).
- Forgetting 0! = 1.
Frequently asked questions
Why is 0! = 1?
By mathematical convention, it ensures formulas like C(n,0) = 1 and recursion n! = n × (n−1)! work correctly.
How big does n! get?
Very large. 20! ≈ 2.4 × 10¹⁸. 100! has 158 digits.
What is the maximum n?
5,000. The result has 16,326 digits.