Factorial Calculator
Counting Every Possible Arrangement
The factorial of a number counts how many distinct ways a full set of items can be ordered — five books on a shelf can be arranged in 120 different sequences, and that number is 5!. Factorials grow explosively fast: 10! is already over three and a half million, and 170! is the largest factorial that fits in a standard double-precision float before overflowing, which is why this calculator caps input at that value.
The Formula
By definition, 0! = 1 (there's exactly one way to arrange zero items: do nothing). Factorials are only defined for non-negative whole numbers.
Where Factorials Are Used
- Permutations and combinations — both formulas are built directly from factorials.
- Probability — counting the number of possible outcomes in card games, lotteries, and arrangement problems.
- Series expansions — Taylor series in calculus divide each term by a factorial.
- Scheduling problems — the number of ways to order a sequence of tasks or events.
| n | n! |
|---|---|
| 0 | 1 |
| 5 | 120 |
| 10 | 3,628,800 |
| 20 | 2,432,902,008,176,640,000 |
The jump from 10! to 20! illustrates why factorial growth is described as faster than exponential — each additional term multiplies by a larger number than the one before it.
How to Use This Calculator
- Enter a whole number between 0 and 170 in the Number field.
- Select Calculate to see the factorial, formatted with thousands separators.
Related Calculations
Factorials feed directly into arrangement counting — see the Permutation Calculator for ordered selections and the Combination Calculator for unordered ones.