Factorial Calculator
Calculate the factorial of any number from 0 to 170. See the full step-by-step expansion and the number of digits in the result.
How to Calculate a Factorial
- Enter a non-negative integer between 0 and 170 in the input field.
- Click Calculate to compute n! instantly.
- View the full expansion showing each multiplication step.
- Check the digit count to understand the magnitude of the result.
クイックリファレンス
| 変換元 | 変換先 |
|---|---|
| 3! | 6 |
| 5! | 120 |
| 7! | 5,040 |
| 10! | 3,628,800 |
| 12! | 479,001,600 |
| 0! | 1 |
使用例
- •Combinatorics — calculate 10! = 3628800 to find the number of ways to arrange 10 items.
- •Probability — use 52! to determine the number of possible shuffles of a standard card deck.
- •Calculus — compute Taylor series coefficients that involve n! in the denominator.
計算式
n! = n × (n−1) × (n−2) × ... × 2 × 1. By definition, 0! = 1. Factorials grow extremely fast: 20! already exceeds 2.4 × 10¹⁸.
よくある質問
Why does 0! equal 1?
By convention 0! = 1. This makes many formulas (such as combinations and the binomial theorem) work consistently. It also represents the fact that there is exactly one way to arrange zero objects.
Why is there a limit of 170?
170! ≈ 7.26 × 10³⁰⁶ is the largest factorial that fits in a standard 64-bit floating-point number. Beyond that, the value exceeds the representable range (Infinity). The calculator uses BigInt for exact integer results above 20!.
What are factorials used for?
Factorials are fundamental in combinatorics (permutations, combinations), probability, Taylor series in calculus, and many areas of discrete mathematics.