Factorial & Combinatorics
Calculate factorials, permutations P(n,r), and combinations C(n,r).
10! =
3628800
7 digits
First 20 factorials:
0!
1
1!
1
2!
2
3!
6
4!
24
5!
120
6!
720
7!
5040
8!
40320
9!
362880
10!
3628800
11!
39916800
12!
479001600
13!
6227020800
14!
87178291200
15!
1307674368000
16!
20922789888000
17!
355687428096000
18!
6402373705728000
19!
121645100408832000
About This Tool
The Factorial Calculator computes n!, permutations P(n,r), and combinations C(n,r) using BigInt arithmetic for exact results. Supports n up to 170.
A factorial is the product of all positive integers from 1 to n. Permutations count ordered selections; combinations count unordered selections.
How to Use
- Select a mode tab: Factorial, Permutations, or Combinations.
- Enter the value of n (0–170).
- For permutations and combinations, also enter r.
- The result updates instantly.
Use Cases
Used in probability calculations, counting problems, algorithm complexity analysis, and mathematics education.
FAQ
- What is the maximum n? — Up to 170. 171! is astronomically large and impractical for most purposes.
- What is the difference between permutations and combinations? — Permutations P(n,r) count ordered selections (e.g., 1st–3rd place). Combinations C(n,r) count unordered selections (e.g., choosing 3 representatives).