The factorial n!
About this calculator
The factorial n! is the product of every positive integer up to n. It appears wherever you count arrangements — password permutations, deck shuffles, and the n! terms in Taylor series.
Enter n and the calculator multiplies 1 through n. Zero factorial returns 1 by convention, which keeps combinatorics formulas consistent.
Values beyond 170 exceed IEEE double range; the tool warns when that happens. For choosing r items from n without caring about order, use the [[permutation-combination]] calculator. For Pascal row entries try the [[pascals-triangle]] calculator. For large products use the [[big-number]] calculator.
Common uses
- Compute n! for probability homework
- Verify permutation formulas manually
- Explore how fast factorials grow
- Check 0! and small n values quickly
Frequently asked questions
What is 10!?
3,628,800. That is 1 × 2 × … × 10 — the number of ways to order 10 distinct objects.
Why is 0! equal to 1?
There is exactly one way to arrange zero objects — the empty arrangement. Defining 0! = 1 keeps C(n,0) = n!/0!/(n−0)! = 1.
Can factorials be negative?
No. Factorial is defined only for non-negative integers. Fractions and negatives have generalized gamma extensions, but n! for negative integers is undefined here.
How is factorial related to permutations?
n! counts ordered arrangements of n distinct items. Choosing r from n without order divides by r! — see the permutation-combination calculator.