Factorial Calculator
Enter a whole number below to instantly get its factorial.
What Is a Factorial?
n! multiplies every whole number from n down to 1. It grows extremely fast — factorials are the reason the combination and permutation calculator works the way it does.
Factorials grow far faster than exponential functions do. 5! is only 120, but 10! is already 3,628,800, and 15! is over a trillion (1,307,674,368,000) — this explosive growth is why factorial-based combinatorics problems can spiral to enormous numbers almost immediately, even for modest inputs.
Worked example
Calculate 6!.
6 × 5 × 4 × 3 × 2 × 1 = 720
6! = 720
A second example, the edge case: what is 0!?
There's nothing to multiply, so the recursive pattern doesn't directly apply — 0! is defined as 1 by convention, which keeps formulas like the combination formula consistent at their edges.
0! = 1
Common mistake
A common mistake is stopping the multiplication too early — thinking 5! means just 5 × 4 = 20. It doesn't. The chain continues all the way down to 1: 5! = 5 × 4 × 3 × 2 × 1 = 120.
Keep going
- Factorials are the building block of nCr and nPr; the combination calculator uses factorials under the hood to count arrangements and groupings. Combination Calculator
Frequently Asked Questions
What is a factorial?
A factorial, written n!, is the product of every whole number from n down to 1. 5! = 5 × 4 × 3 × 2 × 1 = 120.
What is 0! equal to?
0! is defined as 1, not 0. This isn't arbitrary — it makes formulas like the combination formula work correctly for edge cases, such as choosing 0 items from a set.
What is a factorial used for?
Factorials count the number of ways to arrange a set of items in order, and they're the building block behind the combination and permutation formulas.
How fast do factorials grow?
Extremely fast. 5! is 120, 10! is 3,628,800, and 20! is over 2.4 × 10¹⁸ — already larger than the number of seconds since the Big Bang (roughly 4.35 × 10¹⁷). That explosive growth is why factorials are only practical to compute directly for fairly small n.
Is 4! the same as 4²?
No, they're easy to mix up but very different. 4! = 4 × 3 × 2 × 1 = 24, while 4² = 4 × 4 = 16. A factorial multiplies a descending chain of whole numbers; an exponent multiplies the same number by itself.
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