Factorial Calculator
The factorial (n!) of a whole number.
Input sheet
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A factorial multiplies every whole number from 1 up to n, and it explodes in size astonishingly fast. Factorials are the backbone of permutations, combinations, and probability.
How it works
n! multiplies every whole number from 1 to n. Values above 170! overflow double precision.
n! counts the number of ways to arrange n distinct items in order — 5! = 120 orderings of five books on a shelf. By definition 0! equals 1, the single way to arrange nothing.
Growth is extreme: 10! already exceeds three million, and standard double-precision arithmetic loses exactness beyond about 170!, which is why this tool caps the input there.
n! = n × (n−1) × (n−2) × … × 2 × 1
Worked examples
Computing 10!. → 3,628,800
10 × 9 × 8 × … × 1 = 3,628,800 — the number of ways to order ten items.
Computing 5!. → 120
5 × 4 × 3 × 2 × 1 = 120.
Tips & gotchas
- By convention 0! = 1, which keeps the permutation and combination formulas consistent.
- Factorials only apply to non-negative whole numbers; fractions use the related gamma function instead.
- Because the values grow so fast, even modest n quickly exceeds what fits in ordinary numeric precision.
FAQ
Why is 0! equal to 1?
There is exactly one way to arrange an empty set — do nothing. Defining 0! as 1 also makes the combination formula nCr work when r equals 0 or n.
Can I take the factorial of a negative or decimal number?
Not with the ordinary factorial. The gamma function extends the idea to those values, but the plain factorial is for non-negative integers only.
Why does this tool stop at 170!?
171! exceeds the maximum value a standard double-precision number can hold, so results beyond 170! would overflow to infinity.
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