Math

Factorial Calculator

What this does

Compute n! for any whole number from 0 to 170, with digit counts and scientific magnitude shown for the huge results.

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Runs in your browser

Calculator inputs

How to use it

Using the factorial calculator

  1. 01

    Enter a whole number

    Between 0 and 170 inclusive.

  2. 02

    Read the factorial

    The full product appears grouped with thousands separators.

  3. 03

    Check magnitude rows

    Digit count and power-of-ten size help compare enormous results at a glance.

Good to know

How fast factorials explode

A deck of cards can be shuffled 52! ≈ 8×10⁶⁷ ways; more than atoms in the galaxy. Ten items already offer 3.6 million orderings, which is why brute-force search dies quickly and combinatorics needs smarter tools.

Why 0! equals 1

The empty product is conventionally 1: there is exactly one way to arrange zero objects. This convention keeps permutation formulas like nPr = n!/(n−r)! working cleanly at the boundaries instead of special-casing them.

The 170 ceiling

Computers store numbers as floating-point values capped near 1.8×10³⁰⁸. Since 171! overflows that envelope, the calculator refuses rather than returning Infinity; honest failure beats silent nonsense.

How it's calculated

The math behind this calculator

n! = n × (n−1) × … × 2 × 1 with 0! = 1 by definition

Direct iterative multiplication computes the product exactly as doubles allow. JavaScript numbers overflow past 170! (about 7.3×10³⁰⁶), so that ceiling is enforced with a clear message; negative and non-integer inputs are rejected because the factorial is only defined on whole numbers.

Assumptions & limitations

  • Only whole numbers 0 through 170 are accepted.
  • Results beyond about 21 digits carry double-precision rounding in their trailing digits.
  • 0! equals 1 by mathematical convention.

Worked example

5! = 5 × 4 × 3 × 2 × 1 = 120; the number of ways to arrange five distinct items in order.

FAQ

Frequently asked questions

Why does 171 fail?
It exceeds the largest value a double-precision float can hold (~1.8×10³⁰⁸); 170! is the last representable factorial.
Can I compute 4.5 factorial?
No; plain factorials need whole numbers. The generalized gamma function extends the idea, but it is outside this tool’s scope.
Is 0! really 1?
Yes, by definition of the empty product; it keeps counting formulas consistent at zero items.
Are the huge results exact?
Up to roughly 20! yes; larger products keep about fifteen significant digits, so trailing digits may round.

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