Shuffle a deck of cards and you are almost certainly holding an arrangement no human has ever seen — there are 52! of them, a 68-digit number. The factorial n! multiplies every positive integer down to 1: 5! = 5 × 4 × 3 × 2 × 1 = 120. It counts arrangements — the ways to order n distinct items — which makes it the engine of combinatorics: 52! ≈ 8 × 10⁶⁷ possible card shuffles, more than the atoms in the galaxy's stars.

By definition 0! = 1 (there is exactly one way to arrange nothing), a convention that keeps the formulas consistent. Factorials also build the permutation and combination formulas: P(n, r) = n!/(n−r)! counts ordered selections, C(n, r) = n!/(r!(n−r)!) unordered ones — the calculator shows both for r = 2. Growth is ferocious (20! already has 19 digits), so the calculator caps n at 20 to keep results exact. Enter n and get n!, P(n,2), and C(n,2).

With the pre-filled defaults — n 7 — the Factorial Calculator returns n! 5,040, Permutations P(n,2) 42, Combinations C(n,2) 21. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.