Factorial Calculator (n!)

How it works

The factorial n! multiplies every whole number from n down to 1: 5! = 5×4×3×2×1 = 120. Its natural meaning is counting arrangements — 5! is the number of ways to order 5 distinct objects, which is why factorials sit inside every permutation and combination formula. By convention 0! = 1: there is exactly one way to arrange nothing (the empty arrangement), and the convention keeps formulas like C(n,k) consistent at the edges. Factorials outgrow everything. 10! is 3.6 million; 20! passes 2 quintillion; 170! ≈ 7.3×10³⁰⁶ is the last one a computer's standard floating-point numbers can hold, which is why this calculator stops there. Beyond counting, factorials appear in probability, Taylor series and the mathematics of e.