Factorial Calculator n! – Steps & Big Numbers

A factorial counts ordered arrangements, so it multiplies every whole number from n down to 1: 5! = 5×4×3×2×1 = 120, the number of ways to order five books on a shelf. The value explodes fast — 10! = 3,628,800 and 20! = 2,432,902,008,176,640,000. Zero factorial is defined as 0! = 1 so that formulas like C(n,r) = n!/(r!(n-r)!) stay valid at the boundaries. This calculator lists each partial product (5, 20, 60, 120) so the growth is visible, and it switches to scientific notation for large n. Standard floating-point doubles overflow beyond 170! ≈ 7.26×10³⁰⁶, the hard ceiling for everyday tools; the calculator warns when you approach it and explains the exact-math alternative.

1. 1

   Enter n

   Type a non-negative integer such as 5 or 20

2. 2

   Chain the multiplications

   Multiply n × (n−1) × … × 1, printing each partial product

3. 3

   Handle 0 and 1

   Both return 1: 0! = 1 by definition and 1! = 1

4. 4

   Format large results

   Switch to scientific notation past 20! and warn near the 170! limit

• 1

  0! = 1, not 0 — the empty product convention

• 2

  Factorials outrun exponentials: 20! ≈ 2.43×10¹⁸ but 20³ is only 8,000

• 3

  Doubles stop at 170!; beyond that use logs or big-integer math

• Assuming 0! = 0 instead of the defined value 1

• Believing (n+1)! is roughly n! + n; actually (n+1)! = (n+1)×n!, so 6! = 6×120 = 720

• Applying factorial to non-integers without the gamma function

• Trusting calculator displays past 170! where doubles overflow to infinity