Factorial Calculator: n! Exact, Digits & Trailing Zeros

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Formula at a glance

Factorial Calculator: Factorial — n! = n × (n − 1) × … × 2 × 1, 0! = 1. Example: 20! → 20!: 2,432,902,008,176,640,000 — How the Factorial Calculator works: Factorial — n! = n × (n − 1) × … × 2 × 1, 0! = 1

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📘 About the Factorial Calculator

The factorial n! multiplies all whole numbers from 1 to n: 5! = 120. It counts the ways to arrange n different objects and appears in permutations and combinations, probability, and the Taylor series of eˣ and sin x. Factorials grow astonishingly fast — 70! is more than 10¹⁰⁰.

Enter n. The calculator gives the exact value with big-number arithmetic, the number of digits, trailing zeros (from factors of 5) and Stirling’s approximation. Double factorials multiply every second number, and non-whole numbers use the gamma function (0.5! = √π/2).

🧮 Formula

Factorial

n! = n × (n − 1) × … × 2 × 1, 0! = 1

Trailing zeros

⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …

Stirling

n! ≈ √(2πn)·(n/e)ⁿ

✏️ Worked examples

20!

You enter
n	20
Type	Factorial n!

You get
20!	2,432,902,008,176,640,000
Number of digits	19
Trailing zeros	4
Stirling’s approximation	2.4227868 × 10^18

2,432,902,008,176,640,000.

100!

You enter
n	100
Type	Factorial n!

You get
100!	9.332621544 × 10^157 (158 digits)
Number of digits	158
Trailing zeros	24
Stirling’s approximation	9.3248476 × 10^157

9.332621544 × 10^157 (158 digits).

🧭 How to use this calculator

What you enter

n
Type

What you get

20!
Number of digits
Trailing zeros
Stirling’s approximation

❓ Frequently asked questions

Why is 0! equal to 1?

There is exactly one way to arrange nothing, and it keeps formulas like n! = n × (n − 1)! and nC0 = 1 consistent.

How many zeros are at the end of 100!?

24 — from ⌊100/5⌋ + ⌊100/25⌋ = 20 + 4.

Can you take the factorial of a decimal?

Yes, through the gamma function: x! = Γ(x + 1). For example 0.5! ≈ 0.8862.

n! Factorial Calculator (n!)