Overview
The factorial n! counts the ways to arrange n distinct items and appears in combinations, probability and Taylor series. Factorials grow extremely quickly, so the calculator provides the digit count, trailing zeros and scientific notation alongside the value itself. It supports n up to 170 within ordinary floating-point limits.
Formula
n! = ∏(k = 1 to n) k, and 0! = 1.
How it works
Enter n
A nonnegative whole number up to 170.
Multiply the integers
The calculator evaluates 1 × 2 × … × n.
Read the properties
The value, digit count and trailing zeros appear.
Check scientific notation
Useful for very large results.
Worked examples
Example 1: 5!
5! = 120, with 3 digits and one trailing zero.
Example 2: 10!
10! = 3,628,800, with two trailing zeros.
Frequently asked questions
Why is 0! equal to 1?
There is exactly one way to arrange an empty set, and this definition keeps combination formulas consistent.
How are trailing zeros counted?
By adding ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …, since each pair 2×5 creates a trailing zero.
Why is the limit 170?
Because 171! exceeds the largest finite floating-point value and would be represented as infinity.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.