The rule
n! = n × (n−1) × … × 2 × 1
Why it works
The factorial multiplies every whole number from 1 up to n. It counts the number of ways to arrange n distinct objects in order, which is why it sits underneath almost all of combinatorics.
How to do it by hand
- Multiply every whole number from 1 up to n
- Equivalently, multiply n by the previous factorial
- 0! is 1 by definition
- The result grows faster than any exponential
What is worth knowing
Factorials grow at a genuinely startling rate: 20! is already larger than 2⁶⁰, and 70! exceeds what a double-precision float can hold, which is why this calculator uses exact big-integer arithmetic. Above 21! a floating-point result is not merely rounded but wrong in its final digits, and quietly so. The convention that 0! = 1 is not arbitrary either: there is exactly one way to arrange nothing, and defining it that way is what makes the formula for combinations work at the edges.