Factorial Calculator
Result
120
Result
Add this free factorial calculator to your website or blog.
This is defined this way because it makes mathematical formulas work. The number of ways to arrange 0 items is 1 (do nothing). It's also necessary for the binomial theorem and other formulas to work correctly.
Factorials increase incredibly quickly. 10! = 3,628,800. 20! = 2,432,902,008,176,640,000. By 70!, you're already past the number of atoms in the universe!
If you have 5 books, there are 5! = 120 different ways to arrange them on a shelf. In general, n items can be arranged in n! ways.
The most common error. Remember: 0! = 1, not 0. It's a special definition that makes math work cleanly.
5! ≠ 5^5. Factorial means 5×4×3×2×1 = 120. Exponent means 5×5×5×5×5 = 3,125. Very different!
Factorials are only defined for non-negative integers. (-5)! is undefined.