Factorial Calculator
Calculate the factorial ($n!$) of any non-negative integer. Factorials are fundamental in counting arrangements and determining probabilities.
Result ($n!$)
0
What is a Factorial?
A Factorial (denoted by an exclamation mark "$!$") is the product of all positive integers from 1 up to a given number $n$. For example, $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. Factorials grow extremely fast—while $10!$ is over 3 million, $20!$ is already in the quintillions!
Frequently Asked Questions
Why is $0!$ equal to 1? +
In mathematics, $0!$ is defined as 1 to keep formulas consistent, especially in combinations and permutations. It represents the idea that there is exactly one way to arrange zero items: by doing nothing.
How are factorials used in real life? +
They are used to find the number of ways to arrange objects. If you have 6 books, there are $6!$ (720) different ways to arrange them on a shelf. They are also vital in statistics and calculus.
What is the limit of this calculator? +
This tool calculates up to $170!$. Beyond that, the result becomes larger than "Number.MAX_VALUE" in JavaScript and is represented as "Infinity."
What are Permutations and Combinations? +
These are methods of counting that rely on factorials. Permutations are for when the order matters, and Combinations are for when the order does not matter.
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