Factorial Calculator – Guide & Formulas
Calculate the factorial of any positive integer (n!) instantly. Explore the multiplication step expansion, scientific notation for large figures, a...
An elegant calculator to find the factorial of any non-negative integer. It outputs the full multiplication sequence, standard integer format, and scientific notation for large factorial solutions.
Key Takeaway
Use the free Factorial Calculator to calculate the factorial of any positive integer (n!) instantly. explore the multiplication step expansion, scientific notation for large figures, a... Get instant results with step-by-step explanations.
How to Use the Factorial Calculator
- Type any non-negative integer in the input field.
- See the instant calculation of n!.
- Review the step-by-step expansion showing all factors.
- Copy the calculation summary to save or share.
The Formula
Variable Definitions
- n: The non-negative integer input
- n!: The factorial product of all integers up to n
Arranging 5 Books on a Shelf
Find the total number of ways to arrange 5 unique books in a row.
- Step 1: Input n = 5.
- Step 2: Calculate 5! = 5 * 4 * 3 * 2 * 1.
- Step 3: The result is 120 unique arrangements.
Frequently Asked Questions
Why is 0! equal to 1?
In mathematics, 0! is defined as 1 to maintain consistency with permutations formulas (e.g. nPr) and other algebraic structures. Conceptually, there is exactly one way to arrange zero objects: the empty arrangement.
What is the limit of the factorial calculator?
To prevent browser lockups, this calculator handles values of n up to 170. Factorials above 170 exceed the maximum safe floating-point values in JavaScript (Infinity).
Is there a formula for non-integer factorials?
Yes. The Gamma function, Γ(z), generalizes factorials to real and complex numbers, where Γ(n) = (n-1)! for positive integers.