Free online factorial calculator. Instantly calculate large factorials (n!) up to 170. Features scientific notation and interactive sliders.
Calculate factorials (n!) instantly with our frictionless slider. Perfect for combinatorics, probability, and advanced mathematics. This free online tool allows you to calculate factorials quickly and accurately. No sign-up or installation required.
What is a Factorial?
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.
For example, the value of 5! is: 5 × 4 × 3 × 2 × 1 = 120.
Why are Factorials Important?
Factorials are fundamental in combinatorics, which is the study of counting, arrangement, and permutation.
- Permutations: If you have 5 different books and want to arrange them on a shelf, there are exactly 5! (120) different ways to organize them.
- Combinations: Factorials are used in the binomial coefficient formula, which determines how many ways you can select a subset of items from a larger set.
- Calculus: Taylor series and Maclaurin series rely heavily on factorials to estimate complex functions like sine and cosine.
Frequently Asked Questions
What is the factorial of zero (0!)?↓
By mathematical convention, 0! equals 1. This ensures that combinatorial formulas, like calculating permutations of zero items, remain mathematically consistent.
Why does the calculator stop at 170?↓
The factorial of 170 (170!) is approximately 7.25 × 10³⁰⁶. In standard 64-bit floating-point computing architecture (which runs web browsers), any number larger than 170! causes an 'overflow' and is treated as Infinity.
Can you calculate the factorial of a negative number?↓
No. The standard definition of a factorial applies only to non-negative integers. Advanced functions like the Gamma function extend factorials to complex numbers, but traditional n! requires n ≥ 0.
