Factorial Calculator
Compute factorials quickly with our factorial calculator. Enter a number and get accurate n! results instantly with step-by-step explanations.
Factorial is only defined for non-negative integers. Larger values will be displayed with abbreviated notation.
▶Formula Used
How It Works
The factorial calculator computes the product of all positive integers less than or equal to the input number. For a number n, its factorial (written as n!) equals n × (n-1) × (n-2) × ... × 3 × 2 × 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! equals 1.
Example
For example, to calculate 6!:\n6! = 6 × 5 × 4 × 3 × 2 × 1\n6! = 6 × 5 × 24\n6! = 6 × 120\n6! = 720
Frequently Asked Questions
What is a factorial?
A factorial is the product of all positive integers less than or equal to a given positive integer. It's denoted by the integer followed by an exclamation mark (!). For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
What is the value of 0 factorial?
By definition, 0! = 1. This is a special case that's established to make many mathematical formulas work consistently.
Why do factorials grow so quickly?
Factorials involve multiplying a sequence of increasing numbers together, which leads to exponential growth. For example, while 5! is just 120, 10! is already over 3.6 million, and 20! is over 2.4 quintillion.
Where are factorials used in real life?
Factorials are used in probability theory, combinatorics (counting problems), and statistics. They help calculate permutations (arrangements) and combinations (selections) of objects, which are essential in fields ranging from mathematics to computer science.
How does this calculator handle very large factorials?
For larger factorials (beyond 170!), our calculator uses BigInt for precise calculation and displays the result in abbreviated format (K, M, B, etc.). You can copy the full number if needed.