Free Mathematical Calculator

Professional Factorial Calculator

Calculate the factorial of any non-negative integer using precise BigInt calculations. Get the complete result, multiplication sequence, digit count, and calculation details instantly.

Factorial Input

Enter a non-negative integer

The factorial of a number is the product of that number and every positive integer below it.

Number (n)

Enter a whole number from 0 to 5,000. Negative numbers and decimal values do not have a standard factorial.

Calculation Result

5! =

120

Number of digits 3

Multiplications 4

What Is a Factorial?

A factorial is a mathematical operation applied to a non-negative integer. It is represented by an exclamation mark after the number. For example, the factorial of 5 is written as 5!.

To calculate a factorial, multiply the selected number by every positive integer below it until you reach 1.

n! = n × (n − 1) × (n − 2) × ... × 2 × 1

For example, 5 factorial is calculated as 5 × 4 × 3 × 2 × 1, which equals 120. By mathematical definition, both 0! and 1! are equal to 1.

How the Factorial Calculator Works

Enter your number

Type a non-negative whole number into the calculator input field.

Start the calculation

Select the Calculate Factorial button. The calculator multiplies all positive integers from your number down to 1.

Review the exact result

The result panel displays the factorial value, total digits, and number of multiplication operations.

Where Are Factorials Used?

Factorials are commonly used in permutations, combinations, probability, statistics, algebra, computer science, and mathematical series. They help calculate how many different arrangements can be created from a group of objects.

For example, if five different books are placed on a shelf, they can be arranged in 5!, or 120, different ways.

Factorial Examples

0! 1

1! 1

3! 6

5! 120

7! 5,040

10! 3,628,800

Important Rule

The value of 0! is defined as 1. This definition keeps formulas involving combinations and permutations mathematically consistent.

Frequently Asked Questions

Factorial Calculator FAQs

Find answers to common questions about factorial notation, calculations, limits, and mathematical applications.

When an exclamation mark appears after a non-negative integer, it represents the factorial operation. For example, 5! means 5 × 4 × 3 × 2 × 1.

Zero factorial is defined as 1 because there is exactly one way to arrange zero objects: the empty arrangement. This definition also keeps combination formulas consistent.

Standard factorial notation is defined only for non-negative integers. Negative integers do not have a factorial under the standard factorial definition.

Traditional factorial calculations use whole numbers. The Gamma function can extend factorial-like calculations to many decimal and complex values, but it is a more advanced mathematical concept.

The factorial of 10 is 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, which equals 3,628,800.

Factorial values grow extremely quickly. For example, 20! already contains 19 digits. This calculator uses JavaScript BigInt to preserve exact integer values for large supported inputs.