Factorial Calculator (n!)

Calculate the factorial (n!) of any non-negative whole number instantly with our free online Factorial Calculator. Perfect for students, mathematicians, statisticians, programmers and anyone working with permutations, combinations or probability.

✔ Factorials (n!) • ✔ Large numbers • ✔ Maths & statistics • ✔ Free calculator

What is a Factorial Calculator?

A Factorial Calculator calculates the factorial of a non-negative integer, written as n!. A factorial is found by multiplying the number by every positive whole number below it until reaching 1.

Factorials grow extremely quickly and are fundamental in mathematics, probability, statistics, combinatorics, cryptography and computer science.

What is a Factorial?

The factorial of a number is the product of all positive integers from that number down to 1.

For example:

• 1! = 1
• 2! = 2 × 1 = 2
• 3! = 3 × 2 × 1 = 6
• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

The Special Case: 0!

One of the most important mathematical rules is:

Although this may seem unusual, it is a standard mathematical definition that keeps many formulas in algebra, probability and combinatorics consistent.

Worked Examples

Example 1 — 5!

• 5 × 4 × 3 × 2 × 1
• = 120

Example 2 — 6!

• 6 × 5 × 4 × 3 × 2 × 1
• = 720

Example 3 — 8!

• 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
• = 40,320

Example 4 — 10!

• 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
• = 3,628,800

Common Factorial Values

n	n!
0	1
1	1
2	2
3	6
4	24
5	120
6	720
7	5,040
8	40,320
9	362,880
10	3,628,800
12	479,001,600
15	1,307,674,368,000
20	2,432,902,008,176,640,000

Where Are Factorials Used?

Real-World Example

Suppose eight runners compete in a race.

This means there are 40,320 different possible finishing orders.

Interesting Factorial Facts

• Factorials grow much faster than powers or exponential functions.
• 10! already exceeds 3.6 million.
• 20! is greater than 2.43 quintillion.
• 100! contains 158 digits.
• Factorials are essential in advanced mathematics and scientific computing.

Things to Remember

• Factorials are only defined for non-negative whole numbers.
• 0! always equals 1.
• Values grow extremely quickly as n increases.
• Decimal and fractional values do not have ordinary factorials.
• Large factorials require arbitrary-precision arithmetic.

Common Mistakes

• Assuming 0! equals 0.
• Trying to calculate factorials of negative numbers.
• Forgetting to multiply every integer down to 1.
• Confusing factorials with exponentiation.
• Underestimating how rapidly factorial values grow.

This calculator automatically performs the multiplication and accurately handles extremely large factorial values.

Frequently Asked Questions

What is 0!?

0! = 1.

Why does 0! equal 1?

It is a mathematical definition that keeps many algebraic, combinatorial and probability formulas consistent.

Can factorials be calculated for large numbers?

Yes. This calculator supports very large factorials using high-precision arithmetic.

Can decimal numbers have factorials?

Not with the standard factorial function. Advanced mathematics extends factorials to non-integer values using the Gamma function.

Where are factorials used?

They are used throughout mathematics, statistics, probability, engineering, computer science and scientific research.

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