Factorial free online calculator

Free online factorial calculator.

Enter the non negative integer number (n) and press the Calculate button:

!

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Result

Calculation

The factorial formula is:

n! = 1⋅2⋅3⋅4⋅...⋅n

For example:

1! = 1

2! = 1 x 2 = 2

3! = 1 x 2 x 3 = 6

4! = 1x2 x 3 x 4 = 24

5! = 1 x 2 x 3 x 4 x 5 = 120

6! = 1 x 2 x 3 x 4 x 5 x 6 = 720

7! = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 5,040

8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 40,320

9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 = 362,880

10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3,628,800

11! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 = 39,916,800

12! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 = 479,001,600

13! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 = 6,227,020,800

14! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 = 87,178,291,200

15! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 = 1,307,674,368,000

16! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 = 20,922,789,888,000

17! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 = 355,687,428,096,000

18! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 = 6,402,373,705,728,000

19! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 = 121,645,100,408,832,000

20! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 = 2,432,902,008,176,640,000

Factorial calculation formula and explanation with examples

The factorial is a mathematical operation that is used to calculate the product of all positive integers from 1 up to a given number. It is represented by the exclamation mark (!) symbol, with the number preceding it. For example, 5! (read as "5 factorial") equals 5 x 4 x 3 x 2 x 1, which is equal to 120.

The factorial function has many applications in mathematics, statistics, physics, and engineering. It is used to solve problems involving permutations and combinations, probability, binomial distributions, and more.

To calculate the factorial of a number, we start by multiplying the given number by all the positive integers less than it, all the way down to 1. For example, to find the factorial of 5, we would perform the following calculation:

5! = 5 x 4 x 3 x 2 x 1

= 120

In general, the formula for the factorial of a positive integer n is:

n! = n x (n-1) x (n-2) x ... x 2 x 1

It's important to note that the factorial function is only defined for positive integers. We cannot calculate the factorial of a negative number or a non-integer.

Factorials can become very large very quickly, so it's important to be careful when using them in calculations. For example, the factorial of 20 is 2,432,902,008,176,640,000, which is a very large number that is difficult to work with. Many calculators, including the factorial calculator on JustFreeTools, have built-in features to handle large factorials.

In addition to the factorial of a single number, the factorial function can also be used to calculate combinations and permutations. Combinations are the number of ways to choose a subset of items from a larger set, while permutations are the number of ways to order a set of items. These calculations involve dividing the factorial of the larger set by the factorial of the smaller set and the factorial of the difference between the two sets.

In conclusion, the factorial function is an essential tool in mathematics and has many applications in various fields. By understanding how to calculate factorials and their related concepts of combinations and permutations, we can solve complex problems with ease. The factorial calculator on JustFreeTools provides a quick and easy way to calculate factorials and is a useful tool for students, professionals, and anyone who needs to work with large numbers.