Factorial Calculator
Find the factorial of any integer between 0 and 10,000. For help in using the calculator, read the Frequently-Asked Questions or review the Sample Problem.
Frequently-Asked Questions
Instructions: To find the answer to a frequently-asked question, simply click on the question.
What is a factorial?
A factorial is the product of an integer and every smaller positive integer. This product is represented by the symbol n!, which is called n factorial. By convention, 0! = 1. Thus,
0! = 1
2! = (2)(1) = 2
3! = (3)(2)(1) = 6
4! = (4)(3)(2)(1) = 24
5! = (5)(4)(3)(2)(1) = 120
and so on ...
Factorials can get very big, very fast. The term 10,000! is the largest factorial that the Factorial Calculator can evaluate. The term 10,000! is equal to about 2.846 x 1035659.
For an example that computes a factorial, see Sample Problem 1.
What is Scientific Notation?
The Factorial Calculator uses Scientific notation to express very large numbers. Scientific notation is a way to write numbers that are too large or too small to be concisely written in a decimal format.
With scientific notation, any positive integer can be expressed as a number between 1 and 10 multiplied by a power of 10. Here is an example of a number written using scientific notation:
3.02 * 1012 = 3,020,000,000,000
What is E Notation?
The Factorial Calculator uses E notation to express very large numbers. E notation is a way to write numbers that are too large or too small to be concisely written in a decimal format.
With E notation, the letter E represents "times ten raised to the power of". Here is an example of a number written using E notation:
3.02E12 = 3.02 * 1012 = 3,020,000,000,000
How accurate is the Factorial Calculator?
The Factorial Calculator displays results in three formats: scientific notation, E notation, and ordinary integers.
The integer results are exact for all computations up to 10,000 factorial (10,000!). Results reported in scientific notation and E notation are also exact up to 21 factorial (21!). Beyond 21 factorial, results reported in scientific notation and in E notation are very good approximations, accurate to 14 significant digits.
What is the biggest factorial this calculator can handle?
The Factorial Calculator can compute a factorial for any number up to 10,000.
Beyond 10,000, the calculator reports a lower-bound estimate. Here's the logic. The value of 10,000! is approximately 2.846 x 1035659. Therefore, we know the factorial of any integer greater than 10,000 will be at least 1035663. So, for any integer bigger than 10,000, the calculator reports that the factorial value will be more than 1035663.
Sample Problem
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A standard deck of playing cards has 13 spades. How many
ways can these 13 spades be arranged?
Solution:
The solution to this problem involves calculating a factorial. The first card chosen can be any of 13 spades; the second, any of the remaining 12 spades; the third, any of the remaining 11 spades; and so on. Since we want to know how 13 cards can be arranged, we compute the value for 13 factorial.
13! = (13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) = 6,227,020,800
Note that the above calculation is a little cumbersome to compute by hand, but it can be easily computed using the Factorial Calculator. To use the Factorial Calculator, do the following:
- Enter "13" for n.
- Click the "Calculate" button.
The answer, 6,227,020,800, is displayed in the "Factorial of n" textbox, as shown below.
