Factorial Calculator

Find the the factorial of any number between 1 and 170. For help in using the calculator, read the Frequently-Asked Questions or review the Sample Problem.

• Enter a number in the unshaded text box.
• Click the Calculate button to display the factorial value of that number.
 Number ( n ) n Factorial

Instructions: To find the answer to a frequently-asked question, simply click on the question.

What is a factorial?

In general, n objects can be arranged in n(n - 1)(n - 2) ... (3)(2)(1) ways. 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 170! is the largest factorial that the Factorial Calculator can evaluate. The term 171! produces a result that is too large to be processed by this software; it is bigger than 10 to the 308th power.

For an example that computes a factorial, see Sample Problem 1.

What is E-Notation?

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

The Factorial Calculator uses E notation to express very large numbers. For example, the term 170! is expressed in E notation as 7.25741561530799E+306.

How accurate is E-Notation?

If the Factorial Calculator displays a result in E notation, that result is not exact. It is an approximation, accurate to within 16 significant digits.

1. 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. Since we want to know how 13 cards can be arranged, we need to compute the value for 13 factorial.

13! = (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) = 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 "n Factorial" textbox.