Factorial Value
Factorial: 3,628,800
Factorial Calculator
Calculate n factorial (n!).
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Results
Factorial
What is this calculator for?
The Factorial Calculator computes number theory properties including prime factors, greatest common divisors, and least common multiples for mathematical analysis.
How to Use This Calculator
Enter the values below, then press Calculate (or press Enter). The calculator updates your results instantly. Try different values to see how your inputs change the outcome.
- Number — enter a numeric amount. A typical Number would be 10.
- Review your results — the key output is highlighted, with supporting figures below.
What You'll Need
- Number
- a numeric amount range 0–170 · required
About This Calculator
The Factorial Calculator computes n factorial, the product of all positive integers from 1 to n, supporting factorial calculations. Factorials grow extremely quickly and are fundamental to combinatorics, probability theory, and many areas of mathematical analysis. This calculator handles values up to 170, covering virtually all practical applications from permutations and combinations to statistical distributions and series expansions.
Simply enter a non-negative integer into the Factorial Calculator. The calculator instantly computes the factorial using efficient multiplication, displaying the result in a readable format. For factorial applications, values up to 170 are supported, covering the full range of practical combinatorial and statistical calculations.
The Factorial Calculator makes factorial calculations instant and error-free, whether you are working on combinatorics problems, probability calculations, or mathematical series. Factorials appear throughout mathematics and statistics, and having a reliable calculator for factorial work saves time and ensures accuracy in your computations.
Formula
n! = n * (n-1) * (n-2) * ... * 2 * 1
Worked Examples
Frequently Asked Questions
What is a factorial and how is it calculated for factorial?
The factorial of a non-negative integer n, written as n followed by an exclamation point, is the product of all positive integers from 1 to n. For example, 5 factorial equals 5 times 4 times 3 times 2 times 1 which equals 120. By definition, 0 factorial equals 1. The Factorial Calculator handles these calculations instantly for your factorial work.
How quickly do factorials grow for factorial applications?
Factorials grow faster than exponential functions. While 10 factorial is about 3.6 million, 20 factorial exceeds 2.4 quintillion. This extremely rapid growth is why factorials quickly exceed standard number representations, which is why the Factorial Calculator supports values up to 170 for factorial calculations.
What are factorials used for in factorial applications?
Factorials are fundamental to permutations and combinations in counting problems, probability theory, statistical distributions, Taylor series in calculus, and algorithm analysis. They appear in formulas for arrangements, lottery odds, quality control sampling, and many other practical factorial applications.
Why is 0 factorial equal to 1 for factorial?
The mathematical definition of 0 factorial equals 1 is necessary for consistency across many formulas. For example, the number of ways to arrange 0 items is exactly one way doing nothing. The combination formula also requires 0 factorial equals 1. This convention ensures all factorial formulas involving factorials work correctly at boundary cases.
What is the maximum factorial value the Factorial Calculator can calculate?
The Factorial Calculator supports factorials up to 170 factorial, which produces a number with approximately 307 digits. Values beyond 170 exceed the maximum representable number in standard floating-point arithmetic. For most practical factorial applications, even values as large as 20 factorial are rarely needed.