Factorial Calculator
Calculate the factorial of any number instantly, even large ones. Enter n, get n factorial. No signup. Ideal for probability, combinatorics, statistics and maths.
Result
| Factorial |
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This factorial calculator computes the factorial of any number instantly, even large ones, directly in your browser. Enter a number and read its factorial, the product of all whole numbers up to it. No account, no install, so students and anyone working with probability, combinatorics or statistics can calculate factorials on any device in seconds.
How to Calculate a Factorial Step by Step
- Enter your number. Type the whole number whose factorial you want into the input field. The factorial is written with an exclamation mark, so the factorial of five is written five with an exclamation mark.
- Calculate the factorial. The tool multiplies together all the whole numbers from one up to your number, giving the factorial. For five, that is five times four times three times two times one.
- Read the result. The factorial appears instantly. Even for modest numbers the result grows very large, so the calculator handles the big numbers that quickly exceed what you can compute by hand.
- Understand zero factorial. Note that the factorial of zero is defined as one, which surprises people but is essential for the maths of combinatorics to work consistently.
- Use it in a formula. Apply the factorial in a probability, permutation or combination calculation, where factorials are the core building block.
What a Factorial Is and Why It Grows So Fast
The factorial of a whole number is the product of all the whole numbers from one up to it, written with an exclamation mark after the number. So the factorial of four is four times three times two times one, which is twenty four. This simple operation, multiplying a descending run of whole numbers, appears throughout mathematics, especially anywhere you count the number of ways things can be arranged or chosen.
Factorials grow astonishingly fast, faster than exponential growth. The factorial of ten is already over three million, and the factorial of twenty is measured in quintillions. This explosive growth is why factorials quickly become impossible to compute by hand and why even calculators reach their limits: the factorial of a moderately large number has hundreds of digits. The rapid growth reflects how quickly the number of possible arrangements of things multiplies.
The factorial of zero is defined as one, which puzzles many people since it seems there is nothing to multiply. The definition is not arbitrary: it makes the formulas of combinatorics work consistently. There is exactly one way to arrange zero objects, the empty arrangement, so counting arrangements gives one. Defining zero factorial as one also lets the recursive pattern, where each factorial is the number times the previous factorial, extend cleanly down to zero.
Factorials are the engine of combinatorics, the mathematics of counting arrangements and selections. The number of ways to arrange a set of objects in order is the factorial of how many there are. Permutations and combinations, which count ordered and unordered selections, are built from factorials. This is why factorials are essential in probability and statistics, where questions constantly reduce to counting the possible outcomes, and factorials do that counting.
This Calculator Versus Multiplying by Hand
| Number | Factorial | Value |
|---|---|---|
| 0 | 0 factorial | 1 |
| 1 | 1 factorial | 1 |
| 5 | 5 factorial | 120 |
| 10 | 10 factorial | 3,628,800 |
| 20 | 20 factorial | a quintillion scale number |
Who Uses a Factorial Calculator
Pro Tips for Working With Factorials
Common Factorial Mistakes to Avoid
Related Tools You May Need Next
Factorials underpin counting, so our GCD and LCM Calculator and general Scientific Calculator complement this for broader maths. To express a resulting probability, the Percentage of a Number calculator converts it to a percentage.
Frequently Asked Questions
What is a factorial?
The factorial of a whole number is the product of all the whole numbers from one up to that number, written with an exclamation mark after it. So the factorial of four is four times three times two times one, which equals twenty four. Factorials appear throughout mathematics, especially in combinatorics and probability, wherever you need to count the number of ways things can be arranged or selected.
How do I calculate a factorial?
Enter the whole number whose factorial you want, and the calculator multiplies together all the whole numbers from one up to it, giving the result instantly. For example, the factorial of five is five times four times three times two times one, which is one hundred and twenty. Because factorials grow very quickly, the calculator handles the large numbers that soon become impossible to compute by hand.
Why is zero factorial equal to one?
The factorial of zero is defined as one, which seems odd but is not arbitrary. There is exactly one way to arrange zero objects, the empty arrangement, so counting arrangements gives one. This definition also keeps the formulas of combinatorics consistent and lets the recursive pattern, where each factorial equals the number times the previous factorial, extend cleanly down to zero. So zero factorial equals one, not zero.
Why do factorials get so large so quickly?
Factorials grow faster than exponential growth because each step multiplies by an ever larger number. The factorial of ten already exceeds three million, and the factorial of twenty reaches into the quintillions. This explosive growth reflects how rapidly the number of possible arrangements of things multiplies as you add more items, which is exactly why factorials quickly become impossible to compute by hand.
What are factorials used for?
Factorials are the foundation of combinatorics, the mathematics of counting arrangements and selections. The number of ways to arrange a set of objects in order is the factorial of how many there are. Permutations and combinations, which count ordered and unordered selections, are built from factorials. This makes them essential in probability and statistics, where many questions reduce to counting the possible outcomes.
Can I calculate the factorial of a decimal?
The standard factorial is defined only for whole numbers, so taking the factorial of a fraction or decimal does not fit the basic definition. There is an advanced mathematical extension, called the gamma function, that generalises factorials to other numbers, but for the counting and probability problems where factorials are normally used, you work with whole numbers, which is what this calculator computes.
What is the difference between a factorial and a power?
A factorial multiplies together a descending run of whole numbers, so the factorial of four is four times three times two times one. A power raises a single number to an exponent, so four to the power of two is four times four. These are entirely different operations that grow at different rates and give different results, so it is important not to confuse the factorial of a number with a power of it.
Is the factorial calculator free?
Yes, it is completely free with no account and no usage limit. You can calculate as many factorials as you like, including large ones, as often as you like, at no cost. It runs entirely in your browser on any device, so there is nothing to download or install, and the factorial appears instantly whenever you enter a number, even when the result is a very large figure.