Get the value of n! instantly with a Factorial Calculator
A factorial, written n!, multiplies every whole number from 1 to n. This Factorial Calculator computes n! for any valid non-negative integer you enter, and it flags invalid inputs.
- Step 1: Enter a whole number n (0, 1, 2, 3, …).
- Step 2: Click Calculate to compute n!.
- Step 3: If you need a new value, click Reset and enter a different n.
- Step 4: Read the output: the exact factorial value (when supported) and a note when values get too large.
What is a factorial?
A factorial is a special product defined for non-negative integers. The definition is simple: n! = 1 × 2 × 3 × … × n. By convention, 0! = 1.
Factorials grow extremely fast. Even moderate values like 20! already produce a large number, and larger inputs can exceed typical JavaScript number limits.
Factorial formula (and what each part means)
The factorial formula is:
n! = ∏k=1n k
- n is the non-negative integer you want the factorial of.
- n! is the product of all integers from 1 up to n.
- 0! equals 1 because the product over an empty set is defined as 1.
How the Factorial Calculator computes n!
This calculator uses an exact integer method for values it can safely represent. For typical web use, it computes factorial using BigInt when possible, so you get an exact result for a wide range of inputs.
Because factorial values explode in size, the calculator also includes validation and safety checks. If you enter a negative number, a non-integer, or a value outside the supported range, it shows a clear error message.
Common factorial use cases
Factorials are a core tool in math and computer science. You’ll see them in counting problems, probability, and algorithms where order matters.
- Permutations: The number of ways to arrange n distinct items is n!.
- Combinations & binomial terms: Factorials appear in formulas like \(\binom{n}{k} = \frac{n!}{k!(n-k)!}\).
- Probability: Many discrete probability distributions use factorials.
- Algorithms: Factorials relate to recursion depth, search space size, and runtime growth.
Practical examples
Example 1: Counting arrangements
If you have 5 distinct books and want to arrange them on a shelf, the number of possible orders is 5!. Compute it with the calculator to get the exact count.
Answer: 5! = 120.
Example 2: Using factorials in a binomial coefficient
Suppose you need \(\binom{6}{2}\), which counts how many ways to choose 2 items from 6 without regard to order. The formula uses factorials: \(\binom{6}{2} = \frac{6!}{2!4!}\). Use the Factorial Calculator to compute each factorial part.
Answer: \(\binom{6}{2} = 15\).
Tips for entering values
- Enter whole numbers only (integers). For example, use 7, not 7.5.
- Factorials are defined for non-negative integers. Negative values are not valid.
- If you’re working with large values, expect factorials to become very large quickly.
Frequently Asked Questions
What is the definition of n!?
The factorial n! is defined for non-negative integers as the product of all whole numbers from 1 through n. It is written as n! = 1 × 2 × 3 × … × n. By convention, 0! = 1.
Can a factorial be computed for negative numbers?
No. Factorial is only defined for non-negative integers in the basic counting sense. Negative inputs like -3 are invalid for n!. If you need related values for negatives, you must use the Gamma function, not standard factorial.
Why do factorial values get so large so fast?
Each step multiplies by the next integer. Going from n to n+1 multiplies the result by (n+1). That repeated multiplication causes factorials to grow super quickly, producing huge integers even for moderate n.
What is the difference between 0! and 1!?
0! equals 1 by definition, representing an empty product. Meanwhile, 1! equals 1 × 1, which is also 1. So both 0! and 1! equal 1, but they come from different product structures.
How do I use a factorial calculator correctly?
Enter a non-negative integer n, then click Calculate. Make sure the input has no decimals and is not negative. The output shows n! exactly when supported by the calculator. If the input is invalid or too large, you’ll see an error.