Factorial CalculatorFree online math calculator — instant results, no sign-up
Calculate the factorial of a nonnegative integer up to 170.
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About the Factorial Calculator
The Factorial Calculator calculates n!, the product of all positive integers from 1 through a nonnegative integer n. It accepts whole numbers from 0 through 170, with a default input of 10 that gives 3,628,800. Factorials are used to count arrangements of distinct objects and to calculate permutations and combinations.
- Nonnegative integer
- Enter the unitless whole number n from 0 through 170 whose factorial you want to calculate; the default is 10.
Formula and method
n! = ∏(k = 1 to n) k for n ≥ 1, with 0! = 1; for the default input, 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800.
- nThe nonnegative integer entered, restricted to 0 through 170.
- !The factorial operator, indicating multiplication of all positive integers up to the number before it.
- ∏The product symbol, instructing multiplication over the stated range.
- kThe integer multiplication index, running from 1 through n.
Check that the input is a whole number within the permitted range. Begin with a product of 1 and multiply it successively by each integer from 1 through n. For n = 0, no multiplication is needed and the product remains 1. With the default input n = 10, the product is 3,628,800.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Nonnegative integer10
Results
- Result3,628,800
How to use the Factorial Calculator
- 1Find the Nonnegative integer input, which defaults to 10.
- 2Keep 10 to reproduce the worked example, or enter a whole number from 0 through 170.
- 3Run the calculation using the page's calculation control.
- 4Read the Result row: for the default input, it displays 3,628,800.
- 5Interpret this as 10!, the product of all positive integers through 10, rather than 10 raised to a power.
Reading your result
The Result row reports n!, a unitless factorial value. For the default input of 10, Result = 3,628,800. In a counting context, this is the number of ways to arrange 10 distinct objects in a sequence when every object is used exactly once.
Limitations
Only nonnegative integers from 0 through 170 are supported; negative numbers, fractional inputs, and larger integers are outside this tool's scope. Factorials grow rapidly, and large results may be displayed in scientific notation or rounded depending on the calculator's numeric precision. The upper limit of 170 is consistent with the finite range of standard double-precision arithmetic, but being within that range does not guarantee that every integer digit is preserved. The tool does not extend factorials to nonintegers using the gamma function.
Common questions
Why is 0! equal to 1?+
The factorial of zero is an empty product, which is defined as 1. This also matches the counting interpretation: there is exactly one way to arrange no objects.
Why does the calculator stop at 170?+
The tool limits inputs to 170. This is also the largest integer whose factorial fits within the finite magnitude range of standard double-precision floating-point numbers; the next factorial exceeds that range.
How does the default input produce 3,628,800?+
For the default input of 10, multiply 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. The product is 3,628,800.
Does n! count arrangements when some objects are identical?+
Not directly. The value n! counts arrangements when all n objects are distinct. If objects repeat and are indistinguishable, divide n! by the factorial of each repeated group's size.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.