Factorial Calculator
Enter integer n to find n!. n! = factorial(Integer n).
How the result changes
Only integer n changes; all other inputs stay at your current values. Each dot represents one whole-number input. This is not a forecast of real-world outcomes.
About this calculation
Factorial: find n! from integer n. Counting formulas distinguish arrangements from selections. A factorial counts orders of distinct items; permutations and combinations adapt that count.
Formula
n! = factorial(Integer n)
Worked example
With Integer n: 6, n! is 720.
Calculation method
The rule is n! = factorial(Integer n).
For this factorial example, changing integer n from 6 to 7 while keeping the other inputs fixed changes n! from 720 to 5,040.
Reading n!
Order matters for permutations, but not for combinations. This distinction changes the count even when the same items are chosen. In the worked values on this page, integer n 6 produce n! 720.
Practical use
Use these counts to enumerate possible orders or groups in a defined finite set. The specific task here is to find n! from integer n.
Limits and common mistakes
The total and chosen counts must be nonnegative integers, and chosen items cannot exceed total items. Verify integer n before interpreting n!; a value measured on another basis would answer a different question.
Why the relationship works
Counting starts with a clear rule about order and repetition. Factorial counts complete arrangements of distinct objects. Permutations count ordered choices of a specified size; combinations count unordered selections. If two choices contain the same objects in a different order, only a permutation counts them separately. The factorial rule uses integer n in n! = factorial(Integer n); read each symbol as the field named on this page.
Interpreting another set of values
For factorial, the fields labeled integer n are the known quantities. The calculator solves for n! using n! = factorial(Integer n). Clarify whether the output is an integer count, a selected term, or a sum of terms. The index and the rule about order or repetition determine which mathematical object is being counted. When comparing two calculations, keep their units and input definitions identical.
For a second factorial check, keep the other default inputs fixed and change integer n from 6 to 8. n! changes from 720 to 40,320. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.
Checks and limits
Use whole-number item counts. For selections, chosen items cannot exceed total items. Factorial and choice counts can grow beyond an ordinary numeric display; if every digit matters, use an exact-integer method rather than a rounded decimal value. The reported n! is 720 in the worked example. Keep its stated unit or counting convention when checking it against another calculation.
Inputs
- Integer n