Permutation calculator
Count ordered selections of r distinct items from n items. Each item can appear only once in a selection.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Total items n | Use a whole number in the stated format. Fractions and rounding are not interchangeable with exact integer inputs. |
| Positions r | Use a whole number in the stated format. Fractions and rounding are not interchangeable with exact integer inputs. |
Understanding your result
Read Permutations in the units and model stated on this page. The formula P(n, r) = n! ÷ (n − r)! defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Using a different mathematical definition or operation than the one stated by this tool.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
How many ordered arrangements can I make without repeating items?
Enter the number of available distinct items and the number of positions. Different orders count as different arrangements, and each item can be used once.
Common uses
- Count possible ordered selections.
- Arrange distinct items into a fixed number of positions.
How it works
Multiply n by n − 1 and continue for r factors. A different order counts as a different outcome. Repetition is excluded. Inputs must be whole numbers with 0 ≤ r ≤ n ≤ 1,000; selecting zero items gives one empty arrangement.
Worked example
Selecting and ordering 3 items from 10 gives 10 × 9 × 8 = 720 permutations.