Permutation (nPr) Calculator
Calculate the number of ways to arrange r items from a group of n when the order of selection matters.
Your results
Calculation breakdown
- Permutation
- nPr = n! / (n − r)!
Worked example
Awarding 1st, 2nd and 3rd place medals among 10 racers (where order matters) gives 10P3 = 720 possible outcomes.
Assumptions
- Permutations count arrangements where order matters; use Combination if order does not matter.
- Large n and r values are computed iteratively to avoid factorial overflow, but results above n ≈ 170 may lose precision.
How this calculator works
Enter the total number of items (n) and how many are arranged (r). The calculator returns nPr, the number of distinct ordered arrangements possible, useful for ranking, seating or scheduling problems.
Frequently asked questions
How is a permutation different from a combination?
A permutation counts different orderings as separate outcomes, while a combination treats them as the same.
What does nPr mean?
nPr represents the number of ways to arrange r items chosen from a total of n, where order matters.
What if r is larger than n?
That's not valid — you can't arrange more items than exist in the group, so the calculator will show an error.
Editorial review and responsibility
Reviewed by the CalcAussie editorial team on 21 September 2026. Review scope: Method, Australian terminology, material assumptions, source links and user-facing limitations.
Calculator results remain estimates based on the figures entered. Check material decisions against current official information and report a suspected error so it can be reproduced and corrected.