Permutation Calculator
Count ordered selections of distinct items without selecting an item more than once.
Permutations (order matters)
Distinct items and no repetition. Use whole numbers with 0 ≤ r ≤ n ≤ 10,000. Zero positions have one empty arrangement. Exact output is limited to 2,000 digits.
Formula checked · NumberSwift · Review process
How this calculator works
For the first position there are n choices, then n−1 for the second, continuing until r positions are filled. Reordering the same selected items creates another outcome. This makes permutations suitable for distinct rankings or assignments. The calculation uses exact BigInt products and avoids overflow from floating-point factorials. Use Combination if rearranging the selected items should not count as a new choice.
Formula
nPr = n!/(n−r)! = n × (n−1) × … × (n−r+1).
Assumptions & limitations
Distinct items and no repetition. Use whole numbers with 0 ≤ r ≤ n ≤ 10,000. Zero positions have one empty arrangement. Exact output is limited to 2,000 digits.
Worked example
Filling 3 ordered positions from 10 candidates gives 10 × 9 × 8 = 720 permutations. The same items chosen without order give only 120 combinations.
Our approach to calculations ↗Common questions
Does this allow repeated items?
No. Each chosen item is removed from later choices. Independent positions with repetition would use n^r instead.
What happens when r equals n?
The tool returns n factorial: every full ordering of all distinct items.
Can I enter fractional n or r?
No. This tool counts discrete items and positions, so both inputs must be whole numbers.