Permutations Calculator

Calculate permutations (ordered arrangements). Free online nPr calculator.

The Permutations Calculator computes the number of ordered arrangements when selecting r items from n total items. In permutations, order matters—ABC is different from BAC. This tool calculates nPr = n!/(n-r)! for any valid inputs. Essential for counting problems, probability, and combinatorics.

Common use cases

  • Password possibilities with no repeats
  • Race finishing orders
  • Seating arrangements
  • PIN code combinations
  • Scheduling ordered events

How to use

  1. Enter total items (n)
  2. Enter items to arrange (r)
  3. Click calculate for nPr
  4. View the factorial calculation
  5. Compare with combinations if needed

FAQ

What is a permutation?

An ordered arrangement of items. Selecting 3 from ABCD: ABC, ABD, ACB, etc. are different permutations.

What is the formula?

P(n,r) = n!/(n-r)! where n is total items and r is items selected.

How is this different from combinations?

Permutations count order (ABC ≠ BAC); combinations don't (ABC = BAC). nPr = nCr × r!

Can r equal n?

Yes, P(n,n) = n! counts all possible arrangements of all items.