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Permutations (nPr) Calculator

Find how many ways you can arrange a smaller group chosen from a larger set, where order matters.

How to use

  1. Enter your values in the fields above.
  2. Press Calculate to see your result instantly.
  3. Use the Share button to copy a link to your result.

About this calculator

nPr counts the number of ways to arrange r items chosen from a set of n distinct items where order matters, calculated as nPr = n! ÷ (n − r)!. It differs from combinations (nCr), which count selections where order doesn’t matter — choosing a 1st, 2nd, and 3rd place finisher from 10 racers is a permutation problem, while choosing any 3 finalists from the same 10 without ranking them is a combination problem.

Statistics and probability courses use nPr to calculate the odds of specific orderings, like the chance of guessing an exact sequence of outcomes, or how many distinct ways a set of songs can be played in a playlist, and it appears in computer science whenever an algorithm needs to enumerate ordered arrangements, such as generating all possible orderings of a list for testing or optimization.

This calculator takes n and r and returns the number of possible ordered arrangements.

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