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Calculation Machine

Permutation Calculator

Ordered arrangements nPr.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Permutations nPr
720
With repetition (n^r)
1,000
Combinations nCr
120
Ratio P/C
6

Quick answer

A permutation counts arrangements where order matters: nPr = n!/(n−r)!.

The formula

nPr = n! / (n − r)!

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Total items n10
  • Choose r3

Result

  • Permutations nPr720
  • With repetition (n^r)1,000
  • Combinations nCr120
  • Ratio P/C6

How to use the Permutation Calculator

  1. 1Enter the total number of items.
  2. 2Enter how many you are arranging.
  3. 3Compare with combinations if order does not matter.

Frequently asked questions

Permutation or combination?

Permutation when order matters (podium places), combination when it does not (lottery).

What is nP0?

1 — there is one way to arrange nothing.

About this calculator