Permutation Calculator

Calculate the total number of permutations in a set. Permutation is the total different ways in which a set of unique objects can be ordered. For example, a set of 1 apple and 1 orange has two permutations. It can be set as apple/orange or orange/apple.

Permutation Formula

The total number of permutations can be calculated using this formula:

P(n,r) = n!/(n-r)!

  • Where p is the number of permutations
  • n is the number of elements
  • r is the number of elements to choose from a set.
  • ! stands for factoria

How to calculate Permutations

Lets look at an example of how to calculate permutations. Lets assume you have a set of 6 unique objects. We will represent these with letters A,B,C,D,E & F. We want to see how many permutations these can be ordered in a set of 5. Therefore, only 5 of the letters will be used for any order of these objects. An example of two permutations would be ABCDE & ABCDF. In each case only 5 objects are used, but the permutation itself is unique.

Next, you need to enter the number of objects (6) and sample size (5) into the calculator above.

Click calculate and you get 720 permutations without repetitions. If you allow repetitions, i.e. using an object more than once, the total number of permutations goes up to 7,776.

For more related calculators, visit our math calculators.