Below is a *permutation calculator*, which will calculate the number of permutations, or ordered sets you can choose from a larger whole. Enter the number of things in the set **n** and the number you need to choose in your sample **r** and we’ll compute the number of permutations.

*If you don’t actually care the order of the selection, use the combination calculator (or change the input in the tool).*

## Permutation Calculator

**Table of Contents**show ▼

## What is a Permutation?

A *permutation* tells you how many ways there are to arrange – and usually also, to choose a subset of – a set.

If you already have an ordered set, the number of permutations tells you how many ways there are to arrange those members. If you are choosing a subset from a larger whole, it means how many ways you can choose the subset, and also how you can arrange your choice.

## Permutations vs. Combinations

*Permutations* are closely related to the concept of *combinations*. Combinations, however, are order agnostic. That is – combinations refer to how many subsets you can choose out of a whole set without caring about the order.

The best way to remember is: “a combination lock is a lie”. Since you can’t enter the code into a lock in *any *order, a combination lock is actually a *permutation lock*. That is, if your combo is 4-26-3 you have to enter it in exactly that order to open the lock.

## Formula for Permutations

The formula for the calculating permutations is:

Where:

- n – the size of the set
- r – the size of the subset you are choosing

Note that the factorial of 0 is 1. In the case where you are not picking a subset and only reordering the larger set, you only need to calculation n!.

### Example Permutation Calculation

Let’s say you have 4 letters: **A, B, C, D**

How many permutations are there when choosing a 2 letter subset?

At 12 permutations, this one is small enough to spell out each one (and verify it by exhaustion). This is every possible order of 2 letters from A, B, C, D:

- AB AC AD
- BA BC BD
- CA CB CD
- DA DB DC

And there you go – 12 permutations.

## Using the Permutation Calculator

To compute the total number of permutations, first enter “n”, the total number of things in your set. Next, enter “r” which is how large of a subset you would like to calculate. (If you aren’t taking a subset, **r** can be the same as **n**).

After that, leave the “Permutations or Combinations?” pulldown menu on **Permutations**, unless you don’t care about order.

Hit Calculate and we’ll let you know how many permutations there are.

*Enjoyed that? Visit our other calculators and tools.*