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Permutation Calculator



n = , r =



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

In this exapmle we have n = and r = . by Putting these values in above formula, we have:

P(n,r) = ?

P(n,r) = P(,)


What is Permutation?

The possible ways in which a set of numbers or digits can be arranged in a unique way is called permutation. For example, the permutations of ABC would be BCA or CAB.

Lets say we have 4 objects, there would be 4 times 3, 3 times 2, 2 times 1 or a total of 24 possible permutations. With the exclamation mark, the process is called the factorial.

Factorial equation is

n! = n*(n-1)*(n-2)*...1

So as per permutation equation

4! =4*3*2*1 = 24

This is read as "four factorial" which is equals to 24.

What is Permutation formula?

The permutations formula is the number of permutations "n" with different objects taken "r" at a time is:


Where 0 < r < = n

npn = n!/(n−r)!

npn calculator uses the same permutation formula to get accurate results. Moreover, you can also use our mean calculator, midpoint calculator & sig fig calculator without any hidden charges.

How to find Permutations and Combinations?

Lets say we want to find how many different signals can be made by 3 flags out of 4 flags of different colors.

According to the permutations formula, here n=4 and r=3 as we need to make a combination of 3 flags out of 4 flags. Therefore

4P3 = 4!/(4−3)!

4P3 = 24/1

4P3 = 24

So there are 24 signals which can be made by 3 flags from 4 flags of different colours.

So the number of permutations and combinations of n objects taken k at a time is


How do you find the order of Permutations?

Suppose we have 4 objects and we select 2 at a time. In this example, we used the first two numbers, 4 and 3 of 4!. The remaining numbers of 4! are 2 and 1 or 2!.

In general, for n objects n! Divided by (n-k)! Where k is the number of objects, we take from the total of n objects. So for this example 4! Divided by


Which is


and it equals 12.

Use remainder calculator & rounding calculator to deal with floating numbers & decimal numbers.

What is Permutation Calculator?

Finding permutations and combinations by hands is quite a hassle to do. It becomes even worse when it comes to calculate permutations for large values. For that, permutation calculator comes into play.

A permutation calculator allows you to calculate permutations of "r" elements within a set of "n" objects easily. There are several online calculators which can be used to calculate permutations. Permutation calculator uses formula for permutations to find result quickly.

How to use Permutation Calculator?

Our permutation calculator is very simple & easy to use. To use our permutation calculator, follow these steps.

  • Select the number of permutations you want to calculate.
  • Enter the total number of object "n" in the first field.
  • Enter the number of elements taken at a time "r" in the second field.

You will get the number of permutations within a few seconds after entering the selected values in the right fields. Such simplicity and easy to follow steps make our permutation calculator one of the best calculators which you can find online.

We also have other tools like Arithmetic Sequence Calculator & Covariance Calculator for your learning & practice on run time.

Shaun Murphy

Last updated: September 09, 2020

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.

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Luis Ramirez
Excellent. It's a joy to use your permutations calculator. I wanted to know the number of permutations of a phrase of 4 words. It gave me: P (4,1) = 4 P (4,2) = 12 P (4,3) = 24 I guess the total number of permutations of the 4-word phrase must be the SUM, ie, 40 permutations. I hope I am correct. Thanks a thousand. Sincerely A satisfied user