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Permutation Calculator

Permutation Calculator



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An online permutation calculator helps you to find the number of possible subsets that can be obtained including the subsets of same items in different orders. This npr calculator determine the number of permutations that’s the result when we choose r objects from n numbers of set. In Mathematics, the permutation is the number of ways to get the r elements from the n objects of dataset where the order of the element matters. Keep reading to know about npr formula, manual calculation, permutation calculations manually & with this permutations calculator and much more.

The permutations meaning can be more clear with the help of diagram below:

Permutation Calculator

Also, you can try our online combination calculator that readily calculates the number of possible combinations of any large dataset.

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What is the Permutation Formula?

The formula to get the number of permutations of n objects taken the r elements is as follows:

$$  P(n,r) = \frac{n!}{(n-r)!} $$


n is the total number in the dataset

r is the number you select from this dataset & nPr is the number of permutations

This permutation calculator consider this formula for all the permutation calculations for the elements of small as well as large dataset.

Formula for Permutation with Repetition:

The formula for permutations with repetition objects is as follows:

$$ P(n,r) = \frac {n!}{(n_1! n_2! n_3!,,, n_k!)} $$

Here, n1 is the identical elements of type 1, n2 is the identical elements of type 2,……, nk is the identical elements of type k.

(!)this symbol is for the factorial of any number you want. In this, you must multiply all the integers below and equals to the number for which you want the factorial. To find the factorial of the number, you can also try our online factorial calculator that helps you to calculate the factorial of the given n numbers.

How to Calculate Permutations (Step-by-Step):

The calculations for calculating permutations are very easy with this handy permutations calculator that uses the basic permutations formula for accurate results. For better understand about manual calculation, ahead to the example:

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The name of the company begins with three letters. If the letters S, P, D, F, I, J, then how many permutations of these letters can be made if the letter is used only once?


The permutation equation is:

$$ P(n,r) = \frac{n!}{(n-r)!} $$


The total numbers of letters (n) = 6

Chosen letters (r) = 3


$$ P(6,3) = \frac{6!}{(6-3)!} $$

$$ P(6,3) = \frac{6!}{(3)!} $$

$$ P(6,3) = \frac{6*5*4*3!}{(3)!} $$

$$ P(6,3) = 6*5*4 $$

$$ P(6,3) = 120 Number of permutations $$

Example 2:

At the racing start, there are 15 competitors to wins the gold, silver & bronze medal. Calculate number of permutations for the top three medalists from 15 competitors?


The npr formula is:

$$ P(n,r) = \frac{n!}{(n-r)!} $$


The total competitors (n) = 15

Medalists (r) = 3


$$ P(15,3) = \frac{15!}{(15-3)!} $$

$$ P(15,3) = \frac{15!}{(12)!} $$

$$ P(15,3) = \frac{15*14*13*12!}{(12)!} $$

$$ P(15,3) = 15*14*13 $$

$$ P(15,3) = 2730 total permutations $$

Simply enter the values in the designated fields of this online calculator to get the instant results of your permutation related problems and to verify the answer of all above mentioned examples.

Permutations & Combinations:

There is a field to find the r combinations out of n elements. In this the order of the combination doesn’t matter. If you know the permutation, you can easily calculate the combination with the help of following formula:

\(C(n,r) = \frac{P(n,r)}{P(r,r)}=\frac{P(n,r)}{r!}\)

How to Find the Number of Permutations with nPr Calculator:

This number permutation calculator is shows you the instant results for the given inputs, just take a look at these mentioned steps:


  • Firstly, select the name of the elements.
  • Then, enter the total number of elements.
  • Very next, enter the number of element which you want to choose.
  • Then, select the finding parameter from dropdown menu.
  •  Next, enter the values of elements.
  • Lastly, click on the calculate button.


Once you click on calculate button, the permutation formula calculator shows:

  • Permutation
  • Permutation with repetition
  • Step-by-step calculation


Simply choose the calculation parameter from the dropdown, the permutations calculator displays the result according to your selected input.

Frequently Ask Questions (FAQ’s):

What is permutation used?

It is used in almost all fields of science & in Mathematics. In Computer science, it is used for sorting algorithms, in Physics, describes the state of particle and describes the RNA sequences in Biology.

 How do you do permutations?

The only difference between the combination & permutation is ordering. In permutations, we care about the order of elements while in combination don’t care about the ordering of the elements. For example: If the locker has pin code 4587 and if you enter 8574 it won’t open because it’s a different order.

Final Words:

The permutation calculations takes place in various fields of sciences and highly understandable for K-12 education. Well, it doesn’t matter at all whether you need to find the permutations of the small or even large dataset values, the online permutation calculator do all within seconds.


From the authorized source of Wikipedia : Definition & formulas of permutation.

From the site of mathisfun : Difference between combination and permutation

From the source of : How to calculate permutation manually.

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