Circular Permutation Calculator

Circular permutation calculator calculates number of ways that arrange items in a cirluar order.

Circular permutation formula

Circular permutation formula is
(n-1)!

where
n = the number of objects

We use n−1 instead of n because, in a circular arrangement, rotating the items keeps them in the same order.

This results in fewer distinct arrangements compared to a linear arrangement, so the number of ways to arrange items in a circle is (n−1)!.

Circular Permutation Example

For example, if 12 kids are seated at a round table, the number of possible seating arrangements is a circular permutation, calculated as:

(12-1)!
=11!
= 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
=39,916,800