A circular permutation is one in which the things are arranged along a circle. It is also called closed permutation.

The number of circular permutations of n distinct objects is (n−1)!.

In this formula, anti-clockwise and clockwise order of arrangements are considered as distinct permutations.

If there are n things and if the direction is not taken into consideration, the number of circular permutations is ½(n−1)!.