Circular Permutation Calculator

Use this page when rotations should count as the same arrangement, like seats around a round table.

Number of items around the circle

Enter the total number of distinct items arranged in one circle.

Result

Enter values to calculate.

What your result means

The explanation updates with the current inputs.

Calculation work

When to use this

Use this formula when the question matches this rule set

Round tables, circular displays, necklace-like placements where only rotation is ignored.

What this result means

Rotating the full arrangement does not create a new result, so the total is one factorial smaller than a linear arrangement.

Formula: (n - 1)!

Calculator inputs

Match the wording in the question to these fields before you interpret the result.

This is the number of distinct items arranged around one circle.

What to enter: Enter the total number of items around the table, ring, or circle.

How to use it: Use n when full rotations count as the same arrangement.

Example: 7 guests around a round table means enter 7.

Worked examples

Seat 7 guests around a round table.

7 distinct items around a circle can be arranged in 720 ways.

Arrange 5 distinct fruits in a circular platter.

5 distinct items around a circle can be arranged in 24 ways.