CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Circular Permutation Calculator

Count arrangements of distinct objects around a fixed circle when rotations are equivalent.

Counting & Combinatorics

Arrange distinct objects around a circle

Rotations treated as equal

Exact count

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Enter the number of distinct objects.
  2. Treat rotated copies as the same arrangement.
  3. Read the exact circular-permutation count.

Calculation method

Fix one object to remove rotational duplicates

Once one object is fixed as an anchor, the remaining n−1 distinct objects may be ordered freely.

Worked example

Seat six people around a table

Rotating everyone together does not create a new relative seating order.

(6−1)! = 120

Supported inputs

Precision and limits

Discrete domain

Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.

Exact integers

Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.

Reflection

Clockwise and counterclockwise orders are distinct. Mirror-equivalent necklaces require a different model.