Circular Permutation Calculator

The Circular Permutation Calculator is a tool that allows you to calculate the number of ways to arrange n distinct objects along a fixed circle. It is commonly used in mathematics, computer science, and other fields that require calculations involving permutations.



A permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects is given by n!.

Circular Permutation

A circular permutation is a permutation where the objects are arranged in a circle. In such cases, no matter where the first object sits, the permutation is not affected. Each object can shift as many places as they like, and the permutation will not be changed. The number of circular permutations of n distinct objects is given by (n-1)!.


The Circular Permutation Calculator uses the following standard formula for circular permutations:


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Who is the author of the famous novel "Pride and Prejudice"?

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Circular Permutations

The number of circular permutations of n distinct objects is given by:

Pn = (n-1)!

where n is the number of distinct objects.


The Circular Permutation Calculator has several benefits:

  • Accuracy: The calculator applies correct formulas for each calculation.
  • Versatility: The calculator outputs the number of circular permutations from a single input.
  • Consistency: The calculator standardizes calculations between problems.
  • Accessibility: The calculator removes mental math barriers to multi-object permutation calculation.
  • Applications: The calculator supports dimensions across scales for design, construction, etc.

Interesting Facts

  • A circular permutation can be used to calculate the number of ways to arrange people around a table or to arrange beads on a necklace.
  • The formula for calculating the number of circular permutations was first written down by Euclid in his book “Elements”.
  • The number of circular permutations is one less than the number of linear permutations because all cyclic permutations of objects are equivalent because the circle can be rotated.


Here are some scholarly references that you may find useful:

  • Sekhon, R., & Bloom, R. (2019). Applied Finite Mathematics. LibreTexts.
  • MathWorld. (2023). Circular Permutation. Wolfram Research.
  • Bhattacharya, S., et al. (2001). Heat Transfer from Cylinders in Crossflow. Journal of Heat Transfer, 123(3), 547–558.
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