Permutação Circular
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(n−1)!
About this calculator
The circular permutation calculator determines how many different ways n objects can be arranged in a circle. Unlike a linear line, rotations that produce the same relative order are considered identical. The formula used is (n-1)!, where n is the number of objects. For example, for 5 people around a round table, the calculation results in 4! = 24 distinct arrangements.
This tool is useful in combinatorics problems, such as arranging people around a table, placing objects in a circle, or planning rotations. Circular permutation is applied whenever absolute position does not matter, only the relative order among elements. Therefore, rotations that keep the sequence invariant are disregarded.
Important considerations: circular permutation assumes positions are indistinguishable under rotation. If reflections (mirrorings) are also considered equivalent, as in necklaces or bracelets, the calculation changes to (n-1)!/2. Additionally, the calculator works only for n ≥ 1; for n=0 or negative, there are no possible arrangements. Always check whether the context considers rotations only or also inversions as identical.
Frequently asked questions
What is the difference between circular permutation and linear permutation?
In linear permutation, absolute order matters, so for n objects we have n! arrangements. In circular permutation, rotations are considered equivalent, resulting in (n-1)! arrangements.
How to calculate circular permutation for necklaces or bracelets?
For objects that can be flipped (like necklaces), reflections are also identical. In that case, the formula is (n-1)!/2, provided n > 2.
Can I use the calculator for n = 1?
Yes, for n = 1, (1-1)! = 0! = 1. There is only one way to arrange a single object in a circle.
What if I have repeated objects in a circle?
The formula (n-1)! assumes distinct objects. For repeated objects, you need circular permutation with repetition, which is more complex and not available in this calculator.
Does clockwise or counterclockwise order matter?
Yes, unless specified, circular permutation considers that two arrangements that are mirror images (clockwise vs counterclockwise) are different. If they are considered the same, use (n-1)!/2.