Circular Permutation Calculator
Find the number of ways to arrange objects in a circle where rotations are considered identical.
Σ The Formula
Real World Examples
# About This Calculator
Circular Permutation counts the distinct ways to arrange $n$ objects in a closed loop. Unlike linear permutations where the start and end of the line are fixed, a circle has no fixed beginning.
To calculate this, we "fix" one object in a single position to break the rotational symmetry. We then arrange the remaining $n-1$ objects in the remaining positions in a linear fashion, resulting in $(n-1)!$ arrangements.
How To Use
- Enter the **Total Number of Objects (n)**.
- The result will show the number of unique circular arrangements.
- Note: This assumes the circle can be rotated but not flipped (like people at a table). For objects that can be flipped (like a necklace), the result should be divided by 2.
Frequently Asked Questions
Why (n-1) and not n?+
What about flipped circles (necklaces)?+
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About
Circular Permutation counts the distinct ways to arrange $n$ objects in a closed loop. Unlike linear permutations where the start and end of the line are fixed, a circle has no fixed beginning.
To calculate this, we "fix" one object in a single position to break the rotational symmetry. We then arrange the remaining $n-1$ objects in the remaining positions in a linear fashion, resulting in $(n-1)!$ arrangements.