# Circular Permutation Calculator

> Count arrangements of distinct objects around a circle when rotations are considered identical.

Page: https://askcalculators.com/calculator/circular-permutation-calculator/
Definition: https://askcalculators.com/calculator/circular-permutation-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/circular-permutation-calculator/schema.json
Version: 1.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/circular-permutation-calculator/?n=8&reflectionsSame=0

## Inputs
- n: Number of distinct objects n; type=number; required; default=8; min=1; max=1000
- reflectionsSame: Treat mirror images as identical; type=checkbox; optional; default=false

## Outputs
- permutations: Circular permutations; format=text; primary
- formulaUsed: Formula used; format=text

## Formula
rotational arrangements = (n − 1)!; with equivalent reflections divide by 2 for n > 2

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.