Math & StatisticsFormula-based · Runs in your browser

Circular Permutation Calculator

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

Preparing saved example…

Inputs

Enter the values you know. Optional fields may be left empty.

Local save controls below
Required

Result

Updates as valid inputs change.

Calculated locally
Circular permutations
Formula used

Saved locally, explained clearly

Drafts, calculations, scenarios, and workflow progress stay in this browser unless you export them.

Opening local database…

Calculation steps

Follow what happened from the selected formula to the displayed answer.

Show substituted values and intermediate working
Calculate current inputs to see the working.
  1. 1

    Formula selected

    The calculator uses the following formula or method.

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

  2. 2

    Values entered

    Your values are placed into the calculation.

    Enter values to see what is used in this step.

  3. 3

    Result calculated

    The formula or method produces the following result values.

    Results will appear after a successful calculation.

  4. 4

    Answer formatted

    Displayed values are rounded and formatted using each output’s configured precision.

Scenario comparison

Save working scenarios, then select two or three to compare. Formula versions and inputs remain visible.

No scenarios saved for this calculator yet.

Recent calculations

Successful calculations are retained locally according to your privacy settings.

No local history for this calculator yet.

Data and privacy

What this calculator does

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

How it works

The calculator evaluates rotational arrangements = (n − 1)!; with equivalent reflections divide by 2 for n > 2. Inputs are checked before calculation, and invalid values such as zero denominators or out-of-range selections produce a clear error instead of a misleading result.

Input query strings and outputs

Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.

Input query strings

2
  • ?n= Number of distinct objects n

    Number · Required · Default: 8

  • ?reflectionsSame= Treat mirror images as identical

    True or false · Optional · Default: false

Outputs

2
  • permutations Circular permutations

    Text · Primary output

  • formulaUsed Formula used

    Text

Inputs and results

The inputs are Number of distinct objects n, Treat mirror images as identical. Results include Circular permutations, Formula used.

Sources
  • No external reference is listed for this calculator. Its formula and variable definitions are shown above.
Limitations
  • Results depend on the selected method and input assumptions. Displayed decimals may be rounded; retain appropriate precision for later calculations.