{
  "id": "circular-permutation-calculator",
  "version": "1.0.0",
  "name": "Circular Permutation Calculator",
  "shortName": "Circular Permutation",
  "description": "Count arrangements of distinct objects around a circle when rotations are considered identical.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "circular",
    "permutation",
    "calculator",
    "circular permutation calculator"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "new",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/circular-permutation-calculator.json",
    "qualifiedReview": "pending",
    "qualifiedReviewer": null,
    "qualifiedReviewDate": null,
    "formulaVersion": "1.0.0",
    "referenceCoverage": "references-pending",
    "releaseTestScope": "Catalog and regression checks are not a professional formula audit; consult release evidence.",
    "historicalMetadataDate": "2026-09-01",
    "historicalMetadataNotice": "The imported date is not evidence of a completed human review."
  },
  "urls": {
    "page": "/calculator/circular-permutation-calculator/",
    "definition": "/calculator/circular-permutation-calculator/definition.json",
    "schema": "/calculator/circular-permutation-calculator/schema.json",
    "llms": "/calculator/circular-permutation-calculator/llms.txt",
    "legacyDefinition": "/calculator/circular-permutation-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/circular-permutation-calculator/?n=8&reflectionsSame=0",
  "queryParameters": {
    "n": {
      "label": "Number of distinct objects n",
      "type": "number",
      "required": true,
      "default": 8
    },
    "reflectionsSame": {
      "label": "Treat mirror images as identical",
      "type": "checkbox",
      "required": false,
      "default": false
    }
  },
  "inputs": [
    {
      "id": "n",
      "label": "Number of distinct objects n",
      "type": "number",
      "required": true,
      "defaultValue": 8,
      "min": 1,
      "max": 1000,
      "step": 1
    },
    {
      "id": "reflectionsSame",
      "label": "Treat mirror images as identical",
      "type": "checkbox",
      "defaultValue": false
    }
  ],
  "outputs": [
    {
      "id": "permutations",
      "label": "Circular permutations",
      "format": "text",
      "primary": true
    },
    {
      "id": "formulaUsed",
      "label": "Formula used",
      "format": "text"
    }
  ],
  "formula": {
    "expression": "rotational arrangements = (n − 1)!; with equivalent reflections divide by 2 for n > 2"
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "n": 8,
        "reflectionsSame": false
      }
    }
  ],
  "sources": []
}