{
  "id": "cubic-equation-3rd-order-polynomial-calculator",
  "version": "1.0.0",
  "name": "Cubic Equation Calculator - 3rd Order Polynomial",
  "shortName": "Cubic Equation Calculator - 3rd Order Poly",
  "description": "Solve a cubic polynomial ax³ + bx² + cx + d = 0 for all real or complex roots.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "cubic",
    "equation",
    "calculator",
    "3rd",
    "order",
    "polynomial",
    "cubic equation 3rd order polynomial calculator"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "new",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/cubic-equation-3rd-order-polynomial-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/cubic-equation-3rd-order-polynomial-calculator/",
    "definition": "/calculator/cubic-equation-3rd-order-polynomial-calculator/definition.json",
    "schema": "/calculator/cubic-equation-3rd-order-polynomial-calculator/schema.json",
    "llms": "/calculator/cubic-equation-3rd-order-polynomial-calculator/llms.txt",
    "legacyDefinition": "/calculator/cubic-equation-3rd-order-polynomial-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/cubic-equation-3rd-order-polynomial-calculator/?a=1&b=-6&c=11&d=-6",
  "queryParameters": {
    "a": {
      "label": "Coefficient a",
      "type": "number",
      "required": true,
      "default": 1
    },
    "b": {
      "label": "Coefficient b",
      "type": "number",
      "required": true,
      "default": -6
    },
    "c": {
      "label": "Coefficient c",
      "type": "number",
      "required": true,
      "default": 11
    },
    "d": {
      "label": "Coefficient d",
      "type": "number",
      "required": true,
      "default": -6
    }
  },
  "inputs": [
    {
      "id": "a",
      "label": "Coefficient a",
      "type": "number",
      "required": true,
      "defaultValue": 1,
      "step": 0.001
    },
    {
      "id": "b",
      "label": "Coefficient b",
      "type": "number",
      "required": true,
      "defaultValue": -6,
      "step": 0.001
    },
    {
      "id": "c",
      "label": "Coefficient c",
      "type": "number",
      "required": true,
      "defaultValue": 11,
      "step": 0.001
    },
    {
      "id": "d",
      "label": "Coefficient d",
      "type": "number",
      "required": true,
      "defaultValue": -6,
      "step": 0.001
    }
  ],
  "outputs": [
    {
      "id": "roots",
      "label": "Roots",
      "format": "text",
      "primary": true
    },
    {
      "id": "discriminant",
      "label": "Cubic discriminant",
      "format": "number",
      "digits": 8
    },
    {
      "id": "classification",
      "label": "Root classification",
      "format": "text"
    }
  ],
  "formula": {
    "expression": "roots solve ax³ + bx² + cx + d = 0 using the depressed-cubic (Cardano) form"
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "a": 1,
        "b": -6,
        "c": 11,
        "d": -6
      }
    }
  ],
  "sources": []
}