{
  "id": "surface-area-calculator",
  "version": "2.0.0",
  "name": "Surface Area Calculator",
  "shortName": "Surface area",
  "description": "Calculate total and component surface areas for nine common three-dimensional shapes.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "surface area",
    "sphere surface area",
    "cone surface area",
    "cylinder surface area",
    "tank surface area",
    "capsule surface area",
    "frustum surface area",
    "ellipsoid surface area"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "migrated",
  "migratedDate": "2026-08-25",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/surface-area-calculator.json",
    "qualifiedReview": "pending",
    "qualifiedReviewer": null,
    "qualifiedReviewDate": null,
    "formulaVersion": "2.0.0",
    "referenceCoverage": "references-listed",
    "releaseTestScope": "Catalog and regression checks are not a professional formula audit; consult release evidence.",
    "historicalMetadataDate": "2026-08-25",
    "historicalMetadataNotice": "The imported date is not evidence of a completed human review."
  },
  "urls": {
    "page": "/calculator/surface-area-calculator/",
    "definition": "/calculator/surface-area-calculator/definition.json",
    "schema": "/calculator/surface-area-calculator/schema.json",
    "llms": "/calculator/surface-area-calculator/llms.txt",
    "legacyDefinition": "/calculator/surface-area-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/surface-area-calculator/?shape=sphere&sphereRadius=5",
  "queryParameters": {
    "shape": {
      "label": "Solid",
      "type": "select",
      "required": true,
      "default": "sphere"
    },
    "sphereRadius": {
      "label": "Sphere radius",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "shape",
        "equals": "sphere"
      }
    },
    "coneRadius": {
      "label": "Cone radius",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "shape",
        "equals": "cone"
      }
    },
    "coneHeight": {
      "label": "Cone height",
      "type": "number",
      "required": true,
      "default": 4,
      "showWhen": {
        "field": "shape",
        "equals": "cone"
      }
    },
    "cubeEdge": {
      "label": "Cube edge",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "shape",
        "equals": "cube"
      }
    },
    "cylinderRadius": {
      "label": "Cylinder radius",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "shape",
        "equals": "cylinder"
      }
    },
    "cylinderHeight": {
      "label": "Cylinder height",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "shape",
        "equals": "cylinder"
      }
    },
    "boxLength": {
      "label": "Tank length",
      "type": "number",
      "required": true,
      "default": 10,
      "showWhen": {
        "field": "shape",
        "equals": "box"
      }
    },
    "boxWidth": {
      "label": "Tank width",
      "type": "number",
      "required": true,
      "default": 6,
      "showWhen": {
        "field": "shape",
        "equals": "box"
      }
    },
    "boxHeight": {
      "label": "Tank height",
      "type": "number",
      "required": true,
      "default": 4,
      "showWhen": {
        "field": "shape",
        "equals": "box"
      }
    },
    "capsuleRadius": {
      "label": "Capsule radius",
      "type": "number",
      "required": true,
      "default": 2,
      "showWhen": {
        "field": "shape",
        "equals": "capsule"
      }
    },
    "capsuleHeight": {
      "label": "Cylinder-section height",
      "type": "number",
      "required": true,
      "default": 6,
      "showWhen": {
        "field": "shape",
        "equals": "capsule"
      }
    },
    "capBallRadius": {
      "label": "Ball radius",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "shape",
        "equals": "spherical-cap"
      }
    },
    "capHeight": {
      "label": "Cap height",
      "type": "number",
      "required": true,
      "default": 2,
      "showWhen": {
        "field": "shape",
        "equals": "spherical-cap"
      }
    },
    "frustumTopRadius": {
      "label": "Top radius",
      "type": "number",
      "required": true,
      "default": 2,
      "showWhen": {
        "field": "shape",
        "equals": "frustum"
      }
    },
    "frustumBottomRadius": {
      "label": "Bottom radius",
      "type": "number",
      "required": true,
      "default": 4,
      "showWhen": {
        "field": "shape",
        "equals": "frustum"
      }
    },
    "frustumHeight": {
      "label": "Frustum height",
      "type": "number",
      "required": true,
      "default": 6,
      "showWhen": {
        "field": "shape",
        "equals": "frustum"
      }
    },
    "ellipsoidA": {
      "label": "Ellipsoid axis a",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "shape",
        "equals": "ellipsoid"
      }
    },
    "ellipsoidB": {
      "label": "Ellipsoid axis b",
      "type": "number",
      "required": true,
      "default": 4,
      "showWhen": {
        "field": "shape",
        "equals": "ellipsoid"
      }
    },
    "ellipsoidC": {
      "label": "Ellipsoid axis c",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "shape",
        "equals": "ellipsoid"
      }
    }
  },
  "inputs": [
    {
      "id": "shape",
      "label": "Solid",
      "type": "select",
      "required": true,
      "defaultValue": "sphere",
      "options": [
        {
          "label": "Ball / sphere",
          "value": "sphere"
        },
        {
          "label": "Cone",
          "value": "cone"
        },
        {
          "label": "Cube",
          "value": "cube"
        },
        {
          "label": "Cylinder",
          "value": "cylinder"
        },
        {
          "label": "Rectangular tank",
          "value": "box"
        },
        {
          "label": "Capsule",
          "value": "capsule"
        },
        {
          "label": "Spherical cap",
          "value": "spherical-cap"
        },
        {
          "label": "Conical frustum",
          "value": "frustum"
        },
        {
          "label": "Ellipsoid",
          "value": "ellipsoid"
        }
      ],
      "width": "full"
    },
    {
      "id": "sphereRadius",
      "label": "Sphere radius",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "sphere"
      },
      "width": "half"
    },
    {
      "id": "coneRadius",
      "label": "Cone radius",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "cone"
      },
      "width": "half"
    },
    {
      "id": "coneHeight",
      "label": "Cone height",
      "type": "number",
      "required": true,
      "defaultValue": 4,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "cone"
      },
      "width": "half"
    },
    {
      "id": "cubeEdge",
      "label": "Cube edge",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "cube"
      },
      "width": "half"
    },
    {
      "id": "cylinderRadius",
      "label": "Cylinder radius",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "cylinder"
      },
      "width": "half"
    },
    {
      "id": "cylinderHeight",
      "label": "Cylinder height",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "cylinder"
      },
      "width": "half"
    },
    {
      "id": "boxLength",
      "label": "Tank length",
      "type": "number",
      "required": true,
      "defaultValue": 10,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "box"
      },
      "width": "half"
    },
    {
      "id": "boxWidth",
      "label": "Tank width",
      "type": "number",
      "required": true,
      "defaultValue": 6,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "box"
      },
      "width": "half"
    },
    {
      "id": "boxHeight",
      "label": "Tank height",
      "type": "number",
      "required": true,
      "defaultValue": 4,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "box"
      },
      "width": "half"
    },
    {
      "id": "capsuleRadius",
      "label": "Capsule radius",
      "type": "number",
      "required": true,
      "defaultValue": 2,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "capsule"
      },
      "width": "half"
    },
    {
      "id": "capsuleHeight",
      "label": "Cylinder-section height",
      "type": "number",
      "required": true,
      "defaultValue": 6,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "capsule"
      },
      "width": "half"
    },
    {
      "id": "capBallRadius",
      "label": "Ball radius",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "spherical-cap"
      },
      "width": "half"
    },
    {
      "id": "capHeight",
      "label": "Cap height",
      "type": "number",
      "required": true,
      "defaultValue": 2,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "spherical-cap"
      },
      "width": "half"
    },
    {
      "id": "frustumTopRadius",
      "label": "Top radius",
      "type": "number",
      "required": true,
      "defaultValue": 2,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "frustum"
      },
      "width": "half"
    },
    {
      "id": "frustumBottomRadius",
      "label": "Bottom radius",
      "type": "number",
      "required": true,
      "defaultValue": 4,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "frustum"
      },
      "width": "half"
    },
    {
      "id": "frustumHeight",
      "label": "Frustum height",
      "type": "number",
      "required": true,
      "defaultValue": 6,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "frustum"
      },
      "width": "half"
    },
    {
      "id": "ellipsoidA",
      "label": "Ellipsoid axis a",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "ellipsoid"
      },
      "width": "half"
    },
    {
      "id": "ellipsoidB",
      "label": "Ellipsoid axis b",
      "type": "number",
      "required": true,
      "defaultValue": 4,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "ellipsoid"
      },
      "width": "half"
    },
    {
      "id": "ellipsoidC",
      "label": "Ellipsoid axis c",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "shape",
        "equals": "ellipsoid"
      },
      "width": "half"
    }
  ],
  "outputs": [
    {
      "id": "surfaceArea",
      "label": "Total surface area",
      "format": "number",
      "primary": true,
      "digits": 6
    },
    {
      "id": "lateralArea",
      "label": "Lateral or curved area",
      "format": "number",
      "digits": 6
    },
    {
      "id": "baseArea",
      "label": "Base area",
      "format": "number",
      "digits": 6
    },
    {
      "id": "volume",
      "label": "Volume",
      "format": "number",
      "digits": 6
    },
    {
      "id": "shapeName",
      "label": "Solid",
      "format": "text"
    }
  ],
  "formula": {
    "expression": "Examples: sphere 4πr²; cone πr(r+√(r²+h²)); cylinder 2πr(r+h); box 2(lw+lh+wh)."
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "shape": "sphere",
        "sphereRadius": 5,
        "coneRadius": 3,
        "coneHeight": 4,
        "cubeEdge": 5,
        "cylinderRadius": 3,
        "cylinderHeight": 5,
        "boxLength": 10,
        "boxWidth": 6,
        "boxHeight": 4,
        "capsuleRadius": 2,
        "capsuleHeight": 6,
        "capBallRadius": 5,
        "capHeight": 2,
        "frustumTopRadius": 2,
        "frustumBottomRadius": 4,
        "frustumHeight": 6,
        "ellipsoidA": 3,
        "ellipsoidB": 4,
        "ellipsoidC": 5
      }
    }
  ],
  "sources": [
    {
      "label": "Calculator.net reference calculator",
      "url": "https://www.calculator.net/surface-area-calculator.html"
    }
  ]
}