{
    "name": "Surface Area Calculator",
    "url": "https://calculators.geekmidst.com/calculators/surface-area-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/surface-area-calculator.md",
    "category": "Algebra, geometry & advanced math",
    "description": "Total, lateral and base surface area of a sphere, hemisphere, cube, rectangular box, cylinder, cone or square pyramid, with the volume too.",
    "summary": "Surface area is the total area of every face or curved surface of a solid: the amount of paint, wrapping or sheet material needed to cover it.",
    "also_called": [
        "Total surface area calculator",
        "Lateral area calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "shape",
            "label": "Shape",
            "type": "select",
            "default": "cylinder",
            "options": {
                "sphere": "Sphere",
                "hemisphere": "Hemisphere (closed)",
                "cube": "Cube",
                "box": "Rectangular box (cuboid)",
                "cylinder": "Cylinder (closed)",
                "cone": "Cone (with base)",
                "pyramid": "Square pyramid"
            }
        },
        {
            "name": "sphere_r",
            "label": "Radius",
            "type": "number",
            "default": "3",
            "shown_when": {
                "shape": "sphere"
            }
        },
        {
            "name": "hemi_r",
            "label": "Radius",
            "type": "number",
            "default": "3",
            "shown_when": {
                "shape": "hemisphere"
            }
        },
        {
            "name": "cube_a",
            "label": "Edge length",
            "type": "number",
            "default": "3",
            "shown_when": {
                "shape": "cube"
            }
        },
        {
            "name": "box_l",
            "label": "Length",
            "type": "number",
            "default": "4",
            "shown_when": {
                "shape": "box"
            }
        },
        {
            "name": "box_w",
            "label": "Width",
            "type": "number",
            "default": "3",
            "shown_when": {
                "shape": "box"
            }
        },
        {
            "name": "box_h",
            "label": "Height",
            "type": "number",
            "default": "2",
            "shown_when": {
                "shape": "box"
            }
        },
        {
            "name": "cyl_r",
            "label": "Radius",
            "type": "number",
            "default": "3",
            "shown_when": {
                "shape": "cylinder"
            }
        },
        {
            "name": "cyl_h",
            "label": "Height",
            "type": "number",
            "default": "10",
            "shown_when": {
                "shape": "cylinder"
            }
        },
        {
            "name": "cone_r",
            "label": "Base radius",
            "type": "number",
            "default": "3",
            "shown_when": {
                "shape": "cone"
            }
        },
        {
            "name": "cone_h",
            "label": "Perpendicular height",
            "type": "number",
            "default": "4",
            "shown_when": {
                "shape": "cone"
            }
        },
        {
            "name": "pyr_a",
            "label": "Base edge",
            "type": "number",
            "default": "6",
            "shown_when": {
                "shape": "pyramid"
            }
        },
        {
            "name": "pyr_h",
            "label": "Perpendicular height",
            "type": "number",
            "default": "4",
            "shown_when": {
                "shape": "pyramid"
            }
        }
    ],
    "outputs": [
        {
            "key": "total",
            "label": "Total surface area",
            "format": "number"
        },
        {
            "key": "lateral",
            "label": "Lateral (side or curved) area",
            "format": "number"
        },
        {
            "key": "base",
            "label": "Base area (all bases)",
            "format": "number"
        },
        {
            "key": "volume",
            "label": "Volume",
            "format": "number"
        }
    ],
    "formula": {
        "text": "Sphere 4πr²;  hemisphere 3πr²;  cube 6a²;  box 2(lw + lh + wh);  cylinder 2πr(r + h);  cone πr(r + s), s = √(r² + h²);  square pyramid a² + 2a√(h² + (a/2)²)",
        "variables": {
            "r": "radius",
            "h": "perpendicular height",
            "a": "edge length",
            "l, w": "length and width",
            "s": "slant height"
        }
    },
    "worked_example": {
        "inputs": {
            "shape": "cylinder",
            "sphere_r": "3",
            "hemi_r": "3",
            "cube_a": "3",
            "box_l": "4",
            "box_w": "3",
            "box_h": "2",
            "cyl_r": "3",
            "cyl_h": "10",
            "cone_r": "3",
            "cone_h": "4",
            "pyr_a": "6",
            "pyr_h": "4"
        },
        "steps": [
            "Curved side: 2π × 3 × 10 = 60π ≈ 188.4956.",
            "Two ends: 2 × π × 3² = 18π ≈ 56.5487.",
            "Total: 78π ≈ 245.0442."
        ],
        "result": "A closed cylinder of radius 3 and height 10 has a surface area of about 245.04 square units."
    },
    "interpretation": "Use the lateral area for open shapes, such as a pipe or a tube without ends, and the total for closed containers. Units are the square of the length unit you entered.",
    "assumptions": [
        "Ideal solids with straight sides; the cone and pyramid are right (apex above the centre of the base).",
        "Heights are perpendicular heights, not slant heights."
    ],
    "limitations": [
        "Material estimates need extra for seams, overlaps and waste."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "What is the difference between lateral and total surface area?",
            "answer": "Lateral area excludes the base or bases; total area includes them. For a can, the label covers the lateral area."
        },
        {
            "question": "I only know the slant height of a cone. What now?",
            "answer": "Perpendicular height h = √(s² − r²). Enter that value as the height."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Circle Calculator",
            "url": "https://calculators.geekmidst.com/calculators/circle-calculator"
        },
        {
            "name": "Concrete Calculator",
            "url": "https://calculators.geekmidst.com/calculators/concrete-calculator"
        },
        {
            "name": "Pythagorean Theorem Calculator",
            "url": "https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}