{
    "name": "Cylinder Surface Area Calculator",
    "url": "https://calculators.geekmidst.com/calculators/cylinder-surface-area-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/cylinder-surface-area-calculator.md",
    "category": "Algebra, geometry & advanced math",
    "description": "Find a cylinder’s curved (lateral) area, end area, total closed surface and open-top surface from its radius or diameter and height.",
    "summary": "A cylinder’s surface is a rolled-up rectangle (2πr × h) plus two circular ends. Pick the version you need: curved side only, open-topped or closed.",
    "also_called": [
        "Curved surface area of cylinder 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": "measure",
            "label": "I know the",
            "type": "segmented",
            "default": "radius",
            "options": {
                "radius": "Radius",
                "diameter": "Diameter"
            }
        },
        {
            "name": "r",
            "label": "Radius or diameter",
            "type": "number",
            "default": "3"
        },
        {
            "name": "h",
            "label": "Height",
            "type": "number",
            "default": "10"
        },
        {
            "name": "unit",
            "label": "Length unit",
            "type": "select",
            "default": "cm",
            "options": {
                "mm": "Millimetres (mm)",
                "cm": "Centimetres (cm)",
                "m": "Metres (m)",
                "km": "Kilometres (km)",
                "in": "Inches (in)",
                "ft": "Feet (ft)",
                "yd": "Yards (yd)",
                "u": "No unit (plain numbers)"
            }
        }
    ],
    "outputs": [
        {
            "key": "total",
            "label": "Total surface area (closed)",
            "format": "number"
        },
        {
            "key": "lateral",
            "label": "Lateral (curved) area 2πrh",
            "format": "number"
        },
        {
            "key": "base",
            "label": "Each circular end πr²",
            "format": "number"
        },
        {
            "key": "open_top",
            "label": "Open-top surface (side + one end)",
            "format": "number"
        },
        {
            "key": "volume",
            "label": "Volume πr²h",
            "format": "number"
        }
    ],
    "formula": {
        "text": "Lateral = 2πrh;  End = πr²;  Total = 2πrh + 2πr² = 2πr(r + h);  Open top = 2πrh + πr²",
        "variables": {
            "r": "radius (half the diameter)",
            "h": "height"
        }
    },
    "worked_example": {
        "inputs": {
            "measure": "radius",
            "r": "3",
            "h": "10",
            "unit": "cm"
        },
        "steps": [
            "Lateral = 2π × 3 × 10 = 60π ≈ 188.495559 cm².",
            "Each end = π × 3² = 9π ≈ 28.274334 cm².",
            "Total = 60π + 18π = 78π ≈ 245.044227 cm²."
        ],
        "result": "A closed cylinder 3 cm in radius and 10 cm tall has a surface area of about 245.04 cm²."
    },
    "interpretation": "Use the lateral area for a label or pipe insulation, the open-top figure for a cup or tank without a lid, and the total for a sealed can.",
    "assumptions": [
        "A right circular cylinder: the sides are perpendicular to circular ends.",
        "Sheet thickness, seams and overlaps are ignored."
    ],
    "limitations": [
        "For material orders, add an allowance for seams and waste."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is the curved area 2πrh?",
            "answer": "Unroll the side and it is a rectangle whose width is the circumference 2πr and whose height is h."
        },
        {
            "question": "How does a pipe with no ends work?",
            "answer": "Use the lateral area only; for the inside and outside of a thick pipe, use each radius separately."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Surface Area Calculator",
            "url": "https://calculators.geekmidst.com/calculators/surface-area-calculator"
        },
        {
            "name": "Volume Calculator",
            "url": "https://calculators.geekmidst.com/calculators/volume-calculator"
        },
        {
            "name": "Cone Surface Area Calculator",
            "url": "https://calculators.geekmidst.com/calculators/cone-surface-area-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}