{
    "name": "Sphere Volume Calculator",
    "url": "https://calculators.geekmidst.com/calculators/sphere-volume-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/sphere-volume-calculator.md",
    "category": "Algebra, geometry & advanced math",
    "description": "Find the volume of a sphere or ball from its radius, diameter, circumference or surface area, with the hemisphere volume and capacity in litres.",
    "summary": "A sphere’s volume is ⁴⁄₃πr³. If you can only measure round the outside of a ball, the circumference gives the radius first.",
    "also_called": [
        "Ball volume 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": "given",
            "label": "I know the",
            "type": "select",
            "default": "radius",
            "options": {
                "radius": "Radius",
                "diameter": "Diameter",
                "circumference": "Circumference",
                "surface": "Surface area"
            }
        },
        {
            "name": "value",
            "label": "Value",
            "type": "number",
            "default": "5"
        },
        {
            "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": "volume",
            "label": "Volume",
            "format": "number"
        },
        {
            "key": "radius",
            "label": "Radius",
            "format": "number"
        },
        {
            "key": "diameter",
            "label": "Diameter",
            "format": "number"
        },
        {
            "key": "surface",
            "label": "Surface area 4πr²",
            "format": "number"
        },
        {
            "key": "hemisphere",
            "label": "Hemisphere volume",
            "format": "number"
        },
        {
            "key": "litres",
            "label": "Capacity in litres (0 if no unit chosen)",
            "format": "number"
        }
    ],
    "formula": {
        "text": "V = ⁴⁄₃πr³;  r = d/2 = C/(2π) = √(A/4π);  1 litre = 1,000 cm³",
        "variables": {
            "r": "radius",
            "d": "diameter",
            "C": "circumference (round the widest part)",
            "A": "surface area"
        }
    },
    "worked_example": {
        "inputs": {
            "given": "radius",
            "value": "5",
            "unit": "cm"
        },
        "steps": [
            "r³ = 5³ = 125.",
            "V = ⁴⁄₃ × π × 125 = 500π/3 ≈ 523.598776 cm³.",
            "In litres: 523.598776 ÷ 1,000 ≈ 0.5236 L."
        ],
        "result": "A sphere of radius 5 cm has a volume of about 523.6 cm³, a little over half a litre."
    },
    "interpretation": "Volume grows with the cube of the radius: a ball twice as wide holds eight times as much.",
    "assumptions": [
        "The object is a perfect sphere.",
        "For capacity, the value is the inside measurement."
    ],
    "limitations": [
        "Real balls and tanks have wall thickness; measure the inside radius for capacity."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "How do I measure the radius of a ball?",
            "answer": "Wrap a tape round its widest part to get the circumference, then choose Circumference; the radius is C ÷ 2π."
        },
        {
            "question": "What is the volume of a hemisphere?",
            "answer": "Half the sphere: ⅔πr³, shown as the hemisphere volume."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Volume Calculator",
            "url": "https://calculators.geekmidst.com/calculators/volume-calculator"
        },
        {
            "name": "Surface Area Calculator",
            "url": "https://calculators.geekmidst.com/calculators/surface-area-calculator"
        },
        {
            "name": "Torus Volume Calculator",
            "url": "https://calculators.geekmidst.com/calculators/torus-volume-calculator"
        },
        {
            "name": "Circle Calculator",
            "url": "https://calculators.geekmidst.com/calculators/circle-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}