{
    "name": "Circle Calculator",
    "url": "https://calculators.geekmidst.com/calculators/circle-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/circle-calculator.md",
    "category": "Algebra, geometry & advanced math",
    "description": "Enter any one of a circle’s radius, diameter, circumference or area and get the other three, using π to full precision.",
    "summary": "Every measurement of a circle follows from its radius, so knowing any one of radius, diameter, circumference or area gives you the rest.",
    "also_called": [
        "Circumference calculator",
        "Area of a circle 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",
                "area": "Area"
            }
        },
        {
            "name": "value",
            "label": "Value",
            "type": "number",
            "default": "5"
        }
    ],
    "outputs": [
        {
            "key": "area",
            "label": "Area",
            "format": "number"
        },
        {
            "key": "radius",
            "label": "Radius",
            "format": "number"
        },
        {
            "key": "diameter",
            "label": "Diameter",
            "format": "number"
        },
        {
            "key": "circumference",
            "label": "Circumference",
            "format": "number"
        }
    ],
    "formula": {
        "text": "d = 2r;  C = 2πr = πd;  A = πr²;  r = C ÷ 2π = √(A ÷ π)",
        "variables": {
            "r": "radius",
            "d": "diameter",
            "C": "circumference",
            "A": "area",
            "π": "3.14159265…"
        }
    },
    "worked_example": {
        "inputs": {
            "given": "radius",
            "value": "5"
        },
        "steps": [
            "Diameter = 2 × 5 = 10.",
            "Circumference = 2π × 5 = 10π ≈ 31.415927.",
            "Area = π × 5² = 25π ≈ 78.539816."
        ],
        "result": "A circle of radius 5 has diameter 10, circumference 31.42 and area 78.54 square units."
    },
    "interpretation": "Area grows with the square of the radius: doubling the diameter of a pizza gives four times as much pizza.",
    "assumptions": [
        "A perfect circle in a flat plane."
    ],
    "limitations": [
        "Results are rounded to 6 decimal places."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why does 3.14 give a slightly different answer?",
            "answer": "3.14 is π rounded to two decimals, about 0.05% low. This calculator uses π to double precision."
        },
        {
            "question": "How do I get the area from the diameter?",
            "answer": "Halve the diameter to get the radius, then A = πr², or directly A = πd² ÷ 4."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Surface Area Calculator",
            "url": "https://calculators.geekmidst.com/calculators/surface-area-calculator"
        },
        {
            "name": "Concrete Calculator",
            "url": "https://calculators.geekmidst.com/calculators/concrete-calculator"
        },
        {
            "name": "Length Converter",
            "url": "https://calculators.geekmidst.com/calculators/length-converter"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}