{
  "slug": "circle",
  "title": "Circle Calculator",
  "heading": "Circle Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/circle",
  "summary": "Radius, diameter, circumference, and area from any one value.",
  "description": "Enter whichever measurement you have and the rest follow. Useful for everything from pipe sizing to working out how much edging a round garden bed needs.",
  "formula": "C = 2πr. A = πr².",
  "dateModified": "2026-09-30",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=circle",
  "inputs": [
    {
      "id": "known",
      "label": "What do you know?",
      "kind": "select",
      "hint": null,
      "default": "radius",
      "options": [
        {
          "value": "radius",
          "label": "Radius"
        },
        {
          "value": "diameter",
          "label": "Diameter"
        },
        {
          "value": "circumference",
          "label": "Circumference"
        },
        {
          "value": "area",
          "label": "Area"
        }
      ]
    },
    {
      "id": "value",
      "label": "Value",
      "kind": "number",
      "hint": null,
      "default": 10,
      "unit": null,
      "min": 0,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "area",
      "label": "Area",
      "format": "decimal",
      "hint": null,
      "primary": true
    },
    {
      "id": "radius",
      "label": "Radius",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "diameter",
      "label": "Diameter",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "circumference",
      "label": "Circumference",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "What do you know?: Radius",
      "Value: 10"
    ],
    "outputs": [
      "Area: 314.1593",
      "Radius: 10",
      "Diameter: 20",
      "Circumference: 62.8319"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter what do you know?.",
      "Enter value.",
      "Read your area on the right — it updates as you type.",
      "Hit Share to keep the scenario or send it to someone."
    ]
  },
  "scenarios": [
    {
      "name": "Conservative",
      "description": "Lower-end numbers — what if things land soft?",
      "values": {
        "known": "radius",
        "value": 6
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "known": "radius",
        "value": 10
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "known": "radius",
        "value": 16
      }
    }
  ],
  "limitations": [
    "Results are rounded for display; the underlying calculation keeps full precision.",
    "Very large or very small inputs may hit floating-point limits in the browser.",
    "Inputs outside the accepted range are clamped rather than rejected."
  ],
  "faq": [
    {
      "q": "How does the circle calculator work?",
      "a": "Enter whichever measurement you have and the rest follow. Useful for everything from pipe sizing to working out how much edging a round garden bed needs. The underlying maths is: C = 2πr. A = πr²."
    },
    {
      "q": "What do I need to enter?",
      "a": "2 values: what do you know?, and value. Each field starts with a sensible default, so you can change one number at a time and watch the result move."
    },
    {
      "q": "What does the area result mean?",
      "a": "It is returned as a decimal number and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds."
    },
    {
      "q": "Is this calculator free, and do I need an account?",
      "a": "Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser."
    },
    {
      "q": "How accurate is the result?",
      "a": "It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision."
    },
    {
      "q": "Who is this tool for?",
      "a": "It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet."
    }
  ],
  "related": [
    "https://www.revenuelab.fyi/toolbox/triangle-area",
    "https://www.revenuelab.fyi/toolbox/cylinder-volume",
    "https://www.revenuelab.fyi/toolbox/square-footage"
  ],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Circle Calculator (https://www.revenuelab.fyi/toolbox/circle)"
}