{
  "slug": "pythagorean",
  "title": "Pythagorean Theorem Calculator",
  "heading": "Pythagorean Theorem Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/pythagorean",
  "summary": "Find the missing side of a right triangle.",
  "description": "Enter any two sides of a right triangle and get the third, plus the angles and area. Leave the side you want to solve for at zero.",
  "formula": "a² + b² = c², where c is the hypotenuse.",
  "dateModified": "2026-09-30",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=pythagorean",
  "inputs": [
    {
      "id": "a",
      "label": "Side a",
      "kind": "number",
      "hint": null,
      "default": 3,
      "unit": null,
      "min": 0,
      "max": null
    },
    {
      "id": "b",
      "label": "Side b",
      "kind": "number",
      "hint": null,
      "default": 4,
      "unit": null,
      "min": 0,
      "max": null
    },
    {
      "id": "c",
      "label": "Hypotenuse c",
      "kind": "number",
      "hint": "Leave 0 to solve for it",
      "default": 0,
      "unit": null,
      "min": 0,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "c",
      "label": "Hypotenuse",
      "format": "decimal",
      "hint": null,
      "primary": true
    },
    {
      "id": "a",
      "label": "Side a",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "b",
      "label": "Side b",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "area",
      "label": "Area",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "perimeter",
      "label": "Perimeter",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "angleA",
      "label": "Angle opposite a (°)",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "angleB",
      "label": "Angle opposite b (°)",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "Side a: 3",
      "Side b: 4",
      "Hypotenuse c: 0"
    ],
    "outputs": [
      "Hypotenuse: 5",
      "Side a: 3",
      "Side b: 4",
      "Area: 6",
      "Perimeter: 12",
      "Angle opposite a (°): 36.87",
      "Angle opposite b (°): 53.13"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter side a.",
      "Enter side b.",
      "Enter hypotenuse c — Leave 0 to solve for it.",
      "Read your hypotenuse 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": {
        "a": 1.7999999999999998,
        "b": 2.4,
        "c": 0
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "a": 3,
        "b": 4,
        "c": 0
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "a": 4.800000000000001,
        "b": 6.4,
        "c": 0
      }
    }
  ],
  "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 pythagorean theorem calculator work?",
      "a": "Enter any two sides of a right triangle and get the third, plus the angles and area. Leave the side you want to solve for at zero. The underlying maths is: a² + b² = c², where c is the hypotenuse."
    },
    {
      "q": "What do I need to enter?",
      "a": "3 values: side a, side b, and hypotenuse c. 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 hypotenuse 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/slope",
    "https://www.revenuelab.fyi/toolbox/circle"
  ],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Pythagorean Theorem Calculator (https://www.revenuelab.fyi/toolbox/pythagorean)"
}