{
  "slug": "triangle-area",
  "title": "Triangle Area Calculator",
  "heading": "Triangle Area Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/triangle-area",
  "summary": "Area from base and height, or from three sides.",
  "description": "Two methods in one: the classic half-base-times-height, or Heron's formula when you only know the three side lengths. Heron's also validates whether the sides can form a triangle at all.",
  "formula": "Area = ½ × base × height, or √(s(s−a)(s−b)(s−c)) where s is the semi-perimeter.",
  "dateModified": "2026-09-30",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=triangle-area",
  "inputs": [
    {
      "id": "method",
      "label": "Method",
      "kind": "select",
      "hint": null,
      "default": "base",
      "options": [
        {
          "value": "base",
          "label": "Base and height"
        },
        {
          "value": "heron",
          "label": "Three sides (Heron's)"
        }
      ]
    },
    {
      "id": "base",
      "label": "Base",
      "kind": "number",
      "hint": null,
      "default": 12,
      "unit": null,
      "min": 0,
      "max": null
    },
    {
      "id": "height",
      "label": "Height",
      "kind": "number",
      "hint": null,
      "default": 8,
      "unit": null,
      "min": 0,
      "max": null
    },
    {
      "id": "a",
      "label": "Side a",
      "kind": "number",
      "hint": null,
      "default": 5,
      "unit": null,
      "min": 0,
      "max": null
    },
    {
      "id": "b",
      "label": "Side b",
      "kind": "number",
      "hint": null,
      "default": 6,
      "unit": null,
      "min": 0,
      "max": null
    },
    {
      "id": "c",
      "label": "Side c",
      "kind": "number",
      "hint": null,
      "default": 7,
      "unit": null,
      "min": 0,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "area",
      "label": "Area",
      "format": "decimal",
      "hint": null,
      "primary": true
    },
    {
      "id": "valid",
      "label": "Note",
      "format": "raw",
      "hint": null,
      "primary": false
    },
    {
      "id": "perimeter",
      "label": "Perimeter",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "semi",
      "label": "Semi-perimeter",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "Method: Base and height",
      "Base: 12",
      "Height: 8",
      "Side a: 5",
      "Side b: 6",
      "Side c: 7"
    ],
    "outputs": [
      "Area: 48",
      "Note: Base × height method",
      "Perimeter: 0",
      "Semi-perimeter: 0"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter method.",
      "Enter base.",
      "Enter height.",
      "Enter side a.",
      "Enter side b.",
      "Enter side c.",
      "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": {
        "method": "base",
        "base": 7.199999999999999,
        "height": 8,
        "a": 3,
        "b": 3.5999999999999996,
        "c": 4.2
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "method": "base",
        "base": 12,
        "height": 8,
        "a": 5,
        "b": 6,
        "c": 7
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "method": "base",
        "base": 19.200000000000003,
        "height": 8,
        "a": 8,
        "b": 9.600000000000001,
        "c": 11.200000000000001
      }
    }
  ],
  "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 triangle area calculator work?",
      "a": "Two methods in one: the classic half-base-times-height, or Heron's formula when you only know the three side lengths. Heron's also validates whether the sides can form a triangle at all. The underlying maths is: Area = ½ × base × height, or √(s(s−a)(s−b)(s−c)) where s is the semi-perimeter."
    },
    {
      "q": "What do I need to enter?",
      "a": "6 values: method, base, height, side a, side b, and side 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 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/pythagorean",
    "https://www.revenuelab.fyi/toolbox/circle",
    "https://www.revenuelab.fyi/toolbox/square-footage"
  ],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Triangle Area Calculator (https://www.revenuelab.fyi/toolbox/triangle-area)"
}