{
  "id": "screen-size",
  "version": "2bd6ff2a317a",
  "status": "published",
  "name": "Screen Size Calculator",
  "question": "What are my screen size dimensions?",
  "summary": "Works out the width, height and area of a TV, monitor or phone screen from its diagonal size and aspect ratio, such as 16:9, 21:9 or 4:3.",
  "category": "everyday-life",
  "url": "https://www.acalculator.org/everyday-life/screen-size-calculator",
  "markdown": "https://www.acalculator.org/everyday-life/screen-size-calculator.md",
  "kind": "function",
  "method": "For an aspect ratio a : b and diagonal d: width = d × a ÷ √(a² + b²); height = d × b ÷ √(a² + b²).",
  "assumptions": [
    "The diagonal is the visible picture, corner to corner, as screen sizes are sold.",
    "A 21:9 screen is taken as exactly 21:9; real ultrawides are close to it (2560 × 1080 is 64:27, 2.37:1)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "d": {
        "title": "Diagonal size",
        "description": "The screen size, measured corner to corner across the visible picture.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.00254,
        "maximum": 50.8
      },
      "ar": {
        "title": "Aspect ratio",
        "description": "Width to height: 16:9 for TVs and most monitors, 16:10 for many laptops, 21:9 ultrawide.",
        "type": "string",
        "enum": [
          "16:9",
          "16:10",
          "21:9",
          "4:3",
          "2.39:1",
          "custom"
        ]
      },
      "rw": {
        "title": "Width",
        "description": "The width part of the ratio, for example 32 in 32:9.",
        "type": "number",
        "minimum": 0.01,
        "maximum": 1000
      },
      "rh": {
        "title": "Height",
        "description": "The height part of the ratio, for example 32 in 32:9.",
        "type": "number",
        "minimum": 0.01,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "width": {
      "label": "Width",
      "description": "Diagonal × a ÷ √(a² + b²) for a ratio a : b.",
      "format": "quantity",
      "unit": "in"
    },
    "height": {
      "label": "Height",
      "description": "Diagonal × b ÷ √(a² + b²).",
      "format": "quantity",
      "unit": "in"
    },
    "area": {
      "label": "Screen area",
      "description": "Width × height.",
      "format": "quantity",
      "unit": "in2"
    },
    "ratio": {
      "label": "Ratio",
      "description": "Width ÷ height, as x : 1.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "d": 0.6858,
      "ar": "16:9",
      "rw": 32,
      "rh": 9
    },
    "outputs": {
      "width": 0.5977265033600159,
      "height": 0.33622115814000897,
      "area": 0.2009682972106825,
      "ratio": "1.778:1"
    },
    "text": "A 27 in screen at 16:9 is 23.53 in wide and 13.24 in tall."
  },
  "examples": [
    {
      "given": {
        "d": 0.6858,
        "ar": "16:9"
      },
      "expect": {
        "width": 0.5977265033600159,
        "height": 0.3362211581400089,
        "area": 0.20096829721068246,
        "ratio": "1.778:1"
      },
      "source": "OpenStax, Prealgebra 2e, §9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem (a² + b² = c²), https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem (retrieved 2026-10-03); hand calculation in content.mdx: √(16² + 9²) = √337 = 18.358; 27 × 16 ÷ 18.358 = 23.53 in; 27 × 9 ÷ 18.358 = 13.24 in",
      "tolerance": 1e-12
    },
    {
      "given": {
        "d": 0.508,
        "ar": "4:3"
      },
      "expect": {
        "width": 0.4064,
        "height": 0.30479999999999996,
        "area": 0.12387071999999998,
        "ratio": "1.333:1"
      },
      "source": "OpenStax, Prealgebra 2e, §9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem (a² + b² = c²), https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem (retrieved 2026-10-03); hand calculation in content.mdx: √(4² + 3²) = 5; 20 × 4 ÷ 5 = 16 in; 20 × 3 ÷ 5 = 12 in"
    },
    {
      "given": {
        "d": 0.86,
        "ar": "custom",
        "rw": 32,
        "rh": 9
      },
      "expect": {
        "width": 0.8278798085323531,
        "height": 0.23284119614972432,
        "ratio": "3.556:1"
      },
      "source": "OpenStax, Prealgebra 2e, §9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem (a² + b² = c²), https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem (retrieved 2026-10-03); hand calculation in content.mdx: √(32² + 9²) = √1105 = 33.24; 86 × 32 ÷ 33.24 = 82.79 cm; 86 × 9 ÷ 33.24 = 23.28 cm",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, Prealgebra 2e, §9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem (a² + b² = c² for a right triangle). https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem (retrieved 2026-10-03)"
  ],
  "related": [
    "tv-size",
    "aspect-ratio",
    "ppi"
  ],
  "changelog": []
}