{
  "id": "tv-size",
  "version": "9d8d35ce8396",
  "status": "published",
  "name": "TV Size Calculator",
  "question": "What TV size is right for my room?",
  "summary": "Recommends a TV screen size for your viewing distance from the SMPTE 30° and THX 40° viewing angles, and shows the viewing angle of a TV you already have in mind.",
  "category": "everyday-life",
  "url": "https://www.acalculator.org/everyday-life/tv-size-calculator",
  "markdown": "https://www.acalculator.org/everyday-life/tv-size-calculator.md",
  "kind": "function",
  "method": "Screen width = 2 × distance × tan(angle ÷ 2), at 30° (SMPTE) and 40° (THX); diagonal = width × √(16² + 9²) ÷ 16.",
  "assumptions": [
    "The TV is 16:9, as almost all TVs are, and you sit straight in front of the screen.",
    "The size is the diagonal of the visible picture, as TVs are sold.",
    "SMPTE’s 30° is a smallest comfortable size for a room; THX’s 40° is a cinema-like size."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "d": {
        "title": "Viewing distance",
        "description": "From your eyes, where you sit, to the screen.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.3048,
        "maximum": 30.48
      },
      "tv": {
        "title": "A TV you are looking at",
        "description": "Optional: the diagonal of a 16:9 TV, to see the viewing angle it gives.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.0254,
        "maximum": 25.4
      }
    }
  },
  "outputs": {
    "smpte": {
      "label": "Smallest size (SMPTE, 30°)",
      "description": "The 16:9 screen that fills a 30° viewing angle.",
      "format": "quantity",
      "unit": "in"
    },
    "thx": {
      "label": "Cinema size (THX, 40°)",
      "description": "The 16:9 screen that fills a 40° viewing angle.",
      "format": "quantity",
      "unit": "in"
    },
    "smpteWidth": {
      "label": "SMPTE screen width",
      "description": "2 × distance × tan 15°.",
      "format": "quantity",
      "unit": "in"
    },
    "angle": {
      "label": "Your TV’s viewing angle",
      "description": "2 × arctan(width ÷ (2 × distance)), in degrees.",
      "format": "number"
    },
    "verdict": {
      "label": "Your TV",
      "description": "Below 30°, from 30° to 40°, or above 40°.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "d": 2.4384
    },
    "outputs": {
      "smpte": 1.4992786809496756,
      "thx": 2.0365533024543394,
      "smpteWidth": 1.3067346216480993
    },
    "text": "At 8 ft, a TV of 59 in fills 30° of your view; 80.2 in fills 40°."
  },
  "examples": [
    {
      "given": {
        "d": 2.4384
      },
      "expect": {
        "smpte": 1.4992786809496754,
        "thx": 2.0365533024543394
      },
      "source": "Optimum HDTV viewing distance, Wikipedia (SMPTE: the screen should fill at least a 30° field of view; THX: about 40°), https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance (retrieved 2026-10-03); hand calculation in content.mdx: width 2 × 96 × tan 15° = 51.45 in, diagonal × 18.358 ÷ 16 = 59.0 in; THX 2 × 96 × tan 20° = 69.88 in wide, 80.2 in",
      "tolerance": 1e-12
    },
    {
      "given": {
        "d": 3,
        "tv": 1.651
      },
      "expect": {
        "smpte": 1.8445849913258803,
        "angle": 26.97288754134332,
        "verdict": "Smaller than SMPTE’s 30°: a bigger TV or a closer seat fills more of your view"
      },
      "source": "Optimum HDTV viewing distance, Wikipedia (SMPTE: the screen should fill at least a 30° field of view; THX: about 40°), https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance (retrieved 2026-10-03); hand calculation in content.mdx: SMPTE 2 × 300 × tan 15° = 160.8 cm wide, 184.5 cm (72.6 in); 65 in is 143.9 cm wide, angle 2 × arctan(143.9 ÷ 600) = 27.0°",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Optimum HDTV viewing distance, Wikipedia (SMPTE recommends that the screen fills at least a 30° field of view; THX recommends about 40°). https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance (retrieved 2026-10-03)"
  ],
  "related": [
    "screen-size",
    "projector-throw",
    "ppi"
  ],
  "changelog": []
}