{
  "id": "projector-throw",
  "version": "16aa45482580",
  "status": "published",
  "name": "Projector Throw Calculator",
  "question": "What is my projector throw distance?",
  "summary": "Works out how far a projector must sit from the screen for a given image size, from its throw ratio and the aspect ratio, with the range for a zoom lens.",
  "category": "everyday-life",
  "url": "https://www.acalculator.org/everyday-life/projector-throw-calculator",
  "markdown": "https://www.acalculator.org/everyday-life/projector-throw-calculator.md",
  "kind": "function",
  "method": "Throw distance = throw ratio × image width; image width = diagonal × a ÷ √(a² + b²) for an aspect ratio a : b.",
  "assumptions": [
    "The distance is from the projector’s lens to the screen, with the projector square to the screen.",
    "The throw ratio is the maker’s figure for the image width; keystone or digital zoom changes the picture size."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "tr": {
        "title": "Throw ratio",
        "description": "Distance ÷ image width, from the projector’s specs; 1.5 is common.",
        "type": "number",
        "minimum": 0.05,
        "maximum": 20
      },
      "tr2": {
        "title": "Throw ratio, long end of zoom",
        "description": "Optional: for a zoom lens listed as 1.5 to 2.0, the larger number.",
        "type": "number",
        "minimum": 0.05,
        "maximum": 20
      },
      "d": {
        "title": "Image size (diagonal)",
        "description": "The picture you want, corner to corner; a screen’s size.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.0254,
        "maximum": 50.8
      },
      "ar": {
        "title": "Image aspect ratio",
        "description": "16:9 for most home projectors and screens; 2.39:1 for a cinema-scope screen.",
        "type": "string",
        "enum": [
          "16:9",
          "16:10",
          "21:9",
          "4:3",
          "2.39:1",
          "custom"
        ]
      },
      "rw": {
        "title": "Width",
        "description": "The width part of the image ratio.",
        "type": "number",
        "minimum": 0.01,
        "maximum": 1000
      },
      "rh": {
        "title": "Height",
        "description": "The height part of the image ratio.",
        "type": "number",
        "minimum": 0.01,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "distance": {
      "label": "Throw distance",
      "description": "Throw ratio × image width, lens to screen.",
      "format": "quantity",
      "unit": "ft"
    },
    "distanceMax": {
      "label": "Throw distance, long end of zoom",
      "description": "Long-end throw ratio × image width.",
      "format": "quantity",
      "unit": "ft"
    },
    "width": {
      "label": "Image width",
      "description": "Diagonal × a ÷ √(a² + b²) for an aspect ratio a : b.",
      "format": "quantity",
      "unit": "in"
    },
    "height": {
      "label": "Image height",
      "description": "Diagonal × b ÷ √(a² + b²).",
      "format": "quantity",
      "unit": "in"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "tr": 1.5,
      "d": 2.54,
      "ar": "16:9",
      "rw": 16,
      "rh": 9
    },
    "outputs": {
      "distance": 3.3207027964445324,
      "width": 2.213801864296355,
      "height": 1.2452635486666996
    },
    "text": "A 100 in image at a throw ratio of 1.5 needs a throw distance of 10.89 ft."
  },
  "examples": [
    {
      "given": {
        "tr": 1.5,
        "d": 2.54,
        "ar": "16:9"
      },
      "expect": {
        "width": 2.213801864296355,
        "distance": 3.320702796444533
      },
      "source": "Throw (projector), Wikipedia (throw ratio = distance from the lens to the screen ÷ screen width), https://en.wikipedia.org/wiki/Throw_(projector) (retrieved 2026-10-03); hand calculation in content.mdx: width 100 × 16 ÷ √337 = 87.16 in; distance 1.5 × 87.16 = 130.7 in = 10.89 ft",
      "tolerance": 1e-12
    },
    {
      "given": {
        "tr": 2,
        "d": 1.905,
        "ar": "4:3"
      },
      "expect": {
        "width": 1.524,
        "height": 1.143,
        "distance": 3.048
      },
      "source": "Throw (projector), Wikipedia (throw ratio = distance from the lens to the screen ÷ screen width), https://en.wikipedia.org/wiki/Throw_(projector) (retrieved 2026-10-03) (a 2.0 ratio puts a 60 in wide image 120 in away); hand calculation in content.mdx: 75 × 4 ÷ 5 = 60 in wide"
    },
    {
      "given": {
        "tr": 1.36,
        "tr2": 2.18,
        "d": 3,
        "ar": "16:9"
      },
      "expect": {
        "distance": 3.5560281914681613,
        "distanceMax": 5.7001040127945535
      },
      "source": "Throw (projector), Wikipedia (throw ratio = distance from the lens to the screen ÷ screen width), https://en.wikipedia.org/wiki/Throw_(projector) (retrieved 2026-10-03); hand calculation in content.mdx: width 300 × 16 ÷ √337 = 261.47 cm; 1.36 × 261.47 = 355.6 cm; 2.18 × 261.47 = 570.0 cm",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Throw (projector), Wikipedia (throw ratio R = D ÷ W, the distance from the lens to the screen over the screen width; a 2.0 ratio and a 60 in wide screen need 120 in). https://en.wikipedia.org/wiki/Throw_(projector) (retrieved 2026-10-03)"
  ],
  "related": [
    "tv-size",
    "screen-size",
    "aspect-ratio"
  ],
  "changelog": []
}