{
  "id": "field-of-view",
  "version": "50e3c654cb71",
  "status": "published",
  "name": "Field of View Calculator",
  "question": "What is my lens’s FOV?",
  "summary": "Works out a lens’s horizontal, vertical and diagonal field of view (FOV) from the sensor size and focal length, the area it covers at a distance, and converts a screen FOV between vertical and horizontal for an aspect ratio.",
  "category": "physics",
  "url": "https://www.acalculator.org/physics/field-of-view-calculator",
  "markdown": "https://www.acalculator.org/physics/field-of-view-calculator.md",
  "kind": "function",
  "method": "FOV = 2 × arctan(sensor size ÷ (2 × focal length)), for the width, height and diagonal (√(w² + h²)) of the sensor; covered width = distance × sensor width ÷ focal length. Screen: tan(h ÷ 2) = tan(v ÷ 2) × aspect width ÷ aspect height.",
  "assumptions": [
    "A rectilinear (not fisheye) lens, focused far away: the image forms one focal length behind the lens. Close focusing narrows the view a little.",
    "Type the real focal length and the real sensor size, not a 35 mm equivalent.",
    "The screen mode uses a flat (rectilinear) projection, as games and 3D software do."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "mode": {
        "title": "Find",
        "description": "A camera lens’s field of view, or a screen’s horizontal field of view from its vertical one (or back).",
        "type": "string",
        "enum": [
          "lens",
          "screen"
        ]
      },
      "f": {
        "title": "Focal length",
        "description": "The lens’s focal length, as marked on the lens (not the 35 mm equivalent).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 10
      },
      "sw": {
        "title": "Sensor width",
        "description": "The width of the camera’s sensor or film frame (36 mm for full frame).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 10
      },
      "sh": {
        "title": "Sensor height",
        "description": "The height of the sensor or film frame (24 mm for full frame).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 10
      },
      "d": {
        "title": "Subject distance",
        "description": "Optional: how far away the subject is, to see the width and height the photo covers there.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "k": {
        "title": "I know the",
        "description": "Which field of view you know: the vertical or the horizontal one.",
        "type": "string",
        "enum": [
          "v",
          "h"
        ]
      },
      "fov": {
        "title": "Field of view",
        "description": "The field of view you know, in degrees.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "angle",
        "exclusiveMinimum": 0,
        "exclusiveMaximum": 3.141592653589793
      },
      "aw": {
        "title": "Aspect width",
        "description": "The width part of the screen’s aspect ratio, such as 16 in 16:9.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000
      },
      "ah": {
        "title": "Aspect height",
        "description": "The height part of the aspect ratio, such as 9 in 16:9.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "hfov": {
      "label": "Horizontal FOV",
      "description": "The angle the picture covers from side to side.",
      "format": "quantity",
      "unit": "deg"
    },
    "vfov": {
      "label": "Vertical FOV",
      "description": "The angle the picture covers from top to bottom.",
      "format": "quantity",
      "unit": "deg"
    },
    "dfov": {
      "label": "Diagonal FOV",
      "description": "The angle the picture covers from corner to corner.",
      "format": "quantity",
      "unit": "deg"
    },
    "width": {
      "label": "Width covered",
      "description": "The width of the scene in the picture at the subject distance.",
      "format": "quantity",
      "unit": "ft"
    },
    "height": {
      "label": "Height covered",
      "description": "The height of the scene in the picture at the subject distance.",
      "format": "quantity",
      "unit": "ft"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "mode": "lens",
      "f": 0.05,
      "sw": 0.036000000000000004,
      "sh": 0.024,
      "k": "v",
      "fov": 1.0471975511965976,
      "aw": 16,
      "ah": 9
    },
    "outputs": {
      "hfov": 0.6911111611634243,
      "vfov": 0.47108996144172666,
      "dfov": 0.8166919752489159
    },
    "text": "The field of view is 39.6° across, 26.99° high and 46.79° on the diagonal."
  },
  "examples": [
    {
      "given": {
        "mode": "lens",
        "f": 0.05,
        "sw": 0.036000000000000004,
        "sh": 0.024
      },
      "expect": {
        "hfov": 0.6911111611634243,
        "vfov": 0.47108996144172666,
        "dfov": 0.8166919752489159
      },
      "source": "Wikipedia, Angle of view (photography) (α = 2 arctan(d ÷ 2f); a 50 mm lens on a 36 × 24 mm frame: 39.6° horizontal, 27.0° vertical, 46.8° diagonal). https://en.wikipedia.org/wiki/Angle_of_view_(photography), retrieved 2026-10-02: 39.6°, 27.0° and 46.8°; OpenStax, University Physics Volume 3, §2.6 The Camera (thin lens 1/f = 1/dₒ + 1/dᵢ: a distant object images at the focal length). https://openstax.org/books/university-physics-volume-3/pages/2-6-the-camera, retrieved 2026-10-02",
      "tolerance": 1e-12
    },
    {
      "given": {
        "mode": "lens",
        "f": 0.024,
        "sw": 0.036000000000000004,
        "sh": 0.024,
        "d": 3.048
      },
      "expect": {
        "hfov": 1.2870022175865687,
        "width": 4.572,
        "height": 3.048
      },
      "source": "hand calculation in content.mdx: 2 arctan(36 ÷ 48) = 73.74°; at 10 ft the picture is 10 × 36 ÷ 24 = 15 ft wide and 10 ft high; OpenStax, University Physics Volume 3, §2.6 The Camera (thin lens 1/f = 1/dₒ + 1/dᵢ: a distant object images at the focal length). https://openstax.org/books/university-physics-volume-3/pages/2-6-the-camera, retrieved 2026-10-02",
      "tolerance": 1e-12
    },
    {
      "given": {
        "mode": "screen",
        "k": "v",
        "fov": 1.0471975511965976,
        "aw": 16,
        "ah": 9
      },
      "expect": {
        "hfov": 1.5968513788836172,
        "vfov": 1.0471975511965976
      },
      "source": "hand calculation in content.mdx: 2 arctan(tan 30° × 16 ÷ 9) = 2 arctan(1.0264) = 91.49°",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 3, §2.6 The Camera (thin-lens equation 1/f = 1/dₒ + 1/dᵢ; a distant object images at the focal length). https://openstax.org/books/university-physics-volume-3/pages/2-6-the-camera (retrieved 2026-10-02)",
    "Wikipedia, Angle of view (photography): α = 2 arctan(d ÷ 2f); a 50 mm lens on a 36 × 24 mm frame covers about 39.6° horizontally, 27.0° vertically and 46.8° diagonally. https://en.wikipedia.org/wiki/Angle_of_view_(photography) (retrieved 2026-10-02)"
  ],
  "related": [
    "aspect-ratio",
    "angle",
    "wavelength"
  ],
  "changelog": []
}