{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"field-of-view"},"result":{"entity_type":"calculator","id":"field-of-view","calculator_id":"field-of-view","canonical_url":"https://tttkmbb.com/photography/field-of-view","name":"Field of View Calculator","title":"Field of View Calculator – Angle of View and Frame Coverage by Focal Length and Sensor","category":"photography","category_name":"Photography & Optics","tool_name":"calculate_field_of_view","featured_mcp_tool":false,"description":"Computes the horizontal, vertical and diagonal angles of view of a rectilinear lens from its focal length and the sensor dimensions, and the width and height of the scene covered at a given subject distance.","use_when":"You need the angle of view of a lens on a specific sensor, or how wide a scene (in metres) a lens covers at a known distance.","do_not_use_when":"You want the full-frame equivalent focal length (use crop-factor), or the lens is a fisheye, whose projection is not rectilinear.","inputs":[{"name":"focal_length_mm","label":"Focal length","type":"number","unit":"mm","required":true,"min":1,"max":5000,"description":"Actual (not equivalent) focal length of the lens in millimetres.","example":50},{"name":"sensor","label":"Sensor format","type":"enum","required":false,"default":"full_frame","values":[{"value":"full_frame","label":"Full frame (36 × 24 mm)","aliases":["ff","35mm","full-frame"]},{"value":"aps_c","label":"APS-C (23.5 × 15.6 mm; Nikon, Sony, Fujifilm, Pentax)","aliases":["apsc","aps-c","crop"]},{"value":"aps_c_canon","label":"APS-C Canon (22.3 × 14.9 mm)","aliases":["canon_aps_c","canon"]},{"value":"micro_four_thirds","label":"Micro Four Thirds (17.3 × 13 mm)","aliases":["mft","m43","four_thirds"]},{"value":"one_inch","label":"1-inch type (13.2 × 8.8 mm)","aliases":["1_inch","1-inch","type_1"]},{"value":"medium_format_44x33","label":"Medium format 44 × 33 (43.8 × 32.9 mm)","aliases":["medium_format","gfx","44x33"]},{"value":"smartphone_1_over_2_3","label":"Smartphone 1/2.3-inch (6.17 × 4.55 mm)","aliases":["smartphone","phone","1/2.3"]}],"description":"Sensor format preset providing the sensor width and height.","example":"full_frame"},{"name":"sensor_width_mm","label":"Sensor width","type":"number","unit":"mm","required":false,"max":200,"exclusive_min":0,"description":"Optional sensor width in mm; overrides the sensor preset.","example":36},{"name":"sensor_height_mm","label":"Sensor height","type":"number","unit":"mm","required":false,"max":200,"exclusive_min":0,"description":"Optional sensor height in mm; overrides the sensor preset.","example":24},{"name":"subject_distance_m","label":"Subject distance","type":"number","unit":"m","required":false,"max":100000,"exclusive_min":0,"description":"Optional distance to the subject plane; when given, the covered frame width and height at that distance are returned.","example":10}],"outputs":[{"name":"horizontal_angle_degrees","label":"Horizontal angle of view","type":"number","unit":"°","decimals":2,"description":"2·atan(sensor width / (2·f))."},{"name":"vertical_angle_degrees","label":"Vertical angle of view","type":"number","unit":"°","decimals":2,"description":"2·atan(sensor height / (2·f))."},{"name":"diagonal_angle_degrees","label":"Diagonal angle of view","type":"number","unit":"°","decimals":2,"description":"2·atan(sensor diagonal / (2·f)); the figure lens makers usually quote."},{"name":"sensor_width_used_mm","label":"Sensor width used","type":"number","unit":"mm","decimals":2,"description":"Sensor width applied (preset or override)."},{"name":"sensor_height_used_mm","label":"Sensor height used","type":"number","unit":"mm","decimals":2,"description":"Sensor height applied (preset or override)."},{"name":"frame_width_m","label":"Frame width at subject distance","type":"number","unit":"m","decimals":3,"description":"Scene width covered at subject_distance_m (only when given)."},{"name":"frame_height_m","label":"Frame height at subject distance","type":"number","unit":"m","decimals":3,"description":"Scene height covered at subject_distance_m (only when given)."},{"name":"magnification","label":"Magnification","type":"number","decimals":4,"description":"Sensor width / frame width at the subject distance (only when given)."}],"input_schema":{"type":"object","properties":{"focal_length_mm":{"description":"Actual (not equivalent) focal length of the lens in millimetres. Unit: mm.","type":"number","minimum":1,"maximum":5000,"examples":[50],"x-unit":"mm"},"sensor":{"description":"Sensor format preset providing the sensor width and height.","type":"string","enum":["full_frame","aps_c","aps_c_canon","micro_four_thirds","one_inch","medium_format_44x33","smartphone_1_over_2_3"],"default":"full_frame","examples":["full_frame"]},"sensor_width_mm":{"description":"Optional sensor width in mm; overrides the sensor preset. Unit: mm.","type":"number","maximum":200,"exclusiveMinimum":0,"examples":[36],"x-unit":"mm"},"sensor_height_mm":{"description":"Optional sensor height in mm; overrides the sensor preset. Unit: mm.","type":"number","maximum":200,"exclusiveMinimum":0,"examples":[24],"x-unit":"mm"},"subject_distance_m":{"description":"Optional distance to the subject plane; when given, the covered frame width and height at that distance are returned. Unit: m.","type":"number","maximum":100000,"exclusiveMinimum":0,"examples":[10],"x-unit":"m"}},"additionalProperties":false,"required":["focal_length_mm"]},"output_schema":{"type":"object","properties":{"horizontal_angle_degrees":{"description":"2·atan(sensor width / (2·f)). Unit: °.","type":"number","x-unit":"°"},"vertical_angle_degrees":{"description":"2·atan(sensor height / (2·f)). Unit: °.","type":"number","x-unit":"°"},"diagonal_angle_degrees":{"description":"2·atan(sensor diagonal / (2·f)); the figure lens makers usually quote. Unit: °.","type":"number","x-unit":"°"},"sensor_width_used_mm":{"description":"Sensor width applied (preset or override). Unit: mm.","type":"number","x-unit":"mm"},"sensor_height_used_mm":{"description":"Sensor height applied (preset or override). Unit: mm.","type":"number","x-unit":"mm"},"frame_width_m":{"description":"Scene width covered at subject_distance_m (only when given). Unit: m.","type":"number","x-unit":"m"},"frame_height_m":{"description":"Scene height covered at subject_distance_m (only when given). Unit: m.","type":"number","x-unit":"m"},"magnification":{"description":"Sensor width / frame width at the subject distance (only when given).","type":"number"}}},"formula":"angle = 2·atan(d / (2·focal_length_mm)) with d = sensor width, height or diagonal; frame_width_m = 2·subject_distance_m·tan(horizontal_angle / 2), frame_height_m likewise","method":"Rectilinear lens focused at infinity (thin-lens approximation); at close distances focus breathing and lens extension narrow the real angle slightly. Distance is measured from the lens' front nodal point, which is close to the sensor-plane distance for normal subjects.","sources":[{"name":"Wikipedia – Angle of view (photography)","url":"https://en.wikipedia.org/wiki/Angle_of_view_(photography)","type":"reference","retrieved_at":"2026-09-24"},{"name":"Cambridge in Colour – Digital camera sensor sizes","url":"https://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"50 mm on full frame","inputs":{"focal_length_mm":50,"sensor":"full_frame"},"expected":{"horizontal_angle_degrees":39.6,"vertical_angle_degrees":26.99,"diagonal_angle_degrees":46.79},"url":"https://tttkmbb.com/api/v1/calculate/field-of-view?focal_length_mm=50&sensor=full_frame"},{"name":"200 mm on full frame, subject at 20 m","inputs":{"focal_length_mm":200,"sensor":"full_frame","subject_distance_m":20},"expected":{"horizontal_angle_degrees":10.29,"vertical_angle_degrees":6.87,"frame_width_m":3.6,"frame_height_m":2.4},"url":"https://tttkmbb.com/api/v1/calculate/field-of-view?focal_length_mm=200&sensor=full_frame&subject_distance_m=20"}],"faq":[{"q":"Why do lens makers quote a different angle?","a":"Manufacturers quote the diagonal angle of view for the sensor the lens is designed for. The horizontal angle is what most people mean by 'how wide', so all three are returned."},{"q":"How do I use this for a crop-sensor camera?","a":"Enter the lens' actual focal length and pick the sensor preset (APS-C, Micro Four Thirds ...); the smaller sensor narrows the angle, which is the same effect the crop factor describes."}],"tags":["field of view","angle of view","focal length","frame coverage","sensor size","lens"],"related":[{"calculator_id":"crop-factor","reason":"Equivalent focal length that gives the same angle of view on full frame."},{"calculator_id":"depth-of-field","reason":"How much of the covered scene is in focus."},{"calculator_id":"telescope-magnification","reason":"True field of view of a telescope and eyepiece."}],"links":{"html":"https://tttkmbb.com/photography/field-of-view","markdown":"https://tttkmbb.com/photography/field-of-view.md","json":"https://tttkmbb.com/photography/field-of-view.json","api":"https://tttkmbb.com/api/v1/calculate/field-of-view","schema":"https://tttkmbb.com/api/v1/calculators/field-of-view","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:51:27Z","next_actions":[{"tool":"run_calculator","calculator_id":"field-of-view","reason":"Run Field of View Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/photography/field-of-view.md"}}