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Field of View Calculator

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.

When to use

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.

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

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.

Inputs

Parameter	Type	Unit	Required	Description
`focal_length_mm`	number	mm	yes	Actual (not equivalent) focal length of the lens in millimetres. Range: ≥ 1, ≤ 5000
`sensor`	enum: full_frame \| aps_c \| aps_c_canon \| micro_four_thirds \| one_inch \| medium_format_44x33 \| smartphone_1_over_2_3		default full_frame	Sensor format preset providing the sensor width and height.
`sensor_width_mm`	number	mm	no	Optional sensor width in mm; overrides the sensor preset. Range: > 0, ≤ 200
`sensor_height_mm`	number	mm	no	Optional sensor height in mm; overrides the sensor preset. Range: > 0, ≤ 200
`subject_distance_m`	number	m	no	Optional distance to the subject plane; when given, the covered frame width and height at that distance are returned. Range: > 0, ≤ 100000

Outputs

Output	Type	Unit	Description
`horizontal_angle_degrees`	number	°	2·atan(sensor width / (2·f)).
`vertical_angle_degrees`	number	°	2·atan(sensor height / (2·f)).
`diagonal_angle_degrees`	number	°	2·atan(sensor diagonal / (2·f)); the figure lens makers usually quote.
`sensor_width_used_mm`	number	mm	Sensor width applied (preset or override).
`sensor_height_used_mm`	number	mm	Sensor height applied (preset or override).
`frame_width_m`	number	m	Scene width covered at subject_distance_m (only when given).
`frame_height_m`	number	m	Scene height covered at subject_distance_m (only when given).
`magnification`	number		Sensor width / frame width at the subject distance (only when given).

Example

50 mm on full frame: {"focal_length_mm":50,"sensor":"full_frame"} → {"horizontal_angle_degrees":39.6,"vertical_angle_degrees":26.99,"diagonal_angle_degrees":46.79}

200 mm on full frame, subject at 20 m: {"focal_length_mm":200,"sensor":"full_frame","subject_distance_m":20} → {"horizontal_angle_degrees":10.29,"vertical_angle_degrees":6.87,"frame_width_m":3.6,"frame_height_m":2.4}

GET https://tttkmbb.com/api/v1/calculate/field-of-view?focal_length_mm=50&sensor=full_frame

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/field-of-view (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/field-of-view · Markdown: https://tttkmbb.com/photography/field-of-view.md · JSON definition: https://tttkmbb.com/photography/field-of-view.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="field-of-view"
OpenAPI operationId: calculate_field_of_view
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Angle of view (photography) (reference)
Cambridge in Colour – Digital camera sensor sizes (reference)

FAQ

Why do lens makers quote a different angle?

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.

How do I use this for a crop-sensor camera?

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.

Related calculators

Crop Factor Calculator — Equivalent focal length that gives the same angle of view on full frame.
Depth of Field Calculator — How much of the covered scene is in focus.
Telescope Magnification Calculator — True field of view of a telescope and eyepiece.