CALCULATORS / OPTICS, IMAGING AND ILLUMINATION

Camera field of view calculator

Pinhole camera, angular FOV from sensor and focal length

optics-field-of-view.napkin / editable

Scene coverage comes from your source’s halfWidthAt function. Change focal length or sensor width to change the view cone. Lens distortion and focus effects are omitted.

OPTICS / RAY SCHEMATICSAME SOURCE

Change an input to see the consequences.

field of view1.35 rad✓ passes

BASELINE INPUTS

sensorWidth6.4 mm315focalLength4 mm220distance1000 mm1005000

CALCULATED

fieldOfView1.3495 rad

sceneWidth1600 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Pinhole camera, angular FOV from sensor and focal length
sensorWidth = 6.4 mm in 3..15
focalLength = 4 mm in 2..20
fieldOfView := 2 * atan(sensorWidth/(2*focalLength)) [rad]
check field of view: fieldOfView >= 0.5 rad
scenario telephoto: focalLength = 12 mm

# Scene coverage at a chosen distance, for an ideal rectilinear pinhole camera.
distance = 1000 mm in 100..5000
sceneWidth := distance * sensorWidth / focalLength [mm]
halfWidthAt(x: mm) := x * tan(fieldOfView/2) [mm]

Calculated from your source · not saved

Baseline · Baseline

field of view1.35 rad ✓ passes

telephoto · telephoto

field of view0.52 rad ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

field of view: fieldOfView = 2 * atan(sensorWidth/(2*focalLength)) [rad]
scene width: sceneWidth = distance * sensorWidth / focalLength [mm]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

sensor width: 6.4 mm
focal length: 4 mm
distance: 1000 mm

Calculated

field of view: 1.34948 rad
scene width: 1600 mm

Assumptions and limits

Pinhole camera, angular FOV from sensor and focal length

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Camera field of view. Inputs: sensor size; focal length; working distance. Outputs: angular and linear field of view. Model scope: Paraxial geometry or calibrated radiometric/photometric models. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: sensor size, focal length, working distance
Outputs: angular and linear field of view
Modes: calculate, compare, sweep
Drawing: Ray diagram and camera view

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS