How this instrument works
Field of view (more precisely called angle of view) is the angular extent of a scene that a camera captures onto its sensor, measured in degrees. It depends on two things only: the physical size of the imaging area doing the capturing, and the focal length of the lens projecting the image onto it. A physically large sensor paired with a short focal length sees a broad angle; a small one paired with a long focal length sees a narrow one.
The relationship is right-triangle trigonometry: half the sensor dimension and the focal length form the two legs of a right triangle, and the half-angle of view is the arctangent of their ratio. Doubling that dimension, or halving the focal length, widens the angle of view -- exactly why a 50mm lens looks 'normal' on a full-frame sensor but noticeably tighter on a smaller APS-C or Micro Four Thirds format.
This instrument computes the angle along whichever sensor dimension you enter -- use the width for horizontal field of view, the height for vertical, or the diagonal for the single number most often quoted in lens specifications. Enter dimensions in the same unit (millimetres) that both figures are normally specified in, and the result is independent of that unit as long as both match.
- Enter Sensor dimension (mm) -- the width, height or diagonal of your sensor or film format, in millimetres.
- Enter Focal length (mm) -- the lens's focal length, also in millimetres, matching the sensor dimension's unit.
- Read Field of view (degrees) beneath the inputs -- the full angular extent along the dimension you entered.
- To compare lenses across sensor formats, keep the sensor dimension fixed and vary only the focal length.
Worked example -- 50mm lens on a full-frame sensor
Enter a 36mm sensor dimension (the width of a full-frame 35mm sensor) and a 50mm focal length. Field of view comes out to 2 x atan(36 / (2 x 50)) = 39.5978 degrees -- the horizontal angle of view a 50mm 'normal' lens produces on a full-frame camera, close to what photographers describe as roughly matching natural human perspective.
Questions
How does field of view relate to a lens being 'wide-angle' or 'telephoto'?
A short focal length relative to sensor size produces a wide angle of view -- more scene fits in the frame -- which is what makes a lens 'wide-angle.' A long focal length relative to that same size narrows the angle of view, magnifying a smaller slice of the scene, which is what makes a lens 'telephoto.' The crossover point, often called a 'normal' lens, is roughly where focal length equals the diagonal measurement, producing an angle of view close to human perception.
Why does the same 50mm lens give a different field of view on different cameras?
Because field of view depends on sensor size as well as focal length, and sensors vary by camera format. A 50mm lens on a full-frame 36mm-wide sensor gives about 39.6 degrees of horizontal field of view, but the identical lens on a smaller APS-C chip sees a narrower slice of the scene -- the lens hasn't changed, only how much of its projected image circle that smaller chip captures.
Should I use sensor width, height or diagonal in this calculator?
It depends on which field of view you want: use the sensor's width for horizontal field of view, height for vertical field of view, or diagonal for the single figure most often quoted in camera and lens marketing. The formula is identical either way -- only the sensor dimension you enter changes which angle you get back.
Does field of view change if I switch from photo to video mode?
It can, if video mode uses a cropped portion of the sensor rather than the full imaging area -- many cameras record video from a smaller region than they use for stills, which is equivalent to a smaller sensor dimension and therefore a narrower field of view at the same focal length. Check your camera's specifications for its video crop, then enter that narrower dimension instead.
How is field of view different from angle of view?
In practice, photographers use the terms interchangeably, and this instrument's result is exactly what most sources call 'angle of view' -- the angular extent of the scene captured on the sensor. Some fields, like surveillance and machine vision, reserve 'field of view' for a linear measurement, like the width of the scene in metres at a given distance, but the underlying trigonometry is the same, just expressed in different units.