Field of view and focal length

Written by Paul Bourke
April 2003

See also: Changing to/from vertical/horizontal aperture

Camera and photography people tend to talk about lens characteristics in terms of "focal distance" while those involved in synthetic image generator (such as raytracing) tend to think in terms of field of view for a pinhole camera model, or aperture (different meaning to camera terminology). The following discusses (an idealised at least) way to estimate the field of from the focal distance. view

The focal length of a lens is an inherent property of the lens, it is the distance from the center of the lens to the point at which objects at infinity focus. Note: this is referred to as a rectilinear lens.

That there are three possible ways to measure field of view: horizontally, vertically, or diagonally. The horizontal field of view will be used here, the other two can be derived from this. From the figure above, simple geometry gives the horizontal field of view

horizontal field of view = 2 atan(0.5 width / focallength)

where "width" is the horizontal width of the sensor (projection plane). So for example, for a 35mm film (frame is 24mm x 36mm), and a 20mm (focal length) lens, the horizontal aperture would be almost 84 degrees (vertical aperture of 62 degrees). The above formula can similarly be used to calculate the vertical aperture using the vertical height of the film area, namely:

vertical field of view = 2 atan(0.5 height / focallength)

So for example, for 120mm medium format film (height 56mm) and the same 20mm focal length lens as above, the vertical field of view is about 109 degrees.