Calculating a camera's angle of view

Angular Field of View Calculator

This calculator computes the angular field of view for a lens of a specified focal length on a 35mm camera. For most modern digital SLR cameras (e.g. Canon D60, Canon 10D, Nikon D100, Fuji S2), a focal length multiplier of greater than 1 is appropriate because these cameras have a smaller sensor than a 35mm negative. For these cameras a focal length multiplier of approximately 1.5-1.6 is appropriate. Note: This calculator assumes a standard width/height image ratio of 3:2.

The angle of view of a lens is calculated using the following formula:

2 x tan-1( l / (2 x f) )

where ' l ' is the length of the frame in the direction that you want the reading and ' f ' is the focal length of the lens.


Calculating a camera's angle of view

For lenses projecting rectilinear (non-spatially-distorted) images of distant objects, the effective focal length and the image format dimensions completely define the angle of view. Calculations for lenses producing non-rectilinear images are much more complex and in the end not very useful in most practical applications.

Angle of view may be measured horizontally (from the left to right edge of the frame), vertically (from the top to bottom of the frame), or diagonally (from one corner of the frame to its opposite corner).

For a lens projecting a rectilinear image, the angle of view (α) can be calculated from the chosen dimension (d), and effective focal length (f) as follows:[3]

alpha = 2arctan{d/2f}

d represents the size of the film (or sensor) in the direction measured. For example, for film that is 36 mm wide, d = 36 mm would be used to obtain the horizontal angle of view.

Because this is a trigonometric function, the angle of view does not vary quite linearly with the reciprocal of the focal length. However, except for wide-angle lenses, it is reasonable to approximate

alpha=d/f radians or (180d/pi* f} degrees.