In photography, angle of view (AOV) describes the angular extent of a given scene that is imaged by a camera. It is used interchangeably with the more general term field of view.
It is important to distinguish the angle of view from the angle of coverage, which describes the angle range that a lens can image. Typically the image circle produced by a lens is large enough to cover the film or sensor completely, possibly including some vignetting toward the edge. If the angle of coverage of the lens does not fill the sensor, the image circle will be visible, typically with strong vignetting toward the edge, and the effective angle of view will be limited to the angle of coverage.
A camera's angle of view depends not only on the lens, but also on the sensor. Digital sensors are usually smaller than 35 mm film, and this causes the lens to have a narrower angle of view than with 35 mm film, by a constant factor for each sensor (called the crop factor). In everyday digital cameras, the crop factor can range from around 1 (professional digital SLRs), to 1.6 (consumer SLR), to 2 (Micro Four Thirds ILC) to 6 (most compact cameras). So a standard 50 mm lens for 35 mm photography acts like a 50 mm standard "film" lens on a professional digital SLR, but would act closer to an 80 mm lens (1.6 x 50mm) on many mid-market DSLRs, and the 40 degree angle of view of a standard 50 mm lens on a film camera is equivalent to an 80 mm lens on many digital SLRs.
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. (In the case of a lens with distortion, e.g., a fisheye lens, a longer lens with distortion can have a wider angle of view than a shorter lens with low distortion) 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 (focused at infinity, see derivation), the angle of view (α) can be calculated from the chosen dimension (d), and effective focal length (f) as follows:
represents the size of the film (or sensor) in the direction measured (see below: sensor effects). For example, for 35 mm film which is 36 mm wide and 24 mm high, would be used to obtain the horizontal angle of view and for the vertical angle.
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 radians or degrees.
The effective focal length is nearly equal to the stated focal length of the lens (F), except in macro photography where the lens-to-object distance is comparable to the focal length. In this case, the magnification factor (m) must be taken into account:
(In photography is usually defined to be positive, despite the inverted image.) For example, with a magnification ratio of 1:2, we find and thus the angle of view is reduced by 33% compared to focusing on a distant object with the same lens.
Angle of view can also be determined using FOV tables or paper or software lens calculators.
Example
Consider a 35 mm camera with a lens having a focal length of . The dimensions of the 35 mm image format are 24 mm (vertically) × 36 mm (horizontal), giving a diagonal of about 43.3 mm.
At infinity focus, , the angles of view are: horizontally, vertically, diagonally,
Derivation of the angle-of-view formula
Consider a rectilinear lens in a camera used to photograph an object at a distance , and forming an image that just barely fits in the dimension, , of the frame (the film or image sensor). Treat the lens as if it were a pinhole at distance from the image plane (technically, the center of perspective of a rectilinear lens is at the center of its entrance pupil):
Now is the angle between the optical axis of the lens and the ray joining its optical center to the edge of the film. Here is defined to be the angle-of-view, since it is the angle enclosing the largest object whose image can fit on the film. We want to find the relationship between: the angle the "opposite" side of the right triangle, (half the film-format dimension) the "adjacent" side, (distance from the lens to the image plane) Using basic trigonometry, we find:
which we can solve for α, giving:
