In photography, angle of view 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 of projection by the lens onto the focal plane. For most cameras, it may be assumed that the image circle produced by the lens is large enough to cover the film or sensor completely.^{[1]} If the angle of view exceeds the angle of coverage, however, then vignetting will be present in the resulting photograph. For an example of this, see below.
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For lenses projecting rectilinear (nonspatiallydistorted) images of distant objects, the effective focal length and the image format dimensions completely define the angle of view. Calculations for lenses producing nonrectilinear 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]}
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 wideangle 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 lenstoobject distance is comparable to the focal length. In this case, the magnification factor (m) must be taken into account:
(In photography m 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.
A second effect which comes into play in macro photography is lens asymmetry (an asymmetric lens is a lens where the aperture appears to have different dimensions when viewed from the front and from the back). The lens asymmetry causes an offset between the nodal plane and pupil positions. The effect can be quantified using the ratio (P) between apparent exit pupil diameter and entrance pupil diameter. The full formula for angle of view now becomes^{[4]}:
Angle of view can also be determined using FOV tables or paper or software lens calculators.^{[5]}
Consider a 35 mm camera with a normal lens having a focal length of F = 50 mm. 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, f = F, and the angles of view are:
Consider a rectilinear lens in a camera used to photograph an object at a distance S_{1}, and forming an image that just barely fits in the dimension, d, of the frame (the film or image sensor). Treat the lens as if it were a pinhole at distance S_{2} from the image plane (technically, the center of perspective of a rectilinear lens is at the center of its entrance pupil^{[6]}):
Now α / 2 is the angle between the optical axis of the lens and the ray joining its optical center to the edge of the film. Here α is defined to be the angleofview, since it is the angle enclosing the largest object whose image can fit on the film. We want to find the relationship between:
Using basic trigonometry, we find:
which we can solve for α, giving:
To project a sharp image of distant objects, S_{2} needs to be equal to the focal length, F, which is attained by setting the lens for infinity focus. Then the angle of view is given by:
For macro photography, we cannot neglect the difference between S_{2} and F. From the thin lens formula,
We substitute for the magnification, m = S_{2} / S_{1}, and with some algebra find:
Defining f = S_{2} as the "effective focal length", we get the formula presented above:
A second effect which comes into play in macro photography is lens asymmetry (an asymmetric lens is a lens where the aperture appears to have different dimensions when viewed from the front and from the back). The lens asymmetry causes an offset between the nodal plane and pupil positions. The effect can be quantified using the ratio (P) between apparent exit pupil diameter and entrance pupil diameter. The full formula for angle of view now becomes^{[7]}:
In the optical instrumentation industry the term field of view (FOV) is most often used, though the measurements are still expressed as angles.^{[8]} Optical tests are commonly used for measuring the FOV of UV, visible, and infrared (wavelengths about 0.1–20 µm in the electromagnetic spectrum) sensors and cameras.
The purpose of this test is to measure the horizontal and vertical FOV of a lens and sensor used in an imaging system, when the lens focal length or sensor size is not known (that is, when the calculation above is not immediately applicable). Although this is one typical method that the optics industry uses to measure the FOV, there exist many other possible methods.
UV/visible light from an integrating sphere (and/or other source such as a black body) is focused onto a square test target at the focal plane of a collimator (the mirrors in the diagram), such that a virtual image of the test target will be seen infinitely far away by the camera under test. The camera under test senses a real image of the virtual image of the target, and the sensed image is displayed on a monitor.^{[9]}
The sensed image, which includes the target, is displayed on a monitor, where it can be measured. Dimensions of the full image display and of the portion of the image that is the target are determined by inspection (measurements are typically in pixels, but can just as well be inches or cm).
The collimator's distant virtual image of the target subtends a certain angle, referred to as the angular extent of the target, that depends on the collimator focal length and the target size. Assuming the sensed image includes the whole target, the angle seen by the camera, its FOV, is this angular extent of the target times the ratio of full image size to target image size.^{[10]}
The target's angular extent is:
The total field of view is then approximately:
or more precisely, if the imaging system is rectilinear:
This calculation could be a horizontal or a vertical FOV, depending on how the target and image are measured.
Lenses are often referred to by terms that express their angle of view:
Zoom lenses are a special case wherein the focal length, and hence angle of view, of the lens can be altered mechanically without removing the lens from the camera.
Longer lenses magnify the subject more, apparently compressing distance and (when focused on the foreground) blurring the background because of their shallower depth of field. Wider lenses tend to magnify distance between objects while allowing greater depth of field.
Another result of using a wide angle lens is a greater apparent perspective distortion when the camera is not aligned perpendicularly to the subject: parallel lines converge at the same rate as with a normal lens, but converge more due to the wider total field. For example, buildings appear to be falling backwards much more severely when the camera is pointed upward from ground level than they would if photographed with a normal lens at the same distance from the subject, because more of the subject building is visible in the wideangle shot.
Because different lenses generally require a different camera–subject distance to preserve the size of a subject, changing the angle of view can indirectly distort perspective, changing the apparent relative size of the subject and foreground.
An example of how lens choice affects angle of view. The photos below were taken by a 35 mm still camera at a constant distance from the subject:




This table shows the diagonal, horizontal, and vertical angles of view, in degrees, for lenses producing rectilinear images, when used with 36 mm × 24 mm format (that is, 135 film or fullframe 35mm digital using width 36 mm, height 24 mm, and diagonal 43.3 mm for d in the formula above^{[11]}). Digital compact cameras state their focal lengths in 35mm equivalents, which can be used in this table.
Focal Length (mm)  13  15  18  21  24  28  35  43.3  50  70  85  105  135  180  200  300  400  500  600  800  1200 

Diagonal (°)  118  111  100  91.7  84.1  75.4  63.4  53.1  46.8  34.4  28.6  23.3  18.2  13.7  12.4  8.25  6.19  4.96  4.13  3.10  2.07 
Vertical (°)  85.4  77.3  67.4  59.5  53.1  46.4  37.8  31.0  27.0  19.5  16.1  13.0  10.2  7.63  6.87  4.58  3.44  2.75  2.29  1.72  1.15 
Horizontal (°)  108  100.4  90.0  81.2  73.7  65.5  54.4  45.1  39.6  28.8  23.9  19.5  15.2  11.4  10.3  6.87  5.15  4.12  3.44  2.58  1.72 
Displaying 3d graphics requires 3d projection of the models onto a 2d surface, and uses a series of mathematical calculations to render the scene. The angle of view of the scene is thus readily set and changed; some renderers even measure the angle of view as the focal length of an imaginary lens. The angle of view can also be projected onto the surface at an angle greater than 90°, effectively creating a fish eye lens effect.
Modifying the angle of view over time, or zooming, is a frequently used cinematic technique.
As a visual effect, some first person video games (especially racing games), widen the angle of view beyond 90° to exaggerate the distance the player is travelling, thus exaggerating the player's perceived speed and giving a tunnel effect (like pincushion distortion). Narrowing the view angle gives a zoom in effect.
