Visual angle

The visual angle is the angle that a visual stimulus subtends at the eye. Simply speaking, it is the angle between the light rays (chief rays) from the two ends of the viewed object as they hit the eye. It is usually measured in degrees or minutes of arc. It often is also called the viewed object's subtended angular size. If one looks at a one-centimeter object at a distance of one meter and a two-centimeter object at a distance of two meters, both subtend the same visual angle and their images on the retina are the same size. Therefore, in many cases, if one is interested in the performance of the eye or the first processing steps in the visual cortex, it does not make sense to refer to the absolute size  of a viewed object (its linear size, S meters). What matters is the visual angle, V deg, see visual acuity...

Another way to conceptualize visual angle is to hold one's index finger at arm's length. At this distance, the width of the index finger subtends approximately one degree. The thumb subtends approximately two degrees (O'Shea, 1991).

The visual angle, V (given in radians), can be computed with the formula: V = 2 arctan(S/2D)

Where S is the object's frontal linear size (metric size) in meters, and D is its distance (in meters) from the center of the eye's entrance pupil

For visual angles smaller than about 10 degrees, one can calculate very close approximate values using the simpler equation,

V = S/D radians or, V = 57.3(S/D) degrees

Of course V can be measured directly using a theodolite.

For example, for the moon's diameter, V measures 0.52 degrees (or 0.009 radians) on average. Because, S = 2160 miles and D averages about 238,000 miles. =References= O'Shea, R. P. (1991). Thumb's rule tested: visual angle of thumb's width is about 2 deg. Perception, 20, 415 - 418.