Apparent size - angular diameter

Angular diameter is a magnitude (scalar) that represents the angle made by an object when viewed by an observer. The closer you are to the object, the larger the angular diameter of the object. The further you are from the object, the lesser the angular diameter. This can be illustrated using the diagram below.

Representation of angular diameter

The angular diameter at point B will be smaller than the one at point A. It doesn't describe how big objects are relative to each other, just how big they seem from an observer. For example, consider the sun and the moon. They have a similar angular diameter, roughly 30 arc minutes. This means they seem to be roughly the same size in the sky, as shown in the picture below.

However, the angular diameter isn't quite constant for the aforementioned celestial bodies due to the eccentric (i.e, not circular) nature of orbits. Thus, the moon looks larger at its closest point to earth (perigee) with an angular diameter of 33.81° and smallest and it's furthest point from earth (apogee)  with an angular diameter of 29.72°. The same applies for the sun.

Formula

Angular diameter is commonly measured in arc seconds, or 1/3600th of a degree. Pi = 180° so one radian is 180/pi degrees, thus a radian can be found by dividing the two, giving a value of roughly 206265 arc seconds. Therefore the angular diameter of a celestial body is given by : 

where d is the diameter in km and D is the distance to the body in km. 

Angular diameter of the sun

The value for angular diameter comes out to be about 1913 arc seconds, as demonstrated by the diagram below.

(Note - the slight difference in value is due to rounding off of values.)

Angular diameter of the moon

This gives a value of about 1,866 arc seconds.

Angular diameter of Jupiter

Jupiter is visible in the sky for a few days this month, and looks quite bright, seen near the moon. It could be easily mistaken for a star by the average person, but how big does it actually look?

 = roughly 49 arc seconds.

It can easily be inferred then that the further the object and the smaller it is, the lesser the the angular diameter, and stated previously.