The angular size (angular diameter, apparent size) of an object as seen from a given point is the visual diameter of the object measured as an angle. The visual diameter is the diameter of the perspective projection of the object on a plane through its center that is perpendicular to the viewing direction. Look at the picture.
The angular size, linear size and distance can be calculated using the formulas:
Thus, we can find out distance from the object if we knew its size and its angular size. Binoculars often have special marks which helps to find out angular size of observed object.
Also we can find out object size from its angular size and distance from it. And of course its angular size from its linear size and distance. This is a very frequent way of measuring things in astronomy. In astronomy the sizes of objects in the sky are often given in terms of their angular diameter as seen from Earth, rather than their actual sizes.
Below the calculators which can compute any parameter from two others. By default, distance from sun to earth, sun's diameter and sun's average angular size are used.