The angular magnification is the ratio of the angles formed by the image and the object at the eye. In telescopes the angular magnification (or, better, the ratio of the tangents of the angles under which the object is seen with and without the lens, respectively) can be taken as a measure of the effectiveness of the instrument.
Thus, angular magnification is given by
M = tan (?)/ tan(?0)
where ?0 is the angle subtended by the object at the front focal point of the objective and ? is the angle subtended by the image at the rear focal point of the eyepiece.
Example: The angular size of the full moon is 0.5°, in binoculars with 10x magnification it appears to subtend an angle of 5°, which is roughly 1/10 of the field of view of typical eyepieces.