We can take the concept of angular distance between two objects one step further and speak of the angular size (or angular diameter) of an object -- the angular distance from one side of an object to the other. These angular sizes, an expression of how wide an object appears to be, are expressed in angle measure. For example, the Moon has an angular diameter of half a degree; the Full Moon occupies half a degree in the sky.

The angular diameter of an object depends on two things: the object's actual size, and the distance of the object from us. (Think for a moment and make sure this makes sense.) The formula for angular diameter is


Angular Diameter = 206265 X (Actual diameter / Distance)


The 206,265 is a conversion factor to make sure the angular diameter comes out in seconds of arc. If we wanted the answer in degrees, the conversion factor would be 57.3. Although many solar system objects are larger than the Moon, they are also much farther away. Therefore they appear to be small, and it is more practical to measure their angular sizes in seconds of arc, rather than minutes or degrees. The units of actual diameter and distance are unimportant, as long as they are the same, i.e., both in km, both in miles, etc.

Sample Calculations

To see some sample calculations with angular size, click on the examples below


Updated 7/7/06
By James E. Heath
Copyright 2006 Austin Community College