Blender documentation is conspicuously silent on just what size means for a sun lamp. Since the sun has no actual location to the scene and just outputs parallel rays from a given direction, it cannot be in Blender Units/meters which is what the manual specifies for the rest of the lamps. Presumably it must be some measure of angular diameter.

In this thread tjdolphin arrived at a value of ~0.0031 for a realistic sun through experimentation (quite far from the default value of 1!):

However, while the logic there seems sound to me, Iâ€™ve also found some other opinions on correct sun size, and I havenâ€™t found anything definitive on it. The sunâ€™s angular diameter on Earth is about 0.53 degrees, and I canâ€™t think of any unit for angular diameter with which a figure of 0.0031 would make sense. 0.0031 radians, for example, is ~0.18 degrees.

Iâ€™m both interested in having an accurate sun size for regular scenes on Earth and also rendering scenes set in other solar systems at various distances from their stars. I can handle calculating the appropriate angular diameter of a star at a given distance, but to use it in Blender Iâ€™d need to know what the unit for sun size is, or alternatively to have some confidence that the 0.0031 figure I have for our sun is correct. Iâ€™d imagine Blender would use some real world unit for this, but if not, a correct size for our sun would at least enable me to calculate other cases as multiples of that.