Stellar Radius Determination is generally approximated by the formula relating Luminosity, Temperature, and radius:
L = 4πR²sT4
Or simply to determine the radius in comparison to the Sun:
Both L and T need to be measured or estimated. Temperature is generally related to the B-V Color Index. With a Parallax distance measurement, L is related to the Apparent Magnitude. This yields a very rough estimate: merely basing the temperature on b-v can result in a radius off by as much as 50%.
When a parallax distance is not available, an even rougher estimate can be made using the Mass-Luminosity Relation and Mass-Radius Relation.
More accurate determination uses:
Only a few hundred stars have been measured by these more accurate methods. Using the above formula, an alternate temperature can be calculated, which may be considered more accurate.
One use for the radius is in the study of transiting Extra-Solar Planets, to determine characteristics of the planet's orbit.