Stellar radius determination is generally approximated by the formula relating luminosity, temperature, and radius:
L = 4πR²sT4
Or if the values are known in terms of the Sun's values:
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 more accurate radius in the above formula can sometimes yield a more accurate temperature determination.
One use for the radius is in the study of transiting extra-solar planets, to determine characteristics of the planet's orbit.