How to calculate the radius of a main sequence star based on mass? What would I need in addition to the mass to figure out the radius of a main sequence star?
 A: Well, you would need an accurate stellar evolution model and you would need the age, chemical composition and probably the rotation rate too.
The mass-radius relationship is an area of intense research. Masses and radii are only determined for stars in eclipsing binary systems. These could define an empirical mass-radius relationship, but stellar evolution models tell us that the radius also depends on age. eg pre main sequence stars are larger, and even whilst still on the main sequence, stars gradually get larger by tens of percent over the course of their main sequence lifetime. Practically, this means that knowing the age would be important for stars of mass of about 80% of the Sun or larger. Lower mass main sequence stars would not have departed significantly from their initial main sequence radii even if they were as old as the Galaxy.
The radius will also depend on the chemical composition - both the overall metallicity and the fractional helium abundance are important, through their effects on atmospheric opacities and mean atomic masses. This is an effect at the level of 10-20%.
Lastly, it is becoming apparent that rotation probably plays an important role. In stars less massive than the Sun it appears that rotation-induced magnetic activity inflates stars (for poorly understood reasons). In higher mass stars rotation induces interior mixing that alters internal composition gradients and changes the evolution (as well as centrifugal distortion). Again, these are phenomena that affect radii at the level of 10% or so.
If you want something rough and ready, which at least allows you to account for the effects of age and metallicity, you could interpolate the results tables of radius versus mass that are easily obtained from this website, that reports calculations from the models of Siess, Dufour & Forestini (2000).
