Photometric Stellar Radii
We use flux measurements to determine stellar radii. Take two concentric spheres, one of radius R = star's radius, the other of radius r = distance to the star. Denote the flux at the star by Fo and at Earth by Fo. Then 4r R2 Fo = 4r r2 Fo or the angular radius is i = (Fo /Fo)1/2. We measure Fo and calculate Fo from a model photosphere. Elaboration of this theme can be found in Photospheres.
The parameters of the model photosphere, namely temperature, surface gravity, and metallicity, can be determined from energy distribution measurements (e.g., 1967 ApJ 149, 317; 1968 AJ 73, 769) or from spectral lines (e.g., 2019 ApJ 882, 148.)
Radii are also determined using interferometers, lunar occultations, and eclipsing binaries.
This summary of radius values is from Photospheres, Chapter 14.