How do astronomers measure the radius of a star?

Astronomers employ several methods to determine the radius of a star, depending on the star's characteristics and the available observational data:

• Luminosity and Temperature: For many stars, the radius ($R$) can be calculated using the relationship $L=4\pi R^2\sigma T^4$, where $L$ is the total luminosity and $T$ is the effective temperature. By measuring a star's brightness and distance to find its luminosity, and using spectral analysis to determine its temperature, astronomers can derive the radius. This is the primary method for estimating the dimensions of white dwarf stars.12
• Interferometry: Direct measurement of a star's angular diameter is possible through interferometry, which combines light from multiple telescopes to resolve very small angles. If the distance to the star is known, this angular size can be converted into a physical radius.12
• Eclipsing Binaries: In binary systems where one star passes in front of the other, analyzing the light curves allows astronomers to determine the ratio of the stars' radii and their dimensions relative to the orbit.132
• Occultation: Monitoring the intensity of starlight as it is blocked by the Moon creates diffraction patterns that depend on the star's angular diameter, providing another means of measurement.2