Donaldson R F Star Luminosity, Radius & Temperature Calculator
Enter any two of luminosity, radius and surface temperature to find the third, using the Stefan-Boltzmann law.
How this is worked out
A star's luminosity, radius and surface temperature are tied together by the Stefan-Boltzmann law, L = 4πR²σT⁴ (treating the star as an ideal black-body radiator), where σ is the Stefan-Boltzmann constant. This tool works in solar units (radius and luminosity relative to the Sun) so the results read naturally for comparing stars, converting to watts and solar radii behind the scenes. It also shows the Wien's law peak wavelength, λmax = b/T, the wavelength at which the star's blackbody spectrum radiates most strongly.
Frequently asked questions
Why do cool stars look red and hot stars look blue?
Wien's law: peak wavelength is inversely proportional to temperature, so a cooler star's blackbody spectrum peaks at a longer (redder) wavelength and a hotter star's peaks at a shorter (bluer) one — the Sun's own peak, at 5772 K, falls in the green, though scattering and our eyes' response make it look white-yellow.
Why can a cool star still be very luminous?
Because luminosity depends on the radius squared but temperature to the fourth power — a giant star's huge surface area can easily outweigh its lower temperature. A red giant can be far more luminous than the much hotter but much smaller Sun.
Related tools: Stellar Magnitude & Distance Calculator, Planet Facts Table, Astronomical Distance Converter.
Source / Last verified: NIST, "CODATA Value: Stefan-Boltzmann constant" and "CODATA Value: Wien wavelength displacement law constant" (physics.nist.gov, both exact by the 2019 SI redefinition), and NASA/GSFC, "Sun Fact Sheet" (nssdc.gsfc.nasa.gov, radius 695,700 km, luminosity 3.828×10²&sup6; W, effective temperature 5772 K), all read 1 October 2026. This tool's own Stefan-Boltzmann calculation from the fact sheet's radius and temperature reproduces its luminosity figure exactly (3.828×10²&sup6; W), and its Wien's-law peak for the Sun (502 nm, green) matches the commonly-quoted figure for the Sun's blackbody peak.