Estimate a star’s luminosity from its radius and surface temperature with the Stefan–Boltzmann law.
L/L☉ = (R/R☉)²·(T/T☉)⁴ with T☉ = 5778 K and L☉ = 3.828×10²⁶ W. This treats the star as a black body radiating uniformly; real stars have limb darkening, spots and non-black-body spectra, so results are estimates.
Luminosity (solar luminosities)
How to use this tool
Type the radius in units of the Sun's radius (1 = the Sun). A red giant might be 100 or more.
Type the effective surface temperature in kelvin — 5778 K for the Sun, about 3000 K for a red dwarf, 10000 K for a hot white star.
The tool reports luminosity relative to the Sun, in watts, and as an absolute bolometric magnitude.
Luminosity scales with the fourth power of temperature, so a star twice as hot radiates 16 times more per unit area.
Formula & worked example
A star with twice the Sun's radius at the Sun's temperature has L = 2² = 4 solar luminosities. At twice the temperature and the Sun's radius, L = 2⁴ = 16 solar luminosities.
Limitations — read this before you rely on it
Black-body approximation with a single effective temperature. It ignores limb darkening, starspots, rotation, metallicity and atmospheric absorption, and the magnitude uses the Sun's bolometric magnitude of 4.83.
Frequently asked questions
A star's total energy output per second across all wavelengths. It differs from apparent brightness, which also depends on distance.
The Stefan–Boltzmann law says radiated power per unit area scales with T⁴. A small temperature rise produces a large luminosity rise.
How bright a star would appear from a standard distance of 10 parsecs. Lower (more negative) means brighter; the Sun's absolute bolometric magnitude is about 4.83.
The temperature a perfect black body of the same radius and luminosity would have. Real stellar surfaces are not uniform, so it is a useful average, not a thermometer reading.
Not directly — planets shine mostly by reflected starlight rather than their own thermal radiation, so the black-body luminosity formula does not describe them.