Stellar Luminosity
Calculator

It calculates total luminosity (power output) from a star's radius and surface temperature, using L = 4πR²σT⁴, where σ is the Stefan-Boltzmann constant. The 4πR² term is the star's surface area, and σT⁴ is the power radiated per unit area.

Luminosity scales with the fourth power of temperature but only the square of radius, so a modest temperature increase has an outsized effect. Doubling a star's temperature increases its luminosity 16-fold, while doubling its radius only increases luminosity 4-fold.

Because luminosity depends on both radius and temperature together, a huge but cool star, like a red giant, can outshine a small but hot star, like a white dwarf. This is exactly why the Hertzsprung-Russell diagram needs both temperature and luminosity axes to classify stars usefully.

Results are typically given in watts or, more commonly in astronomy, in solar luminosities (L☉), where the Sun's output is the reference value of 1. Expressing luminosity relative to the Sun makes it far easier to compare stars, since raw watt values are astronomically large.

Yes, the Stefan-Boltzmann law assumes ideal blackbody radiation, which is a very good approximation for most stars including the Sun. Real stellar spectra have absorption lines and deviations, but for total luminosity estimates the blackbody assumption is accurate enough for standard use.