Stellar Luminosity Calculator

In L = 4πR²σT⁴, radius enters squared but temperature enters to the fourth power, so a given percentage increase in temperature grows luminosity far faster than the same percentage increase in radius. Doubling a star's temperature increases its luminosity sixteenfold while doubling its radius only quadruples it. That's why hot, compact stars can outshine cool, enormous ones — surface temperature dominates the energy output.

This calculator's apparent magnitude is actually the absolute magnitude restated at the standard 10-parsec reference distance used to define absolute magnitude in the first place, so the two values come out identical here. It is not adjusted for how far the star actually sits from Earth, so don't read it as "how bright this star looks in the night sky" — computing true apparent magnitude would require the star's real distance as an additional input.

The calculator applies t ∝ M⁻²·⁵, so lifetime falls off steeply as mass rises even though a bigger star has more hydrogen fuel to burn. That's because luminosity (fuel consumption rate) scales with roughly M³·⁵, which outpaces the extra fuel supply — massive stars burn through their reserves much faster than their fuel budget would suggest. This relation is most reliable near solar mass and gets rougher at the extremes of very massive O-type stars or tiny red dwarfs.

The Stefan-Boltzmann law itself, L = 4πR²σT⁴, is purely a statement about radiated surface power — it only needs surface area and temperature, with no mass term at all. Mass enters this calculator only for the separate main-sequence lifetime estimate, since fuel supply and burn rate depend on how much hydrogen the star actually has, which luminosity alone can't tell you.