A star's luminosity — its total power output — depends on how large it is and how hot its surface is, following the Stefan-Boltzmann Law for blackbody radiation.
A star's luminosity — its total power output — depends on how large it is and how hot its surface is, following the Stefan-Boltzmann Law for blackbody radiation. This calculator finds a star's luminosity in watts and in multiples of the Sun's luminosity.
The Sun has R = 6.957×10⁸ m and T = 5778 K. Luminosity = 4π(6.957×10⁸)² × 5.6704×10⁻⁸ × 5778⁴ ≈ 3.85×10²⁶ W ≈ 1.0 L☉, as expected.
Total energy (luminosity) radiated by an object based on surface temperature and area.
Luminosity = 4π × radius² × σ × Temperature⁴.
Because temperature is raised to the fourth power, small increases dramatically raise output.