Luminosity Calculator

Stellar Luminosity from Radius and Temperature

A star's luminosity is the total power it radiates across all wavelengths. For main-sequence stars, luminosity rises sharply with temperature and with the square of radius.

Formula

This is the Stefan-Boltzmann law applied to a spherical blackbody. \(\sigma = 5.670367 \times 10^{-8}\,\text{W/(m}^2\text{K}^4)\), \(R\) is radius in meters, and \(T\) is surface temperature in kelvin.

Solar Units and Magnitude

Comparing to the Sun gives \(L/L_\odot\). Absolute magnitude relates logarithmically to luminosity: \(M = -2.5 \log_{10}(L/L_0)\) with \(L_0 = 3.0128 \times 10^{28}\,\text{W}\). The Sun has \(L_\odot \approx 3.828 \times 10^{26}\,\text{W}\) and \(M \approx 4.74\).