The Luminosity of a star describes how much electromagnetic energy the star is giving off each second. The luminosity of any star is given by the surface area of that star multiplied by the radiant flux that each unit of surface area gives off.
Stars are approximately spherical so the surface area of a star is given by:
SASphere = 4 π R2
and the radiant flux per unit of surface area is given by Stefan–Boltzmann’s law which says:
F = σ T4
where σ is a constant (σ = 5.670 × 10-8 W/m2K4)
Putting those together we get an equation that relates temperature, radius and luminosity is called the Stefan–Boltzmann equation:
The SI unit for Luminosity is watts (W) and if you want to use the other SI units of degrees Kelvin and meters the equation above works perfectly. Often we prefer to use units of solar luminosity because we can then simplify the equation and get rid of any constants.
When using solar units (T☉, R☉, and L☉) the equation looks like
And can be rearranged to solve for the temperature and radius of a star.
A simple simulation is found below for experimenting with these equations: