Relationship of Luminosity to Other Stellar Characteristics
The two triangles show how any two characteristics on either triangle can be used to determine the third characteristic. Both triangles have luminosity in common.
In the left triangular relationship, the apparent brightness, distance, and luminosity are tied together such that if you know any two of the sides, you can derive the third side. For example: if you have luminosity and distance you can get apparent brightness.
The same can be said for the right triangle you can find the third characteristic if you know the other two.
Formulas for Luminosity:
There are two ways to determine the luminosity of an object, one based on the surface area and temperature, and the other based on the inverse square law.
The Luminosity of an object = the amount of energy every square meter produces multiplied by its surface area.
Using the Inverse Square Law, if you know the distance and brightness (Apparent Magnitude), you can determine its actual brightness (Luminosity or Absolute Magnitude).