While I'll agree that the pithy analogies are an excellent conceptual tool, there are actual numbers attached to the Kardaschev Scale.
- Type I: total energy consumption of between 1016 and
1017 watts/year. This is a roughly equal to the insolation of earth.
- Type II: total energy consumption of between 1026 and
1027 watts/year. This is roughly equal to the energy output of the sun.
- Type III: total energy consumption of between 1037 and
1038 watts/year This is supposed to be roughly equal to the inferred output of the Milky Way. But to be honest, I don't understand cosmology well enough to know what factors should be considered in making this estimate so I've no way to judge the relative credibility of my (single) source. YMMV.