Mathematics of the Kardashev Scale

The Kardashev scale is defined by the expression:

K(P)=log P - 610

where P is the power generated by the civilization expressed in Watts. For planetary civilizations P=1016 W, K(P)=1 (e.g. Type I).  For stellar civilizations  P=1026W, K(P)=2 (e.g. Type II).  For galactic civilizations P=1036 W, K(P)=3 (e.g. Type III).  Earth is currently at K(P)~0.7, lower than the threshold for Type I.

Another useful scale is the power available to the individual.  For example, we can set:

KI(P)=K(P)-log I10

where I is the number of individuals in the civilization.  If we assume that a Type I civilization has a population of 10 billion individuals, KI(P)=0. In essence, we see that there is a MW of power per individual for a Type I civlization that has approximately Earth’s population.