Just as with acid strength, base strength can be determined by considering an equilibrium:

The equilibrium constant for a base is Kb.

As before, the term for water does not appear in the expression because it is in vast excess, and can be assumed to be constant.  It is therefore incorporated into the term for Kb.

However, in order to be able to compare acids and bases on one scale, it is more usual to describe base strength in terms of Ka too.  This can be done as follows:

If we consider the following reaction:

Then we can derive an expression for Ka:

Here we have actually measured the strength of the conjugate acid of the base we are interested in.  However, the ease with which BH+ will give up a proton is equivalent to the lack of ease with which B will accept a proton.  Hence if BH+ is a very strong acid, then B is a very weak base, and vice versa.  Hence a strong base will have a large pKBH+ value.