The strength of an acid can be determined by considering the extent to which it dissociates in a given solvent (i.e. to which side this equilibrium lies):

The equilibrium constant in water is given by:

Note that the H₂O term has been incorporated into K_a, as water (the solvent) is in vast excess, and hence the value of its concentration will change negligibly. 

K_a is known as the acidity constant of the acid.  Its value will only be approximate if concentrations are used as shown above; strictly the activities of the species involved should be used.  However, using concentrations will be fairly accurate provided the solution is dilute.  Generally, the numerical value of K_a will be small, and for this reason, K_a is usually converted into pK_a by the following equation:

For example, for methanoic acid, pK_a = 3.77

Thus, the smaller the value of pK_a, the stronger the acid.

Similarly, the strength of a base is determined by using pK_b.  For the example of BOH, a base, in water, K_b can be determined by the following formula:

Again, note that the H₂O term has been incorporated into K_b, as water is in excess.  pK_b can be found from K_b in exactly the same manner as pK_a can be found from K_a.