Acids and bases can be categorized by whether they are a strong acid, a strong base, a weak acid, or a weak base. There are very few strong acids and bases so the majority of acids and bases are weak.

A strong acid, like hydrochloric acid, completely dissociates into hydrogen ions and chloride ions when dissolved in water. A strong base, like sodium hydroxide, dissociates completely into sodium ions and hydroxide ions.

Weak acids and bases partially dissociate and are present in both ionized and un-ionized forms. For example, both acetic acid and its weak conjugate base, acetate, are found in an aqueous solution.

The degree of dissociation of a weak acid or base can be measured using its equilibrium constant. The equilibrium constant for weak acids has a special name, the acid dissociation constant, or, K_a.

For a generic weak acid HA, K_a at a given temperature can be calculated by an equilibrium equation: dividing the concentration of products, A ion and hydronium ion, by the concentration of reactants, HA and water.

As water is liquid and its concentration remains nearly unchanged in the reaction, it is excluded from the equation.

The higher the K_a, the stronger the acid. Nitrous acid is stronger than acetic acid because the K_a of nitrous acid is larger than the Ka of acetic acid. 

The equilibrium constant for weak bases, the base dissociation constant, or K_b, acts in a similar manner to K_a. For a generic weak base B, K_b at a given temperature can be determined by dividing the concentration of products, BH ion, and hydroxide ion, by the concentration of reactant, B.

Like acids, the strength of the bases is also directly proportional to the K_b. For example, ethylamine is relatively stronger than urea because the K_b of ethylamine is larger than the K_b of urea.  

The strength of an acid can also be expressed in terms of percent ionization. The percent ionization of an acid can be calculated by dividing hydronium ion concentration at equilibrium by the initial acid concentration and multiplying it by a hundred. 

Similarly, the percent ionization for bases can be calculated by dividing the hydroxide ion concentration at equilibrium by the initial concentration of base and multiplying it by a hundred. The higher the percent ionization, the stronger the acid or base.