1 Depending on will or discretion; not governed by any fixed rules; as, an arbitrary decision; an arbitrary punishment. It was wholly arbitrary in them to do so. Jer. Taylor. Rank pretends to fix the value of every one, and is the most arbitrary of all things. Landor.

2 Exercised according to one’s own will or caprice, and therefore conveying a notion of a tendency to abuse the possession of power. Arbitrary power is most easily established on the ruins of liberty abused licentiousness. Washington.

3 Despotic; absolute in power; bound by no law; harsh and unforbearing; tyrannical; as, an arbitrary prince or government. Dryden. Arbitrary constant, Arbitrary function (Math.), a quantity of function that is introduced into the solution of a problem, and to which any value or form may at will be given, so that the solution may be made to meet special requirements.