It is well known that the optimal operating parameters of an inductively coupled plasma (ICP) torch strongly depend upon its dimensions. To understand this relationship better, we derive a dimensionless form of the equations governing the behaviour of high-pressure ICPs. The requirement of similarity then naturally leads to expressions for the operating parameters as a function of the plasma radius. In addition to the well-known scaling law for frequency, surprising results appear for the dependence of the mass flow rate, dissipated power and operating pressure upon the plasma radius. While the obtained laws do not appear to be in good agreement with empirical results in the literature, their correctness is supported by detailed numerical calculations of ICP sources of varying diameters. The approximations of local thermodynamic equilibrium and negligible radiative losses restrict the validity of our results and can be responsible for the disagreement with empirical data. The derived scaling laws are useful for the design of new plasma torches and may provide explanations for the unsteadiness observed in certain existing ICP sources.