In this article, we apply dimensional analysis to the optimization of radial magnetic torque couplers. Our goal is to find the design that maximizes the torque potential in a given package size. We consider two types of torque coupler: the permanent-magnet (a.k.a. synchronous) torque coupler, in which both the inner and outer rotors contain permanent magnets; and the variable-reluctance torque coupler, in which the inner rotor contains permanent magnets and the outer rotor contains soft-magnetic teeth. Both types of torque coupler are defined by the same set of independent geometric and material parameters. First, the Buckingham <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula> theorem is used to find the minimal set of dimensionless parameters required for design optimization. Then, using a combination of 2-D and 3-D finite-element analysis, we find and characterize the optimal designs. We explicitly consider torque couplers with eight stable magnetic equilibria (i.e., 45° of rotation between stable equilibria), but the methodology can be repeated for other configurations.