Electrical discharges in gases or plasmas allow dissociation and conversion of molecular precursors, such as methane, at relatively low temperature. In a steady-state reactor geometry, the reaction conversion has been suggested to be dependent on basic process parameters, such as residence time, which, in turn, is a function of reactor volume and gas flow rate, and power. Here, we show, through a combined experimental and modeling study, that, for a plasma-based steady-state reactor, conversion is dependent on gas flow rate and power, but essentially independent of volume. A critical part of the experiments was to confine the plasma volume so that the power and volume could be controlled separately, and a critical part of the modeling was to segment the reactor into a volume containing filamentary discharges and a volume containing an afterglow to capture the spatial heterogeneity of our dielectric barrier discharge. The resulting similarity law for the conversion is consistent with the idea of energy density for a plasma process, but shows how such a reaction scheme is distinct from other chemical approaches.