In this paper, scaling relations pertinent to collisionless-shock experiments are derived. Two oppositely directed, non-relativistic interpenetrating plasma streams are considered. A full set of collisionless Vlasov–Maxwell equations is used to describe the plasma streams. Two scaling parameters are identified for those streams in which the initial temperature is small compared with the final temperature. If the scaling parameters are held constant between the two systems, the knowledge of the behavior of one of the systems allows for a direct prediction of behavior of the other, irrespective of differences in, for example, the plasma density. This similarity covers both hydrogen and non-hydrogen ion species. Reduced versions suitable for assessing electrostatically mediated and magnetically mediated (Weibel-like) models of the shocks are described. In these limiting cases, the number of scaling parameters reduces to one, making the similarity quite broad. The presence of these scaling relations can serve as a basis for making comparisons between models and selecting the most plausible models. A brief discussion is presented of the constraints associated with the role of intra-jet collisions, whose frequency may be non-negligible even if the collisions between the particles of two jets are very rare.