The restart ability is a significant concern in the design of hypersonic inlets, but existing theoretical and empirical formulas can hardly accurately predict the restart characteristics. To develop a universal rapid prediction method, this paper explores the similarity law of the restart phenomenon at variable Mach numbers based on systematic numerical simulation. The corrected contraction angle and internal contraction ratio (ICR) that reflect the influence of multiple geometric and aerodynamic parameters are proposed, and an empirical formula for restart boundaries is established and validated by the literature data. It is revealed that the restart boundaries obey an inherent geometric similarity law, and the discrete relation between Mach number and ICR, emphasized by most existing studies, is not essential. The restart-critical wall pressure characteristics are analyzed, and a self-similar pressure criterion is obtained with the incident shock strength considered.