In this study, a series of numerical experiments are performed on supersonic/hypersonic flows over an adiabatic flat plate with transitionally and fully rough surfaces. The Mach numbers simulated are 4, 5, 6, and 7; the flight heights considered are 20, 24, 28, 32, and 36 km. First, a modified roughness correction is proposed and validated with the measured data for low-speed flat-plate cases. It is verified that for the equivalent sand grain heights in the intermediate and fully rough regimes, there is a good agreement with the semi-empirical formula available in the open literature. Then, this roughness correction is applied to high-speed flow regime to investigate the effects of flight heights and Mach numbers on drag for rough-wall flat-plate cases. It is found that within the roughness measured in real flight, the roughness height change has little effect on drag compared to the variations of both flight heights and Mach numbers. The drag coefficient derivation between rough-wall and smooth-wall conditions, achieves the maximum value of 0.79% for the 60 cases selected.