This paper reports measurements of absolute cross sections, differential in ange, for scattering of 0.5-, 1.5-, and 5.0-keV hydrogen atoms by He, H2, and O2 at laboratory scattering angles between 0.1¿ and 5¿. The measured cross sections are the sums of those for elastic and inelastic collisions having a fast H atom product and are needed for calculating energy transfer to the upper atmosphere from precipitating ring current particles.