The impact-parameter-dependent probability of K-shell ionization by protons has been measured in the energy range 0.5–2.5 MeV for copper, silver, and gold targets. The data are used to test the scaling relations predicted from semiclassical calculations in first Born approximation, with unperturbed projectile trajectory and nonrelativistic hydrogenic electron wave functions. A systematic procedure is described for correcting such calculations for the inadequacy of these approximations, and the correction scheme is tested by comparison partly with experiments, partly with more complete theoretical treatments. The relation between ionization by scattered particles and by particles emitted in nuclear decays or absorbed in compound-nucleus reactions is discussed, and quantitative estimates are derived for the monopole term, which dominates for projectile velocities much lower than the K-shell electron velocity.