The thermally averaged collision-broadened line shape is written in terms of a detuning-dependent broadening rate c() which is evaluated numerically for van der Waals potentials using classical straight trajectories. The results are presented in terms of reduced variables that make it easy to calculate the line shape for any system with arbitrary van der Waals coefficient and temperature. The results show how the line shape makes a smooth transition from a Lorentzian profile in the impact region to the dramatically asymmetric far line wings. The transition zone is characterized by Td1, where is the frequency detuning from resonance and Td is a characteristic collision duration. The lowest-order correction to the Lorentzian line shape due to finite collision duration describes the dominant behavior for Td1. The numerical results are compared with analytic approximations and recent experiments. Averaging over a thermal distribution of relative velocities is shown to alter the line-shape asymmetry substantially, improving agreement between theory and experiment. The temperature dependence of the overall line shape is presented and discussed. © 1984 The American Physical Society.