Chemical and geomorphic evidence suggests that Mars' atmosphere has undergone significant loss or modification since the onset of the Martian geologic record. Analyses of proposed loss processes have been unable to individually account for loss of enough atmosphere to have supported the presence of liquid surface water at the formation time of the oldest observed surface units. Here, we give a simple calculation of the combined effects of major atmospheric loss processes. Considering only impact erosion and using results from an analytical model by Melosh and Vickery <1989>, we obtain an expression for surface pressure as a function of local crater density. Based on tabulated crater densities, the process of atmospheric cratering can account for a loss of 50--90% of the Martian atmosphere since the onset of the geologic record. Stable isotope fractionation measurements suggest that loss of ~90% of atmospheric species to space has occurred via solar wind pick-up-ion sputtering <Jakosky and Jones, 1997>. Combined, ~95--99% of Mars' atmosphere could have been lost to space. Adsorption of CO2 in the regolith and sequestration in the poles as ice or clathrate could account for most of the remaining loss. These calculations suggest that the loss processes of impact erosion, sputtering, and sequestration are together capable of explaining the inferred transition from an early atmosphere on Mars capable of supporting stable liquid surface water to today's climate. ¿ 1998 American Geophysical Union