Volcanic explosions introduce silicate dust particles and sulfur gases into the stratosphere. The sulfur gases are slowly converted to sulfuric acid particles. We have performed radiative transfer calculations at visible and infrared wavelengths to determine the effect of these aerosols on the global energy budget. A numerical method that allows for the vertical inhomogeneity of the atmosphere and that permits an accurate solution of the multiple scattering problem is used to determine the variation of the global albedo with stratospheric aerosol burden. These results are employed together with a calculation of the thermal radiation at the top of the atmosphere to determine the net change in mean surface temperature. Both calculations use measured optical constants for the aerosol species of interest. We find that increases in both silicate and sulfuric acid aerosols lead to an increase in the global albedo. However, this cooling is offset by the enhanced greenhouse warming due to the aerosol opacity at infrared wavelengths. During the first few months following a volcanic explosion, when the aerosols are mostly dust grains of fairly large diameter, the two effects either cancel out or a small net warming of the surface occurs, accompanied by an increase in stratospheric temperatures. Our calculations indicate that the observed heating of the stratosphere following the eruption of Mt. Agung was due chiefly to the absorption of upwelling terrestrial radiation by the added particles. However, at later times, and during most of the posteruption period, smaller sized dust and sulfuric acid aerosol particles caused a net cooling. The integrated effect over all stages following a volcanic eruption is a net cooling of the surface. Our calculations yield an estimate of the globally averaged temperature change caused by a given level of volcanic activity. A study of observed levels of volcanic activity suggests that observed climatic changes may be caused directly by single and especially by multiple volcanic explosions.