Estimates of recharge to bedrock aquifers from infiltration of precipitation can be difficult to obtain, especially in areas with large spatial and temporal variability in precipitation. In the Black Hills area of western South Dakota and eastern Wyoming, streamflow yield is highly influenced by annual precipitation, with yield efficiency (annual yield divided by annual precipitation) increasing with increasing annual precipitation. Spatial variability in annual yield characteristics for Black Hills streams is predictably influenced by precipitation patterns. Relations between precipitation and yield efficiency were used to estimate annual recharge from long-term records of annual precipitation. A series of geographic information system algorithms was used to derive annual estimates for 1000- by 1000-m grid cells. These algorithms were composited to derive estimates of annual recharge rates to the Madison and Minnelusa aquifers in the Black Hills area of western South Dakota and eastern Wyoming during water years 1931-1998 and an estimate of average recharge for water years 1950-1998. This approach provides a systematic method of obtaining consistent and reproducible estimates of recharge from infiltration of precipitation. Resulting estimates of average annual recharge (water years 1950-1998) ranged from 1 cm in the southern Black Hills to 22 cm in the northwestern Black Hills. Recharge rates to these aquifers from infiltration of precipitation on outcrops was estimated to range from 0.9 m 3/s in 1936 to 18.8 m3/s in 1995.