Greensburg is a city in Decatur County, Indiana, United States. The population was counted at 10,260 in the 2000 census. The city is the county seat of Decatur County. According to the United States Census Bureau, the city has a total area of 4.8 square miles (12.5 km²). 4.8 square miles (12.4 km²) of it is land, and 0.04 square miles (0.1 km²) of it (0.83%) is water.