Richhill Township is in the northwestern corner of Greene County. It is bordered to the north, across the Enlow Fork, by Washington County and to the west by the state of West Virginia. Wind Ridge is the primary settlement in the township. Other unincorporated communities include Burdette, Nebo, Time, Crabapple, Durbin, Crows Mills, Ryerson Station, Bristoria, Bryan, Smith Bridge, and Riggs.

According to the United States Census Bureau, the township has a total area of 54.4 square miles (140.8 km2), of which 54.3 square miles (140.6 km2) are land and 0.1 square miles (0.2 km2), or 0.15%, are water.[3] The Enlow Fork of Wheeling Creek forms the northern border of the township (and the Greene County line), and the Dunkard Fork of Wheeling Creek, along with its North and South forks, flow across the southern portion of the township. The Enlow and Dunkard Forks flow west into West Virginia, where Wheeling Creek continues northwest to the Ohio River.