Lafayette Township is one of five townships in Floyd County, Indiana. As of the 2010 census, its population was 7,449 and it contained 2,856 housing units, although it remains one of the two townships in the county without an incorporated community, along with Franklin Township.
According to the 2010 census, the township has a total area of , of which (or 99.35%) is land and (or 0.61%) is water. State Senate District 46, US Congress District 9, State Representative District 72, Indiana Department of Homeland Security District 9.