Bingham is a village in Fayette County, Illinois, United States. The population was 83 at the 2010 census, down from 117 at the 2000 census.The village was named after Judge Horatio Bingham. A post office was established in 1883.Bingham is located in northwestern Fayette County at 39°6′50″N 89°12′45″W / 39.11389°N 89.21250°W / 39.11389; -89.21250, within South Hurricane Township. It is 16 miles northwest of Vandalia, the county seat.According to the 2010 census, Bingham has a total area of 0.27 square miles, all land.As of the census of 2000, there were 117 people, 44 households, and 27 families residing in the village. The population density was 429.6 people per square mile. There were 50 housing units at an average density of 183.6 per square mile. The racial makeup of the village was 100.00% White, There were 44 households out of which 36.4% had children under the age of 18 living with them, 34.1% were married couples living together, 11.