As of the 2010 Census, there were 2,605 persons living in 1,151 households in Carthage. With an area of 2.44 square miles, the population density was 1,067 persons per square mile. There were 1,308 total housing units with an average density of 536 per square mile. Racially, 97.3% of Carthage residents identified themselves as white, 0.3% identified as Black/African American, 0.3% were Native American, and 0.4% identified themselves as Asian. No residents identified themselves as Pacific Islander. 0.5% of the remaining population identified themselves as belonging to some other race, while 1.2% belonged to multiple races. Between all races, 2.0% of the population identified as hispanic or Latino.