Monroe is located at . According to the 2010 census, Monroe has a total area of, all land.
Demographics
2010 census
As of the census of 2010, there were 842 people, 310 households, and 239 families living in the town. The population density was. There were 322 housing units at an average density of. The racial makeup of the town was 99.0% White, 0.2% Asian, 0.1% from other races, and 0.6% from two or more races. Hispanic or Latino of any race were 2.3% of the population. There were 310 households of which 41.0% had children under the age of 18 living with them, 60.6% were married couplesliving together, 11.6% had a female householder with no husband present, 4.8% had a male householder with no wife present, and 22.9% were non-families. 21.9% of all households were made up of individuals and 11.3% had someone living alone who was 65 years of age or older. The average household size was 2.72 and the average family size was 3.15. The median age in the town was 34.7 years. 30.4% of residents were under the age of 18; 6.7% were between the ages of 18 and 24; 25% were from 25 to 44; 23.2% were from 45 to 64; and 14.8% were 65 years of age or older. The gender makeup of the town was 47.3% male and 52.7% female.
2000 census
As of the census of 2000, there were 734 people, 274 households, and 215 families living in the town. The population density was 1,529.3 people per square mile. There were 287 housing units at an average density of 598.0 per square mile. The racial makeup of the town was 97.82% White, 0.14% Native American, 0.41% from other races, and 1.63% from two or more races. Hispanic or Latino of any race were 3.13% of the population. The town holds the distinction of the having the highest percentage of people with Swiss ancestry, followed by nearby Berne, Indiana, according to the 2000 U.S. Census. There were 274 households out of which 36.5% had children under the age of 18 living with them, 66.8% were married couples living together, 8.8% had a female householder with no husband present, and 21.5% were non-families. 19.7% of all households were made up of individuals and 10.2% had someone living alone who was 65 years of age or older. The average household size was 2.68 and the average family size was 3.09. In the town, the population was spread out with 27.1% under the age of 18, 9.4% from 18 to 24, 26.4% from 25 to 44, 21.7% from 45 to 64, and 15.4% who were 65 years of age or older. The median age was 35 years. For every 100 females, there were 96.8 males. For every 100 females age 18 and over, there were 96.0 males. The median income for a household in the town was $42,946, and the median income for a family was $49,821. Males had a median income of $32,308 versus $25,750 for females. The per capita income for the town was $16,682. About 1.4% of families and 4.0% of the population were below the poverty line, including 2.9% of those under age 18 and 11.8% of those age 65 or over.
