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Glenwood is a town in Fairview and Orange townships, Fayette County and Union Township, Rush County in the U.S. state of Indiana. The population was 250 at the 2010 census.
Glenwood was originally called Vienna, and under the latter name was laid out in 1882. The Glenwood post office has been in operation since 1874.
Glenwood is located at 39°37′34″N 85°18′2″W (39.626153, -85.300513).
According to the 2010 census, Glenwood has a total area of 0.18 square miles (0.47 km2), all land.
As of the census of 2010, there were 250 people, 109 households, and 71 families residing in the town. The population density was 1,388.9 inhabitants per square mile (536.3/km2). There were 130 housing units at an average density of 722.2 per square mile (278.8/km2). The racial makeup of the town was 100.0% White. Hispanic or Latino of any race were 0.4% of the population.
There were 109 households of which 28.4% had children under the age of 18 living with them, 51.4% were married couples living together, 8.3% had a female householder with no husband present, 5.5% had a male householder with no wife present, and 34.9% were non-families. 30.3% of all households were made up of individuals and 15.6% had someone living alone who was 65 years of age or older.