Greenwood is located at . According to the United States Census Bureau, the city has a total area of, of which, is land and is water. The town has a peace memorial, created by Ernest Durig from an artificial stone made using concrete and fine white sand. Unveiled in 1937, it was restored in 1982, and sits adjacent to the 1934 City Hall, on the corner of Main Street and Division Street.
As of the census of 2010, there were 1,026 people, 464 households, and 259 families living in the city. The population density was. There were 520 housing units at an average density of. The racial makeup of the city was 97.5% White, 0.9% African American, 0.4% Native American, 0.1% Asian, 0.7% from other races, and 0.5% from two or more races. Hispanic or Latino of any race were 1.5% of the population. There were 464 households, of which 24.4% had children under the age of 18 living with them, 43.8% were married couplesliving together, 7.5% had a female householder with no husband present, 4.5% had a male householder with no wife present, and 44.2% were non-families. 36.6% of all households were made up of individuals, and 16.2% had someone living alone who was 65 years of age or older. The average household size was 2.18 and the average family size was 2.87. The median age in the city was 44.1 years. 22.5% of residents were under the age of 18; 7.6% were between the ages of 18 and 24; 21.2% were from 25 to 44; 27.1% were from 45 to 64; and 21.7% were 65 years of age or older. The gender makeup of the city was 48.1% male and 51.9% female.
2000 census
As of the census of 2000, there were 1,079 people, 468 households, and 287 families living in the city. The population density was 381.9 people per square mile. There were 502 housing units at an average density of 177.7 per square mile. The racial makeup of the city was 99.17% White, 0.19% Native American, 0.09% Asian, 0.09% from other races, and 0.46% from two or more races. Hispanic or Latino of any race were 1.11% of the population. There were 468 households, out of which 27.8% had children under the age of 18 living with them, 50.9% were married couples living together, 6.4% had a female householder with no husband present, and 38.5% were non-families. 34.2% of all households were made up of individuals, and 19.2% had someone living alone who was 65 years of age or older. The average household size was 2.27 and the average family size was 2.93. In the city, the population was spread out, with 23.6% under the age of 18, 7.5% from 18 to 24, 28.5% from 25 to 44, 18.6% from 45 to 64, and 21.8% who were 65 years of age or older. The median age was 38 years. For every 100 females, there were 93.7 males. For every 100 females age 18 and over, there were 93.9 males. The median income for a household in the city was $32,917, and the median income for a family was $43,438. Males had a median income of $33,750 versus $22,132 for females. The per capita income for the city was $18,841. About 5.7% of families and 9.3% of the population were below the poverty line, including 13.1% of those under age 18 and 11.1% of those age 65 or over.
