Appomattox is part of the Lynchburg Metropolitan Statistical Area.
As of the census of 2000, there were 1,761 people, 716 households, and 469 families residing in the town. The population density was 808.7 people per square mile (311.9/km²). There were 767 housing units at an average density of 352.2/sq mi (135.8/km²). The racial makeup of the town was 66.89% White, 32.14% African American, 0.28% Native American, 0.11% from other races, and 0.57% from two or more races. Hispanic or Latino of any race were 0.23% of the population.
There were 1 households out of which 29.3% had children under the age of 18 living with them, 42.7% were married couples living together, 20.0% had a female householder with no husband present, and 34.4% were non-families. 30.4% of all households were made up of individuals and 17.2% had someone living alone who was 65 years of age or older. The average household size was 2.35 and the average family size was 2.92.
In the town the population was spread out with 23.9% under the age of 18, 8.6% from 18 to 24, 27.4% from 25 to 44, 20.8% from 45 to 64, and 19.2% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 82.3 males. For every 100 females age 18 and over, there were 75.2 males.
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