According to the United States Census Bureau, the town has a total area of 2.5 square miles (6.4 km²), of which 2.4 square miles (6.3 km²) is land and 0.1 square mile (0.1 km²) (2.02%) is water.
The swinging bridge across the James River in Buchanan, Virginia. Constructed in 1938, the piers of the bridge were built in 1851.
As of the census of 2000, there were 1,233 people, 540 households, and 359 families residing in the town. The population density was 510.1 people per square mile (196.7/km²). There were 579 housing units at an average density of 239.5 per square mile (92.4/km²). The racial makeup of the town was 90.84% White, 7.95% African American, 0.08% Native American, 0.32% Asian, and 0.81% from two or more races. Hispanic or Latino of any race were 0.73% of the population.
There were 540 households out of which 25.4% had children under the age of 18 living with them, 51.5% were married couples living together, 11.3% had a female householder with no husband present, and 33.5% were non-families. 29.4% of all households were made up of individuals and 15.6% had someone living alone who was 65 years of age or older. The average household size was 2.28 and the average family size was 2.79.
In the town the population was spread out with 20.6% under the age of 18, 6.6% from 18 to 24, 29.2% from 25 to 44, 23.9% from 45 to 64, and 19.7% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 88.5 males. For every 100 females age 18 and over, there were 86.1 males.
The median income for a household in the town was $32,500, and the median income for a family was $37,443. Males had a median income of $29,405 versus $20,565 for females. The per capita income for the town was $16,238. About 6.9% of families and 10.5% of the population were below the poverty line, including 14.2% of those under age 18 and 9.2% of those age 65 or over.