Stanford is part of the Danville Micropolitan Statistical Area.
As of the census of 2000, there were 3,430 people, 1,417 households, and 919 families residing in the city. The population density was 1,114.5 per square mile (430.3 /km). There were 1,522 housing units at an average density of 494.6 per square mile (191.0 /km). The racial makeup of the city was 89.97% White, 8.10% African American, 0.09% Native American, 0.09% Asian, 0.20% from other races, and 1.55% from two or more races. Hispanic or Latino of any race were 1.37% of the population.
There were 1,417 households out of which 29.6% had children under the age of 18 living with them, 46.1% were married couples living together, 15.9% had a female householder with no husband present, and 35.1% were non-families. 31.8% of all households were made up of individuals and 15.2% 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 2.85.
22.8% of the population was under the age of 18, 8.3% from 18 to 24, 28.5% from 25 to 44, 22.1% from 45 to 64, and 18.4% who were 65 years of age or older. The median age was 38 years. For every 100 females there were 84.1 males. For every 100 females age 18 and over, there were 79.7 males.
The median income for a household in the city was $25,087, and the median income for a family was $32,550. Males had a median income of $28,583 versus $20,975 for females. The per capita income for the city was $13,811. About 15.9% of families and 20.6% of the population were below the poverty line, including 27.4% of those under age 18 and 27.8% of those age 65 or over.