|• Total||0.2 sq mi (0.4 km2)|
|• Land||0.2 sq mi (0.4 km2)|
|• Water||0.0 sq mi (0.0 km2)|
|Elevation||600 ft (183 m)|
|• Density||3,165.6/sq mi (1,222.3/km2)|
|Time zone||Eastern (EST) (UTC-5)|
|• Summer (DST)||EDT (UTC-4)|
|GNIS feature ID||1699785|
Bancroft is located at .(38.281970, -85.612437)
According to the United States Census Bureau, the city has a total area of 0.2 square miles (0.52 km2), all of it land.
As of the census of 2000, there were 536 people, 199 households, and 172 families residing in the city. The population density was 3,165.6 people per square mile (1,217.4/km²). There were 202 housing units at an average density of 1,193.0 per square mile (458.8/km²). The racial makeup of the city was 90.11% White, 5.22% African American, 3.54% Asian, 0.19% from other races, and 0.93% from two or more races. Hispanic or Latino of any race were 2.05% of the population.
There were 199 households out of which 32.7% had children under the age of 18 living with them, 77.4% were married couples living together, 6.0% had a female householder with no husband present, and 13.1% were non-families. 12.1% of all households were made up of individuals and 5.0% had someone living alone who was 65 years of age or older. The average household size was 2.69 and the average family size was 2.90.
In the city the population was spread out with 23.9% under the age of 18, 5.2% from 18 to 24, 19.8% from 25 to 44, 36.8% from 45 to 64, and 14.4% who were 65 years of age or older. The median age was 46 years. For every 100 females there were 98.5 males. For every 100 females age 18 and over, there were 92.5 males.
The median income for a household in the city was $79,244, and the median income for a family was $85,230. Males had a median income of $60,893 versus $37,500 for females. The per capita income for the city was $37,746. None of the families and 0.4% of the population were living below the poverty line, including no under eighteens and none of those over 64.