United States Census Bureau: The Census Bureau definitions (new to the 2000 census), which are based on population density, defines rural areas as all territory outside Census Bureau-defined urbanized areas and urban clusters.
An urbanized area consists of a central surrounding areas whose population ("urban nucleus") is greater than 50,000. They may or may not contain individual cities with 50,000 or more; rather, they must have a core with a population density generally exceeding 1,000 persons per square mile; and may contain adjoining territory with at least 500 persons per square mile (other towns outside an urbanized area whose population exceeds 2,500). Thus, rural areas comprise open country and settlements with fewer than 2,500 residents; areas designated as rural can have population densities as high as 999 per square mile or as low as 1 person per square mile.[4]