Measuring the Shape of Urban Areas

Abstract

Criteria are identified for a measure of shape compactness that would be appropriate for urban areas. A variety of types of measures that have been used for the shape of geographic areas are evaluated. The proximity index is selected. This is based on the mean distance from all points in the urban area to the Central Business District (CBD). The index is the ratio of the mean distance to the center of a circle having the same area as the urban area to the mean distance to the CBD for the urban area. The index ranges from 0 (least compact) to 1 (for a circular area). Values of the proximity index are calculated for 59 large urban areas in the United States in 2010 that had been defined using census tracts. Examination of the values and lists of the most compact and least compact urban areas and the maps illustrating the shapes of those areas shows the proximity index to be a reasonable measure of urban area shape.