Compare methods

	Urban Sprawl Measurement	Urban Density Gradient Model
Field	Urban Studies	Human Geography
Family	Process / pipeline	Regression model
Year of origin	2014	1951
Originator	Reid Ewing & Shima Hamidi (building on Galster et al.)	Colin Clark; Edwin Mills & Richard Muth (theory); Bruce Newling (quadratic form)
Type	Composite index combining multiple dimensions of urban form into a sprawl/compactness score	Family of functional models of urban population density as a function of distance from the centre
Seminal source	Ewing, R., & Hamidi, S. (2015). Compactness versus sprawl: A review of recent evidence from the United States. Journal of Planning Literature, 30(4), 413–432.	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.
Aliases	Sprawl Index, Compactness Index of Sprawl, Ewing Sprawl Index, Composite Sprawl Measure	Urban Density Function, Population Density Gradient, Density-Distance Function, Monocentric Density Model
Related	4	4
Summary	Urban sprawl measurement quantifies how compact or sprawling a metropolitan region is by combining several distinct dimensions of urban form into a single composite index. The dominant approach, developed by Reid Ewing, Shima Hamidi and colleagues, captures four factors — development density, land-use mix, activity centering, and street-network connectivity — and folds standardized indicators of each into one score, calibrated so the average region equals 100 and higher values mean greater compactness. Because sprawl is multidimensional, no single variable such as density adequately describes it, which is why the composite-index strategy has become the standard for comparing regions and linking form to outcomes.	The urban density gradient model is the broad family of functional relationships that describe how population density varies with distance from a city's centre. Its canonical member is Colin Clark's 1951 negative-exponential form, but the family also includes Bruce Newling's quadratic-exponential function that permits a density crater at the core, simpler linear and Smeed forms, and the economic micro-foundation supplied by the Muth-Mills monocentric city model. Together these give planners and economists a compact, comparable language for urban spatial structure.