A very comprehensive work (The U.S. Cities That Sprawled the Most (and Least) Between 2000 and 2010) about sprawl and compactness of cities in the US, worth to have a look:
A new report from Reid Ewing and Shima Hamidi of the University of Utah, lead researchers on the aforementioned rankings, gets at that question. Ewing and Hamidi scored the largest 162 U.S. urbanized areas on the Sprawl Index — or, if you’re feeling optimistic, the Compactness Index — for 2010. (Urbanized areas reflect development better than fixed metro area boundaries do.) Then they applied the index to the same cities in 2000 to show the change over time.
(Image credit: CityLab)