I recently calculated the weighted densities for a number of cities using the Census Bureau's "central place/non-central place" classification. As I explained in that post and the comments, this is actually a coarse measure of weighted density because central places themselves are usually large cities with pockets of wildly varying density.

**I have now calculated the weighted density of 34 large urbanized areas using census tracts. (**See my last post for an explanation of weighted (or "perceived") density.)

I took the 32 largest U.S. urbanized areas and added Austin and Honolulu for good measure. I pulled the Census data on each census tract partially or completely contained within each of these urbanized areas. I calculated the standard density (i.e., total population/total land area) for each census tract. I also calculated each census tract's share of the total population of the urbanized area. I then assigned each tract's density a "weight" equal to its share of the total population. I summed the weights to get the weighted density for the urbanized area.

I'm preparing a permanent page with more information on the methodology and limits of this approach. (It's a very good method, though, in my opinion.)

But that technical stuff can wait a few days. Here are the weighted densities, ranked from most dense to least dense:

This approach obviously does a much better job of reflecting our perceptions of a city's density. LA's urbanized area is denser than NY's when using the standard density metric; NY's urbanized area is almost three times denser using weighted density. (LA is still quite dense, though.)

Weighted densities straighten out a lot of other counterintuitive "facts." Austin and Tampa are not really denser than Boston (as the standard density figures suggest), and the sprawling suburbs of Riverside County are not actually denser than Chicago.

Note that Portland's urbanized area is *less dense *than Houston's. The urbanized area most like Portland's, viewed strictly by their density profiles, is Riverside-San Bernardino.

New York is an outlier at the upper end, while Atlanta is an outlier at the lower end.

The "density gradient index" is a term I made up to dignify what is a pretty simple calculation: weighted density divided by standard density. The index would be an even 1 if a city's population were uniformly distributed across the landscape. The larger the index, the more uneven the distribution. I'll go into this in more detail on the permanent page, but you can get a rough idea of a city's urban form just by looking at the weighted density, standard density and density gradient index.

(There really is something called the "density gradient," but it is a curve rather than a number, and there is no "index" for it, as far as I know.)

**Related posts:**

- Perceived density (March 16, 2008).
- More on weighted density for the crackpot blogging stats geeks (March 27, 2008).
- Another feature of weighted density (May 20, 2008).
- The association between density and mode of commute (Sept. 21, 2008).

Note: I don't want to take credit for the idea of weighted density. I'm not the first person to think of this. And it is possible someone has run these calculations before. I've never seen them, though; the calculations above are mine. (I suppose I could have done a Google search. But I really don't care whether this is original work -- this isn't a refereed journal and I don't have to do literature surveys.)

**Update/Correction: **The census data express land area in square meters, and I made a careless error when converting square meters to square miles. It caused me to overstate each city's weighted density by 1.8%. I've corrected that error. (Since the error applied to all of the cities, the relative rankings are unaffected.)