It seems counter-intuitive to most people who’ve been there, but it’s now almost a truism that Los Angeles is the densest city in the US.

According to a paper by Stone and Mees (gated, but I’ve summarised the salient bit here), urbanised Los Angeles is considerably denser than urbanised New York. Indeed, even Sydney is as dense as New York and Melbourne is denser than Chicago.

That might sound strange, but Stone and Mees aren’t wrong. It depends on how density is measured.

The US Census Bureau released a new report this week that helps make sense of the confusion. It distinguishes between the average density and population-weighted density (PWD) of cities.

Average density is straightforward and familiar. It’s the total area of a city divided by its total population (although there are different definitions of some parameters, such as where a city begins and ends). It’s what Stone and Mees use.

PWD, on the other hand, breaks the city up into convenient geographical units like suburbs. It ‘weights’ (multiplies) the density of each suburb by its share of the city’s total population. It gives equal weight to each person rather than each sq km.

Thus the density of a one sq km suburb with 10,000 residents (say) contributes a lot more to the final score than the density of another one sq km suburb with only 1,000 residents. The average density of these two suburbs combined is 5,500, but the PWD is 9,181.

Using 2010 data, the Census Bureau says New York has a slightly higher average density than Los Angeles (it uses different boundaries to the Stone and Mees paper). But when measured by PWD, New York turns the tables decisively – it is two and a half times denser than Los Angeles.

PWD gives due recognition to the large proportion of New York residents who live in the dense core e.g. Manhattan, Brooklyn. Although the outer suburbs are also quite populous, their low density means they contribute considerably less to the final PWD score than they do when average density is measured.

Using PWD, the four densest major cities in the US according to the Bureau are, in order, New York, San Francisco, Los Angeles and Chicago. Los Angeles is still near the top and is much the same density as San Francisco, but both are way behind New York and well ahead of Chicago.

The Census Bureau’s report only shows the four densest major cities. When I discussed PWD about a year and half ago (Does density matter for mode share?), the data I cited used a larger number of cities (see second exhibit).

This data isn’t comparable with the Census Bureau’s data set (different boundaries again and it’s for 2000) but it helps to illustrate the difference between the two ways of calculating density. Moreover it uses superior units (urbanised areas) to the Census Bureau’s metropolitan areas. The rank order of the top four cities when measured by PWD is the same in both sets, though.

Weighted vs average density, selected US cities, 2000 (source: Chris Bradford)

As I noted in my earlier post, relatively sprawling cities like Denver, Phoenix, Houston, Riverside and Portland all rank higher on average density than on PWD. Conversely, cities with relatively dense cores like Chicago, Philadelphia and Boston rank higher on PWD.

The ‘distance’ between cities is also very different on the two measures. The top ranked city is only 1% denser than the second ranked city when average density is used and four times as dense as the bottom ranked city.

However there are much bigger differences when density is measured by PWD. Top ranked New York is two thirds denser than second ranked San Francisco and eight times as dense as sprawling Atlanta.

Stone and Mees argue there’s only a small positive correlation between city density and public transport mode share. They use average density, however, so I’m not persuaded they’re right. I’d like to see the same analysis done using PWD.

I’ve previously discussed a paper that does just that for 30 US cities. It establishes there’s a stronger relationship than Stone and Mees find, but even so it’s not especially strong. It’s an important paper in the context of this discussion so I’ll revisit it shortly as a follow-up to this post.