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.
Now all we need is a European version.