It's difficult to compare population densities between cities because city boundaries don't mean the same thing. E.g. Brooklyn is part of New York, while Oakland isn't part of San Francisco, but Brooklyn and Oakland have similar geographic functions.
As of 2000, about 871,000 people (one San Francisco) lived in Chicago neighborhoods cumulatively as dense as the Mission (~25k/square mile). About 2.4 million people (three San Franciscos) lived in neighborhoods cumulatively as dense as San Francisco (~17K/square mile). Put another way, if San Francisco (~47 square miles) was as dense as the densest 47 square miles of Chicago, it would have 23,500 people per square mile and 1.1 million people.
Chicago is officially much less dense than San Francisco because the way the boundaries are defined, the city proper stretches 20 miles along the lake shore, two-thirds of the way to Gary, Indiana. San Francisco, meanwhile, ends quite abruptly part-way down the Peninsula. But if you look at the population density weighted by the populations of neighborhoods, Chicago is more dense.
Interestingly, Chicago has no reason to be so dense. Aside from the lake, it's flat, easily-built land as far as the eye can see. It's just that historically Chicago has had lax zoning regulation and that has resulted in more density.
You could certainly do that. By that measure San Francisco is actually denser than New York at 6,266 per square mile versus 5,319 per square mile (and 3,524 for Chicago). L.A. wins it all at 6,999 per square mile. Which really puts a hole in the arguments that the Bay Area and L.A. are not dense enough for commuter rail.
It depends on what you're trying to measure, really. If you're talking about space constraints driving up housing prices in the core city, I think it's useful to look at density in the core city and whether it could be higher to create more supply.
Surely these utterly fall apart (perhaps that is what you meant to begin with) when considering actual usage rather than arbitrary geographical boundaries.
Oakland is very much not the geographical equivalent of Brooklyn (you might be able to make some sort of argument for the Bronx or Staten Island). San Francisco is not more densely populated than Manhattan, neither is, by a long stretch LA.
See my calculation here, for Chicago (using 2000 numbers): https://docs.google.com/spreadsheet/ccc?key=0Ak1exuXV7898dDR...
As of 2000, about 871,000 people (one San Francisco) lived in Chicago neighborhoods cumulatively as dense as the Mission (~25k/square mile). About 2.4 million people (three San Franciscos) lived in neighborhoods cumulatively as dense as San Francisco (~17K/square mile). Put another way, if San Francisco (~47 square miles) was as dense as the densest 47 square miles of Chicago, it would have 23,500 people per square mile and 1.1 million people.
Chicago is officially much less dense than San Francisco because the way the boundaries are defined, the city proper stretches 20 miles along the lake shore, two-thirds of the way to Gary, Indiana. San Francisco, meanwhile, ends quite abruptly part-way down the Peninsula. But if you look at the population density weighted by the populations of neighborhoods, Chicago is more dense.
Interestingly, Chicago has no reason to be so dense. Aside from the lake, it's flat, easily-built land as far as the eye can see. It's just that historically Chicago has had lax zoning regulation and that has resulted in more density.