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Discussion Starter · #1 · (Edited)
Usually, when people compare the densities of different urban areas, they look at the total land area/total population. Doing this results in the density value for Los Angeles being greater than that of NYC. While this is ok for trying to figure out how expansive an urban area is relative to its population, it's not good for giving a feel of what kind of densities the typical resident of an urban area lives at, which affects how suitable an urban area is to high usage of public transit, walkability, etc.

Here's how weighted density differs from overall density.

You have a place with 10 people living on 10 acres and another 100 people living on 1 other acre for a total of 110 people on 11 acres.

The overall density is 10 people per acre. (110/11)

The weighted density reflects that 91% of the population lives at a density 100 people per acre and only 9% at 1 person per acre. The weighted density would be 91 people per acre. (0.09*1+0.91*100)

Austin Contrarian looked at the weighted densities of the largest US urban areas, calculated at a census tract level:
http://www.austincontrarian.com/austincontrarian/2008/03/weighted-densit.html

I calculated the weighted densities of several major Canadian urban areas to see how they'd compare.

Some of the above cities, as a result of their small size, are already going to be quite strongly affected by "fringe census tracts" which include pockets of relatively high density suburban development closer to the city but also large amounts of rural land that bring down the density of the census tract. The smaller the urban area, the less accurate the weighted density.

Here are the weighted densities so far (combined with US urban areas from Austin Contrarian) in people per square mile with the urban area population in brackets:

1. New York: 33,029 (17,799,861)
2. San Francisco-Oakland: 15,032 (2,995,769)
3. Toronto: 14,853 (5,178,773)
4. Montreal: 14,128 (3,299,497)
5. Los Angeles: 12,557 (11,789,487)
6. Vancouver: 12,093 (2,189,688)
7. Honolulu: 11,989 (718,182)
8. Chicago: 10,270 (8,307,904)
9. San Jose: 8,766 (1,538,312)
10. Philadelphia: 8,457 (5,149,079)
11. Ottawa: 7,747 (1,022,490)
12. Hamilton: 7,743 (693,793)
13. Boston: 7,711 (4,032,484)
14. Winnipeg: 7,643 (673,856)
15. Calgary: 7,228 (1,101,023)
16. San Diego: 7,186 (2,674,436)
17. Baltimore: 6,952 (2,076,354)
18. Washington: 6,835 (3,933,920)
19. Miami: 6,810 (4,919,036)
20. Quebec City: 6,759 (704,772)
21. Las Vegas: 6,662 (1,314,357)
22. Edmonton: 6,457 (878,827)
23. Victoria: 6,145 (303,963)
24. London, ON: 6,106 (376,032)
25. Regina: 5,992 (193,100)
26. Kitchener: 5,872 (462,262)
27. Milwaukee: 5,830 (1,308,913)
28. Oshawa: 5,820 (297,808)
29. Saskatoon: 5,686 (222,079)
30. Halifax: 5,472 (328,962)
31. St Catharines-Thorold: 5,375 (150,967)
32. Phoenix: 5,238 (2,907,049)
33. Denver: 5,231 (1,984,887)
34. Windsor: 5,193 (283,940)
35. Sacramento: 5,043 (1,393,498)
36. Cleveland: 5,033 (1,786,647)
37. Detroit: 4,955 (3,903,377)
38. Seattle: 4,747 (2,712,205)
39. Dallas-Fort Worth: 4,641 (4,145,659)
40. Riverside-San Bernardino: 4,514 (1,506,816)
41. Houston: 4,514 (3,822,509)
42. Portland: 4,383 (1,583,138)
43. Minneapolis-St Paul: 4,196 (2,388,593)
44. San Antonio: 4,090 (1,327,554)
45. Austin: 3,904 (901,920)
46. Virginia Beach: 3,883 (1,394,439)
47. Pittsburgh: 3,698 (1,753,136)
48. St Louis: 3,566 (2,077,662)
49. Tampa: 3,558 (2,062,339)
50. Cincinnati: 3,274 (1,503,262)
51. Kansas City: 3,041 (1,361,744)
52. Atlanta: 2,362 (3,499,840)

The US numbers are from the 2000 census and the Canadian ones from the 2006 census.

So, any surprises?

I've also got the weighted densities of the Canadian core cities and suburbs for the urban areas I've done (including the former Metropolitan Toronto cities like North York, East York, etc) and can make density distribution graphs if anyone's interested.

Here are cities from other parts of the world I've attempted, but they often had much larger units, which causes them to seem less dense than they really are:

Barcelona (incomplete): 57,915 (3,840,842)
Zaragoza: 41,103 (681,097)
Madrid: 37,610 (5,144,053)
Paris (incomplete): 30,894 (9,508,637 not including some suburbs I haven't added yet)
Budapest (city proper): 14,810 (1,729,031)
Hamburg (city proper): 13,768
Sydney: 6,860 (4,091,720)
 

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These results make more sense than the usual density numbers that get bandied about. Would you mind adding Halifax and Victoria?
 

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***Alexxx***
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I'm still a bit confused as to what is the difference between density and weighted density?

It would be interesting to see some UK cities in comparison like Manchester, Birmingham, Sheffield, Leeds, Liverpool and London. UK cities tend to sprawl a lot more than other European cities...
 

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Discussion Starter · #5 ·
These results make more sense than the usual density numbers that get bandied about. Would you mind adding Halifax and Victoria?
Yeah I can do those, the amount of time it takes for me to calculate these basically depends on the population of the urban area, and those are pretty small.

cool what would be the weighted densities of European and Asian cities?
These take a while to calculate, at least for Canadian cities. Basically, you need to get the populations and densities (or land areas) of all the census tracts in an urban area. Ideally, the urban area should be determined in the same way as the American ones, which might complicate things a little. I'm not familiar with European/Asian census data, so I'm not sure how long it would take. For the American cities it's much easier than the Canadian ones. I'm also only fluent in English and French, and sort of Hungarian, so I might need a little help there too.

I'm still a bit confused as to what is the difference between density and weighted density?
I tried explaining the difference in the OP using an example, but basically the usual density measurements look at the density of the average piece of land in a certain area, while the weighted density looks at the density the average person in a certain area lives at.
 

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Discussion Starter · #6 ·
Added Halifax. While Halifax has decent core density for a city of its size, the peninsula had 60,628 people at a weighted density of 11,062ppsm, the suburbs are quite low density compared to other Canadian cities and there's quite a bit of very low density areas like Hammond Plains Road and Beaver Bank that are barely dense enough to be included.

Also, while you're waiting for Victoria, here's a graph of the density distribution of the 3 largest Canadian urban areas (inhabitants/km2):

It shows Montreal has a lot of people living at density of 9-18,000/km2 and has a greater range of densities than Vancouver and Toronto. Toronto has a smaller range of densities at which a significant portion of it's residents live, making it much more like Los Angeles than Philadelphia or NYC and "peaks" at a slightly higher density than Montreal. Vancouver is basically like a slightly less dense version of Toronto, but with slightly higher proportion of it's population living at densities of about 20,000/km2 (downtown Vancouver)... although that might change by the 2011 census.
 

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Discussion Starter · #7 · (Edited)
Added Victoria, Winnipeg, which has a very similar density distribution to Ottawa and Edmonton, which is very similar to Calgary.

Here's the density distribution for the next 3 densest Canadian cities (at least of the ones I've done):

Quebec City has more variation in density with more low density and a little bit more high density than Ottawa and Hamilton, but much less moderate density (2500-5000/km2).

I'm planning on doing Winnipeg next. Anyone want to guess what its weighted density will be?
 

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spaghetti polonaise
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I like that idea, however it might get difficult to calculate that weighted density as precise as possible for many cities as the administrative district boundaries within the cities might not be suitable enough for that exercise. Take for example Hamburg. The statistics office keeps population data for each of the 104 districts. However, the area size of each district is very different. And some large districts have a rather densely populated core area while the remaining area is sparsely populated. The following image illustrates the problem: The thick lines are the borough borders. Each borough is subdivided into districts (thin lines). The grey layer beneath is illustrating built up area.


http://upload.wikimedia.org/wikiped...isions.svg/608px-Hamburg_Subdivisions.svg.png

The density is 2,373.7/km2 (6,147.8/sq mi). Now finding out the weighted density would be interesting. I was doing a similar exercise once by simply substracting the districts which were largely of rural character from the total land area and population. I ended up having a density of the (somewhat) urban area of around 3000/km2 (about 7,800/sq mi).
 

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Discussion Starter · #10 ·
I suspect the weighted density for Hamburg would be a fair bit higher, probably around 12-18,000ppsm just looking at the administrative districts, and maybe as much as 50% higher still if broken up into pieces more comparable in size to US and Canada census tract. US/Canada census tracts both have about 5000 people, although in Canada at least, it's quite common to have census tracts anywhere as small as 1000 people and as large as 10000 people, with a few that are even up to around 20,000. The ones around 20,000 people are usually in areas that grew very fast and would be broken up into smaller census tracts by the next census.

If Hamburg has 1.8million people and 104 districts, that's 17,000 people in the average district, so about 3 times greater than census tracts... It would be a little problematic around the edge of the urban area if it includes rural areas, but a lot of Canadian census tracts around the fringe include a small subdivision and then a large swath of countryside... so it might not be too bad... How about districts that are fully urbanized? If you divide them into 3 similarly populated pieces, would there still be significant variation? In the case of Toronto for instance, adjacent census tracts in the suburb of Brampton might have densities that are within 10-20% of each other, so if Brampton was divided into sections of 17,000 people instead of 5,000, it wouldn't make a too big difference, but in Toronto's inner suburbs and parts of the inner city where there are highrises, you might have one census tract with a density 3 times greater than the one next to it.

Do you know if other European countries might divide their cities into smaller sections (about 5000 people) when keeping statistics? I would be interested in finding the weighted density of Zaragoza, Spain, I suspect its weighted density might be higher than that of Paris or New York.

Also, I added Kitchener (tri-cities) and Winnipeg.
 

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spaghetti polonaise
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The closest to these canadian census tracts are probably electoral districts which are set up before municipal elections (which are in Hamburg at the same time state eleczions, as Hamburg is one of Germany's 16 federal states). AFAIk these should have about the same amount of inhabitants. But I doubt that they have/publish data about the area size of these electoral districts, so that it is a hassle to determine their population density.

Population density can vary greatly between adjacent administrative districts in Hamburg, even in continious urban areas. The city center for example has a high building density, but a low population density. The districts around the Alster lake in the city center are full with villas, but around them are often more dense districts.

The most dense of the 104 administrative districts is Hoheluft-Ost with 18,086/km2 (ca. 47,000/sq mi), but it just has 0.7km2 (ca. 1.8 sq mi) land area. The least dense one is Waltershof with 5 people on 9 km2 (ca. 23 sq mi), which is due to being a district completely used by the seaport. The largest district in terms of Land area is Wilhelmsburg with 35.3km2 (ca. 91sq mi) which represents almost 5% of Hamburg's total area, and 1424/km2 (ca. 3700/sq mi).

I doubt that the weighted density for Hamburg would be 12-18.000 ppsm or even higher. That would be 4600 - 7000 inhabintants/km2. Hamburg is a very suburban cityscape for its size. It's area is almost as big as NYC, but just has less than 1/4 of NYC's population.

As for Zaragoza, I can imagine that it is much denser than at least Hamburg. If it would be denser than NY, I don't know. But I would say that spanish cities are very dense in comparison to most other european cities.

I don't know how other cities are keeping their statistics. Even within Germany there is no one way to keep statistics about districts, which is due to different status, size and capabilities of each city. The most comprenhensive data in this regard might be available about Hamburg, Berlin and Bremen, as these are city states and their statistics are being conducted at a higher administrative level.
 

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Discussion Starter · #12 ·
The closest to these canadian census tracts are probably electoral districts which are set up before municipal elections (which are in Hamburg at the same time state eleczions, as Hamburg is one of Germany's 16 federal states). AFAIk these should have about the same amount of inhabitants. But I doubt that they have/publish data about the area size of these electoral districts, so that it is a hassle to determine their population density.

Population density can vary greatly between adjacent administrative districts in Hamburg, even in continious urban areas. The city center for example has a high building density, but a low population density. The districts around the Alster lake in the city center are full with villas, but around them are often more dense districts.

The most dense of the 104 administrative districts is Hoheluft-Ost with 18,086/km2 (ca. 47,000/sq mi), but it just has 0.7km2 (ca. 1.8 sq mi) land area. The least dense one is Waltershof with 5 people on 9 km2 (ca. 23 sq mi), which is due to being a district completely used by the seaport. The largest district in terms of Land area is Wilhelmsburg with 35.3km2 (ca. 91sq mi) which represents almost 5% of Hamburg's total area, and 1424/km2 (ca. 3700/sq mi).

I doubt that the weighted density for Hamburg would be 12-18.000 ppsm or even higher. That would be 4600 - 7000 inhabintants/km2. Hamburg is a very suburban cityscape for its size. It's area is almost as big as NYC, but just has less than 1/4 of NYC's population.

As for Zaragoza, I can imagine that it is much denser than at least Hamburg. If it would be denser than NY, I don't know. But I would say that spanish cities are very dense in comparison to most other european cities.

I don't know how other cities are keeping their statistics. Even within Germany there is no one way to keep statistics about districts, which is due to different status, size and capabilities of each city. The most comprenhensive data in this regard might be available about Hamburg, Berlin and Bremen, as these are city states and their statistics are being conducted at a higher administrative level.
Yes but NYC's weighted density is quite a bit higher than that of its urban area. I would expect the weighted density of NYC proper to be between 50,000 and 80,000ppsm... so if Hamburg is 1/4 as dense, it might still have a weighted density of around 15,000ppsm.

15,000ppsm is not that dense. The weighted density for Mississauga is 11,663ppsm. Admittedly, Mississauga has a very high rises, but it still has plenty of single family home neighbourhoods with densities in the 10,000-15,000 range... or even higher if there are some attached homes. Brampton is even more suburban, and it still has a weighted density of 9809ppsm.

This area of Markham has a density of more than 20,000ppsm, despite being just detached single family homes with deep lots, wide streets and a few parks:
http://maps.google.com/maps?q=Markh...=bFRdiNlLGyWL_Ggv-xcCWg&cbp=12,336.05,,0,-3.4

Do you know where I can get density data for Hamburg's districts?

The reason I expect Zaragoza to be so dense is that about 27% of its population lives at densities of 50,000ppsm or more (averaging at 79,300ppsm) while New York's urban area has about 24% of its population living at densities of 50,000ppsm or more (averaging at 82,937ppsm). So relative to its size, its densest 25% are about as dense as New York's... except that looking at google maps, the remaining 75% of Zaragoza looks to be very dense too, while for New York, much of the remaining 75% is much lower density.

My estimates are based off these two sources:
http://www.austincontrarian.com/austincontrarian/2011/04/a-cool-graph-of-city-densities.html
http://www.demographia.com/db-hyperdense.htm
 

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Cool! I've been looking for a tool like this since a long time, since I'm very interested in density but inhabitants per surface is such a crappy indicator. Even cooler would be to know the weighted density of entire countries.
 

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Discussion Starter · #15 ·
English Wikipedia, and in case a quarter doesn't have its own wikipage in english, German Wikipedia.
OK I just finished Hamburg, its density weighted by quarter is 13,768ppsm. I would still expect the weighted density to rise a fair bit if you broke down large quarters into sections of about 5000 people... even if you included areas outside Hamburg proper that are part of the urban area (while excluding areas within the city proper not part of the urban area). It's hard to say whether the density would rise to above that of San Francisco-Oakland though. Hamburg's density distribution appears to be quite similar to that of Montreal.

I added Saskatoon and Windsor too.
 

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spaghetti polonaise
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Thanks for the effort. :) Yes, the municipal borders of Hamburg don't reflect the size of the urban area. But that is a general issue with european cities. Take for example Paris.

As Hamburg is one of the least dense big cities in Germany, or even in Europe by the traditional method, it would be interesting how the city compares with the weighted density.
 

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Discussion Starter · #17 ·
OK I did a few European cities

Zaragoza urban area: 41,103ppsm (681,097 people)
For Zaragoza I used districts, since I couldn't find data on its wards (barrios) which are smaller. The average district had 47,600 people, so much bigger than a census tracts and even quite a bit bigger than Hamburg wards. The densest district was Delicias, with a population of 114,000 and density of 90,000ppsm. Using census tract sized sections, I would expect the weighted density to be at least 50,000ppsm, possibly even 60,000ppsm.

Madrid City proper: 57,089 ppsm (3,273,006 people)
For the city proper, I was able to find information on the wards (barrios), which had 25,600 people each. The densest ward was Embajadores with a density of 125,874ppsm and population of 50,196.

Madrid Urban Area: 37,610 ppsm (5,144,053 people)
The Madrid urban area is the city plus a bunch of suburbs which have 110,000 people on average. The suburbs are actually fairly dense, but include often a lot of undeveloped land, which lowers the density. If census tract sized sections were used, I would expect the urban to have a weighted density of about 50,000 ppsm.

Paris City Proper: 72,917 ppsm (population 2,125,841)
For Paris, I used districts (quartiers) of which there are 80, so about 26,600 people each on average. The densest district was Folie-Mericourt at 117,733 ppsm with 33,002 people. I'm still working on the urban area... but Paris' urban area doesn't seem as dense as Zaragoza or Madrid's. It might end up having a weighted density lower than New York's, although its communes are also (in addition to districts) larger than a typical census tract, so when you take that into consideration, I would expect it to be of similar density to New York or a little denser.

By the way, if anyone knows where I can get data on districts/wards or ideally even smaller units for their city, let me know.

I would expect Spanish and maybe Greek urban areas to have the highest weighted densities in the developed world (unless you count Hong Kong or maybe Singapore), with Japanese and Italian ones being quite dense as well, maybe comparable to Paris and New York. I'm less sure about Eastern European cities, some have lots of "commie-blocks", but because of the greenspace surrounding them, and the fact that they're often not *that* tall (around 10-15 stories), I would expect them to be less dense than Spanish urban areas, but some might compare to NYC or Paris.
 

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Do you know if other European countries might divide their cities into smaller sections (about 5000 people) when keeping statistics? I would be interested in finding the weighted density of Zaragoza, Spain, I suspect its weighted density might be higher than that of Paris or New York.
You could do Barcelona if you like, the city has ridiculous density in its central parts and its adjacent cities (Badalona, Santa Coloma and L'Hospitalet, I'll dig up some numbers for you to look at. For Barcelona alone ca 90% of its 1,6 million inhabitants live on half the municipality, IE 1,5 million in 50 sq kilometres. Santa Coloma according to is own municipal data has an urban density of ca 32,000 per sq kilometre, Badalona ca 25,000 and L'Hospitalet ca 20,000.

Here are the densest neighbourhoods in people/sq miles, these are only neighbourhoods with at least 50,000 people per square kilometre. Including all with at least 40,000 per sq kilometre you'll end up with a list more that twice as long.

Population - density/sq mile - neighbourhood (city)

8,032 - 214,452 - Can Mariner (Santa Coloma)
29,416 - 201,585 - La Florida (L'Hospitalet)
14,927 - 170,681 - Santa Rosa (Santa Coloma)
17,669 - 160,062 - El Fondo (Santa Coloma)
26,928 - 159,738 - La Torrassa (L'Hospitalet)
24,507 - 154,584 - Sants-Bada (Barcelona)
15,379 - 147,524 - Sant Mori (Badalona)
9,959 - 145,817 - El Llatí (Santa Coloma)
34,838 - 138,922 - el Camp d'en Grassot (Barcelona)
13,141 - 136,140 - Sant Joan (Badalona)
38,917 - 135,897 - el Camp de l'Arpa del Clot (Barcelona)
12,418 - 135,477 - Verdun (Barcelona)
21,851 - 133,695 - Navas (Barcelona)
52,890 - 130,336 - La Sagrada familia (Barcelona)

320.872 people living in neighbourhoods with at least 50,000 inh/sq kilometre
these numbers are from 2009 and 2008

If you want to do Barcelona you can check out bcn.cat and there go to http://www.bcn.cat/estadistica/angles/dades/index.htm and there go to figures by neighbourhoods, there are 73 of them.
 
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