A Primer on “Density”

The “D word.” It makes for a great pickup line, but that’s (sadly) not how most people use it. There are likely many blogs and articles written on population density and its complex relationship with transportation energy use, economic growth, how smart you are, etc. I’m not here to discuss those; I’m aware that many readers here are more casual and may just think of “density” as a proxy for something else.

Hong Kong high rise

How does this image make you feel? (Source)

So what are we even talking about? Density has certainly been discussed on streets.mn before, but if you’d like to get back to the basics (and then some), read on!

Defining Density

Before we get into more detail here, let’s step back a level. Floor Area Ratio (FAR) is a broader definition of development density that doesn’t care about how many people inhabit a building or site. It’s a simple ratio: the aggregate floor space divided by the area of the lot the building sits on. Say you have a standard 40′ x 125′ lot (5,000 square feet) with a 2 story home on it. The foundation is 1,000 square feet, giving 2,000 net square feet (the basement is typically excluded from these calculations). The FAR would be 2,000/5,000, or 0.4. Taken with lot coverage and setback regulations, a FAR limit will generally give the maximum height a structure can reach for a given footprint.

Another way to think about population density is in units, or even bedrooms, per land area. New development usually lists the number of units under construction and we can track this long-term using Census and American Community Survey (ACS) data in the form of housing units and households.

We typically think of population density as [number of people] [area (square miles, acres, etc)]. This works pretty well in most cases, but what about non-residential land-uses like offices, retail, restaurants, etc.? Downtown Minneapolis (as defined by the Downtown Council) had about 35,000 residents a few years ago, yet 2011 Census numbers have about 135,000 workers in roughly the same area. The type of jobs in a given area can be a proxy for the intensity of land-use as well. This cool accessibility tool for the New York region breaks down jobs by industry, and you can guess the number of jobs per acre will vary drastically by sector (think of a factory vs. an office full of cubes vs. a small restaurant). Considering jobs, retail, and other destinations is arguably just as important as the population centers when planning transportation networks.

Average jobs+population density per acre along the Southwest LRT corridor.  Map by the author, with background data from the US Census Bureau." width="500" height="386" class="size-medium wp-image-52959" /> Average jobs+population density per acre along the Southwest LRT corridor.  Map by the author, with background data from the US Census Bureau.

Average jobs+population density per acre along the Southwest LRT corridor. Map by Adam Froehlig

Finally, a one acre site may have 15 units and 30 people living on it, giving a gross density of 30 people per acre. But a city isn’t just filled with private lots with residents and jobs. Streets, parks, schools, lakes, rivers, etc all suck up land without adding any population (and rarely jobs or amenities). One can make assumptions of the value of different places vs non-places, but in the end the net density of a city needs to define what it leaves out (and planning decisions will determine how much tax base the city has relative to public rights of way).

Form Matters

Compare the two developments below:


On the left is the now-under-construction 2320 Colfax Ave apartments. On the right, the Horn Towers at 31st Street and Blaisdell Avenue in Minneapolis. Which one is more dense? The Horn Towers, but you may be surprised to learn the difference is not all that much. At 45 units on .48 acres, the Lander HornTowersAerialdevelopment comes in at 96 units/acre, while the three high-rise towers with 491 units sit on a much larger site, netting 131 units/acre, only 40% more “dense” than a relatively low-impact 3.5 story building.

Horn Towers represent the “towers in the park” design made (in?)famous by Le Corbusier (many designs in the US had lower residential densities than the structures they replaced during urban renewal). Your urbanist credentials will dictate whether you think the freed ground space that allows for storm water infiltration, open space, community gardens, and ample parking are worth the trade-off in lost street presence and mixing of uses. There are also complex interactions between land cost and the resulting building’s design, capital, and maintenance costs, even for a site with the same development density.

Population-Weighted Density

WeightedPopulationwithExampleThe traditional people per square mile metric has recently been giving way to a more detailed one. The two top images to the right show how the same overall density for a region can look dramatically different in practice. Most of South Minneapolis, for example, is single family homes. Acres and acres of them, albeit on relatively small lots on a walkable grid. The area east of Munich has pockets of tight development density (apartments, attached homes, smaller lot detached homes) surrounded by open space and farmland. Yet these two have roughly the same population densities.

To calculate the density an average person living in City XYZ experiences, you need to subdivide the area into smaller sections and give equal weight to each resident. Luckily, the US Census gathers data on small areas of land, known as tracts. These are sufficiently small to give a more accurate picture of the density someone experiences “out their front door.” Visually, this would look like:


As a formula, this looks like:

[ (T1 population * T1 Density) + (T2 population * T2 Density) + … + (Tn population * Tn Density) ]
Total Population

This method is similar to the metro-level accessibility rankings done at the University of Minnesota, and it’s a metric that has finally caught on at the US Census from a reporting standpoint. Which brings us to..

Comparing Areas Can Be Tricky

Especially using the traditional people-per-square-mile method. A city like Minneapolis, at 55 square miles, may not be comparable to a city like Portland with nearly three times the land area.

Portland is 145 square miles (Source: bikeportland.org)

Portland is 145 square miles (Source: bikeportland.org)

To put that graphic in perspective, Houston (TX) is over 600 square miles. Seattle comes in at 142. Denver is 155. By definition, comparing a city like Minneapolis to other cities will make us look denser using the average metric. To be comparable, our Saint Louis Parks, Edinas, Richfields, and Robbinsdales would all be annexed in, and they’d almost certainly bring the average density figure down.

Minneapolis_5MileRadiusThis is where weighted density evens the playing field. I used Census data to plot weighted density (for areas inside 1-mile radius rings from the central city hall) for the 51 metropolitan areas over 1 million people. A 5-mile radius may not align with Minneapolis’ borders, or any city for that matter, perfectly (see right). But I’ll contend that the edges of Saint Paul, Saint Louis Park, and Robbinsdale aren’t much different than the sections of Minneapolis left behind.

When comparing against the top 51 metros, Minneapolis ranks 15th for population “within the circle,” yet comes in at the 27th densest. Here’s what that looks like at multiple mile radii:

Minneapolis, Seattle, and Portland highlighted for reference

Minneapolis, Seattle, and Portland highlighted for reference

Of course, our notion of “dense” in the United States is all relative. Weighted density measures for cities/regions across the world are hard to come by. So I took some time to calculate them for a mid-sized German city, Düsseldorf. Düsseldorf has about 600,000 residents in 84 square miles, about the same average density as Minneapolis proper – the low 7,000s per square mile. Using population and land area data from the quarters in the city’s districts (as good a proxy for census tracts as I could come up with), I calculated the weighted density to be over 14,000 people per square mile, good enough for 5th densest in the United States using a 5 mile radius (78 square miles) from city hall, just behind Philadelphia (Minneapolis comes in at 5,200 people per square mile). All of which is to say, in the grand scheme of things, Minneapolis and St Paul are not very “dense” cities by national or international standards.

Anyway, hopefully this helps unearth some of the complexities behind “density” for folks out there. As always, the comment section is a great place to tease out some more details and ask questions!

24 thoughts on “A Primer on “Density”

  1. Dale

    Be careful what you advocate for. Seems like weighted density can just as easily give you towers in the sky. No guarantee that those dense nodes are going to be any sort of fine grained urbanism.

    1. Alex CecchiniAlex Cecchini Post author

      You’re absolutely right. A census tract is large enough that a bunch of towers in the park developments at the site-level would be masked by the tract’s size and produce the same result as far as a weighted density metric is concerned. The smaller the land area used to calculate the components of weighted density, the more fine-grained the resulting number will be, but also perhaps less representative of the every day experience of a resident.

      In general, this is why I included the section on form – if the Lander development had 5 full stories instead of 3 with a setback 4th level, it would have the same unit density (and weighted density number) as Horn Towers. Numbers don’t tell us everything. Or, *those specific metrics* don’t. You could concoct some metric that describes % of block faces lined with buildings, doors, windows. Or % of buildings in a census tract with mixed-uses. Those could complement weighted density to tell a better picture of what an area looks like.

  2. Aaron IsaacsAaron Isaacs

    Excellent thoughtful post. It’s really good to put our rather low density into perspective, especially given the gross over-reaction that so often greets proposed multi-family developments. Most of Minneapolis and St. Paul really resembles and older version of suburban development, as found in other cities.

  3. Matt Brillhart

    Timely: http://www.citylab.com/housing/2015/05/why-new-york-isnt-really-as-dense-as-it-used-to-be/392459/

    The vast majority of Minneapolis is less dense than it used to be too, if you were to compare say Census 1920 to 2010 (both slightly > 380,000). While there have been major increases along the Greenway in Uptown and on all sides of the U of M campus, pretty much the rest of the city has a lower population density than it once was, almost entirely due to falling household sizes. Small houses that used to hold a family of 5 now contain less than half that, on average.

  4. Aaron Berger

    Interesting post. Whenever I try to compare Minneapolis to another metro, I always consider our core city to be both Minneapolis and Saint Paul. The issue I see, as somebody without experience in the area, is that when you draw a 5-mile radius around downtown Minneapolis you’re including fringe Saint Paul but excluding the densest parts of Saint Paul. It’s not a perfect analogy, but I try to imagine what the city would be like if the two downtowns were adjacent instead of separated by ten miles. Back of the envelope, Seattle has 650,000 people on 84 square miles of land. Minneapolis and Saint Paul have 695,000 people on 107 square miles of land; Seattle has 20% more people per square mile. As a visitor for about two days, Seattle’s core certainly seems denser than the cores Minneapolis and Saint Paul, but once you get out of the cores the cities seem fairly similar, housing-wise.

    1. Aaron Berger

      It’s not necessarily a valid comparison, but what happens if you draw a 3.53 mile radius around downtown Minneapolis and downtown Saint Paul? It covers the same land area as a 5-mile radius around one downtown.

      1. Alex CecchiniAlex Cecchini Post author

        It would. unfortunately, the Census tool I used only does “miles from city hall” for the central city of each metropolitan region. Since St Paul isn’t seen as the core city for a separate metro, that calculation can’t be done. It could with GIS, of course. I’m working on using that a bit more but my technical skills just aren’t up to par yet 🙂

    2. Matt Brillhart

      Great comment. I think as a general rule of thumb, if one is talking population, growth, density, jobs in central cities, etc. – when making comparisons to our peer cities like Portland, Seattle, Denver, etc. – ALWAYS use Minneapolis & St. Paul combined. 400,000 people over 55 square miles is puny compared to most of our peer cities. 700,000 people (2014 estimate) on 107 square miles is much more in line with the bulk of our peers, both in population and land area.

      This should probably be the standard for bloggers, demographers, etc. when drawing any kind of comparisons. While it gets trickier due to having two separate counties, data sources, etc., it just seems silly to make any kind of comparisons to other cities, while leaving 40% of our urban core out of the equation.

      1. Alex CecchiniAlex Cecchini Post author

        Agreed, great comment. The thing is, if you’re talking weighted population density, even including both Minneapolis and St Paul will be less comparable to other metros with one core city. If St Paul didn’t exist and Minneapolis had grown out from the core city with the added St Paul population, there would more than likely be much denser inner neighborhoods than we currently have.

        1. Aaron Berger

          Maybe. It’s a historical puzzle with no counterfactual. Saint Paul exists because it has a good river landing. Minneapolis exists because of the Falls. It’s also entirely possible that with only one core city, the metro would have wound up something like Memphis or New Orleans… I don’t know of another model like the Twin Cities (adjacent industrial cities with dispersed pre-automobile development) in the US.

  5. Casey

    I have to take issue with this sentence, “Streets, parks, schools, lakes, rivers, etc all suck up land without adding any population (and rarely jobs or amenities).” Are these all not amenities?

    1. Alex CecchiniAlex Cecchini Post author

      They are most definitely amenities. That’s an admittedly broad term I used, and I didn’t mean it to ascribe no value to any of those things. I meant amenities more in the sense of shopping, restaurants, coffee shops, theaters, etc – private land uses that draw people and add value to neighborhoods.

      We wouldn’t want a city with 0 park land or 0 road space, but a city with (for example) 80% of its land dedicated to park space would also not be reasonable. There’s no “right” amount of schools or parks or roads, only trade-offs.

  6. Walker AngellWalker Angell

    Great post Alex. What I often wonder about is density with regard to daily amenities like grocery, pharmacy, eateries, hardware, schools, and good cappuccinos — the things that drive the bulk of shorter trips that can more easily be converted from private cars.

    How many people does a grocery need to be viable? How best to create an environment that works for this and provides residents with some level of options of where they shop for daily needs? Some people prefer Wholefoods, some Byerly’s, some The Wedge, and some Cub. How do we get away from the move towards our having to drive individual cars to their distribution centers back to their having neighborhood stores (ever think about how many car trips it requires for us as individuals to haul home what can be contained in one truck)?

    1. Adam MillerAdam Miller

      I do almost all my shopping on foot. I could get more stuff on a single trip if I drove, but why do that when it’s two blocks to the grocery store so it’s no big deal to drop in a few times a week (okay, sometimes a few times I day if I forget something)? I pass Target on my way home, so it’s no big deal to grab toilet paper this time and half gallon of milk tomorrow. It’s a bit longer trek to get to the hardware store, but not so far that I can’t make it once every few months.

      The ability to do so is a luxury that is woefully undervalued, but one that’s becoming more available.

      1. Walker AngellWalker Angell

        I think you nailed it with the luxury comment. We’ve become so use to driving cars for even the shortest of trips that we’ve forgotten how much simpler and more enjoyable, and sometimes faster, it is to walk or ride a bike.

  7. Sean Hayford OlearySean Hayford Oleary

    Is it bad if I kind of like Horn Towers? I wouldn’t want to build a whole city like that, but I like it for what it is.

    Although I love the architecture, I’m not sure the site plan is really consistent with a “tower in the garden” idea, since there is no central green space — instead, it’s surface parking. All the real green space is small and low-quality, basically just a buffer around the perimeter.

    A more recent take on the “tower in the garden” vision might be Centennial Lakes — which actually succeeds pretty well in creating a spectacular central garden that wouldn’t be possible with traditional urban forms.

    Also wouldn’t want to build an entire city like that, but no need to use this design as simply a synonym for bad.

    1. Alex CecchiniAlex Cecchini Post author

      I’ve become more agnostic to urban form over the past year or so, and I tried to convey that in the piece a little. I guess in general I do prefer the sidewalk-hugging, mid-rise architecture with neighborhood parks and small courtyards on private lots to the tower model, but I won’t go so far to say it’s the only way we should develop places.

      Small, low-quality green space + parking as the “open space” surrounding towers is pretty par for the course, though, right? Ideally, a common central garden with high quality design would be the norm, but one of the reasons towers in the park got such a bad reputation is that it was poorly implemented for the vast majority of projects.

    2. Adam MillerAdam Miller

      Speaking as someone with no knowledge of architecture, I think tower in a garden works great in the suburbs, at least to the extent that it makes any sense at all to build suburban office parks. Of course, I don’t think it actually makes sense to build suburban office parks, but at least Centennial Lakes is mixed use.

      In the city, I think it creates lifeless dead spots that can tip over to feeling scary.

      Incidentally, while commenting, I realized I can see the the Horn Towers from my office window. It’s like Sarah Palin and Russia.

      1. Sean Hayford OlearySean Hayford Oleary

        Ironically, I think that’s actually the opposite of the idea. My (also fairly limited) understanding of the Le Corbusier-era of thinking is that a city is oppressive and unhealthy, and we need to build high density with lots of green space so that everyone can experience the benefits of being out in nature. In a sense this can be egalitarian, because everybody can have access to nature.

        Of course as others have noted, most of Minneapolis is a fairly (traditional) suburban form, and we have miles of waterways and parks, so this thinking may not apply as much here.

    3. ad3

      Any positivity I might have felt towards the tower in the park idea dissolved once I spent time in the neighborhoods surrounding Boston’s west end. It’s the concept perfectly executed… Manicured park land, tennis courts, playground equipment, a pool, below grade parking, etc. And of course the tall towers. I’m sure it’s nice for some of the residents, but the amenities are underused in general and represents a blot that you can’t even walk through because it’s so easy to get lost on the winding paths and stuck in a dead end! Meanwhile all around it is well used and magnificent public park land and thriving neighborhoods. What a waste.

  8. ad3

    Would love to see some visualizations of your radius data that includes labels for the rest of the cities included!

  9. Cole

    For those who are interested, the following maps are population and employment density for many peer regions at the same scale and breakpoints. I’d point to Seattle as a region that illustrates some of the differences in density because 1) City of Seattle is about the same density as City of Minneapolis but 2) Seattle has a lot of unpopulated land because of industry. The map shows the striking difference.



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