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.

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.

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 development 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

The 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.

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.

This 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:

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!