Serious concerns about global warming have been translated into urgent calls for increasing urban densities, as higher densities are associated with lower carbon emissions from both vehicles and buildings. However, attempts at effective densification have generally failed and urban densities continue to decline in cities across the world. Calls for densification without making room for it have resulted in serious housing supply bottlenecks in many cities and have rendered their housing unaffordable. If affordable densification is to be successful, it is necessary to understand the factors that constitute urban density. A novel way is presented for factoring the average density of cities into constituent factors—three or seven factors—that when multiplied together reconstitute urban density. This factoring methodology is presented together with the preliminary measurement of these factors in 10 cities in 10 world regions. This approach allows, for the first time, a clear understanding of how different cities acquire their density: Hong Kong gets its density from building height; Kinshasa from crowding; and Dhaka and Bogotá from residential coverage. This anatomy of density offers a new outline for a comprehensive strategy for city densification: one that addresses each and every one of the factors that constitute urban density.
Urban density is usually defined as the ratio of the total population of a city and its total area. This is the most appropriate single metric for measuring progress in densification in cities and is now a central objective of the global climate change agenda. However, this metric is rather crude and often hides more than it reveals. The anatomy of density offers a new, simple method for factoring urban density into its constituent factors that when multiplied together reconstitute urban density. This approach offers city leaders and urban planners a new way to consider and develop comprehensive policy options and strategies for city densification that addresses each and every one of the factors that constitute urban density and the tradeoffs between them.
Urban density or, more precisely, urban population density is simply understood
as the ratio of the total number of inhabitants living within a welldefined
footprint of a city and the total area of this footprint. Increasing urban
density, or densification, has been correctly identified as a worthwhile
sustainability objective. First, because urban density translates population
into land consumption: a city with a given population will occupy a smaller
geographical footprint—and will therefore need to convert less of the
surrounding countryside to urban use when its urban density is higher. Second,
because the inhabitants of a more compact city with a higher urban density will
be closer to each other. Other things being equal (
Because of these substantial benefits, densification is now ‘enshrined in
land use planning policy in many countries’ (
Larger cities have more than their share of cases and deaths in part because the larger the city, the larger the number of possible interactions among its inhabitants. And it is this larger number, rather than the overall average proximity of people to each other—expressed by the average density in the city—that accounts for that larger share. In fact, when it pertains to Covid19 cases and deaths, denser metropolitan areas appear to be better able to contain their numbers than more spread out ones.
There are many ways to measure density (for a comprehensive review, see
Main measures of urban density in the literature and selected sources that mention them.



DENSITY CATEGORY  RATIO  REFERENCE 






Persons per dwelling unit 

US Census Bureau ( 


Persons per habitable room 

Blake 


Floor area per person 

UNHabitat ( 


Occupied floor area per person 

WHO ( 






Floor area ratio 

ASPO ( 


Dwelling unit per hectare (ha) 

ASPO ( 






People per residential neighborhood area 

Eldridge ( 


Dwelling units per residential neighborhood area 

ASPO ( 


Dwelling units per ‘developable land’ area 

Galster 






Citywide floor area ratio 

McDonald and McMillen ( 


Citywide floor area per person 

Krehl 


Citywide people per total residential area 

Frenkel and Ashkenazi ( 


Urban density 

James ( 


Builtup area density 

Angel 

Several authors (
lowerdensity commercial and industrial uses contribute to sprawl more than higherdensity residential uses
suggesting that urban density refers to the entire urban footprint rather than be
restricted to residential areas within that footprint. As for the urban
footprint of cities, Banai & DePriest (
Dovey & Pafka (
To the best of the authors’ knowledge, few publications discuss the arithmetic relationships between different density metrics. Different densities are usually treated as discrete quantities, with authors pointing out, for example, that ‘net residential density’ is higher than ‘gross residential density’ because the area in the denominator of the latter is larger than that of the former, but without specifying exactly what their ratio is or what it denotes.
Despite the proliferation of density measures, the authors believe it is vital to preserve urban density as the single key metric for measuring densification. Many measures of density describe important urban phenomena, but a missionoriented public policy that measures its success by pursuing a single goal with a single measure for the city at large is likely to be easier to formulate, garner support, and implement than a policy that seeks to attain disparate goals requiring disparate measures.
The use of urban density in this way is problematic, however, because it may hide more than it reveals, something easily illustrated with five brief examples:
These examples point to the core insight of this paper: the same urban density can be the result of very different phenomena, and any serious densification policy must attend to all these different phenomena if it is to be effective. This is unlikely to occur as long as these different phenomena are hidden under the mantle of a single density measure.
The key research questions posed here are:
What are the measurable factors that interact to create the overall urban density of cities?
How can understanding the ‘anatomy of density’ be used to overcome the limitations of urban density as a single metric?
The answers offer policyactionable insights into cities and preserve urban density as a single metric for measuring densification at the scale of the urban footprint.
Urban density can be factored into its constituent parts in different ways that
expose its anatomy. Factoring is simply defined as breaking down a quantity into its
constituents in such a way that multiplying them by each other yields that quantity
(
To realize these benefits, the factors of urban density must be measured at a scale
that will create results that are comparable among cities and have meaning for the
sustainability goals stated in the introduction. This means measuring the anatomy of
density using averages for each density factor for the urban footprint, meaning the
city or metropolitan area as a whole.
There is more than one way to factor urban density. In total, 10 discrete factors have been identified. These factors can be meaningfully grouped into sets of two, three, four and seven. Each set of factors retains the key characteristic that lends utility to the approach, namely, the product of each set of factors is equal to urban density. This means that any desired change in urban density must come from a change in one of those factors, and that any change in one factor will, all else being held equal, result in a change in urban density. In a decisionmaking context, this new understanding will assist in framing tradeoffs among different policy options. The more detailed the factoring, the more comprehensive the resulting snapshot of urban density.
To illustrate this, the subsequent two sections will provide definitions of numerous
factors of urban density. Section 2.1 will initially focus on three factors and
section 2.2 on the most comprehensive set of seven factors. Both sections will
incorporate some discussion of how increases in each of these factors will, all else
being equal, lead to an increase in urban density. For reference, these
factors—with additional factoring of urban density into two and four factors
as well—are shown in
The two, three, four and seven factors that, when multiplied together, constitute urban density.
‘Urban density’ is defined as the ratio of the ‘total
population’ residing in a given ‘urban footprint’ and the
total area of the urban footprint (top row of
We can decompose urban density into three factors that when multiplied together
yield urban density: ‘floorspace occupancy,’ ‘floor area
ratio’ and ‘residential share’ (third row of
The first factor, floorspace occupancy, is the ratio of the total population of a
city and its total residential floor area, the gross residential floor area,
including wall thicknesses and common areas:
Floorspace occupancy is simply the reciprocal of a more familiar metric: the
average residential ‘floor area per person’ in the city (
Floorspace occupancy is used as a factor of urban density instead of using floor area per person because urban density increases proportionally when it increases. In contrast, urban density decreases proportionally when floor area per person increases.
The second factor is the average residential ‘floor area ratio’, a
metric used to regulate the allowable building volume on a given plot
(
The total area of residential plots is defined net of streets, public spaces or
civic facilities.
The third factor is ‘residential share,’ the share of the total area
of the city’s urban footprint taken up by residential plots, a common
metric used in quantifying urban landuse plans (
All else being equal, a city with a higher share of its land in residential use will be able to host a greater number of people and will have a higher urban density.
It can now be ascertained that when floorspace occupancy, floor area ratio and residential share are multiplied together, everything cancels out and their product equals urban density:
We can also decompose urban density into seven factors (bottom row of
The first factor in a sevenfactor decomposition of urban density is
‘dwelling unit occupancy.’ Dwelling unit occupancy is a measure of
the average number of people occupying a single dwelling unit, typically one
household, large or small, and sometimes doubledup households. It is a more
refined measure of overcrowding than floorspace occupancy because it measures
occupancy in the net floor area of ‘occupied dwelling units,’
disregarding vacant ones (
The denominator of this factor focuses on the total number of occupied dwelling units in the city, a subset of the total number of dwelling units. All else being equal, if a larger total population lives within the occupied dwelling units of the city, the city will have a higher urban density. A low dwelling unit occupancy, due to decreased household size or increased income, lowers urban density.
The second factor is the ‘occupancy rate,’ a measure used in the real estate sector to assess the utilization of the available housing stock:
The denominator of this factor focuses on the total number of dwelling units in the city, units, which make up the total living area of dwelling units. All else being equal, if more dwelling units in a city are occupied (not vacant), a greater number of households will be able to fit in the city and the city will have a higher urban density.
The third factor is ‘dwelling unit packing,’ a measure of the number
of dwelling units that can be fitted in a hectare (ha) of salable or rentable
floorspace net of common areas such as corridors, lobbies, staircases or
elevator shafts. Dwelling unit packing is used as a factor of urban density
instead of ‘dwelling unit size’ (equation 9a) because, other things
being equal, when it increases, urban density increases proportionally. In
contrast, other things being equal, urban density decreases proportionally when
the average dwelling unit size increases:
The denominator of dwelling unit packing focuses on the total living area of all the dwelling units in the city, a subset of the total residential floor area. All else being equal, if this living area is larger, more households will be able to fit in the city and the city will have a higher urban density.
The fourth factor is ‘floor plan efficiency,’ a measure commonly used
by developers to calculate the salable floor space of their buildings, excluding
wall thicknesses, common corridors and staircases, elevator and utility shafts,
lobbies, common public areas and common open floors, storage areas, and areas
dedicated to offstreet parking (
The denominator of this factor focuses on the floor area of residential buildings in the city. All else being equal, if residential buildings have on average more of their total floor area available for the living area of dwelling units (through more efficient designs, for example), more people will be able to live in each building and the city will have a higher urban density.
The fifth factor is ‘building height,’ measured as the average number
of residential floors—exclusive of commercial floors in mixeduse
buildings—in the city as a whole (
The denominator of this factor focuses on the area of residential building footprints, a part of the total residential area of the city. All else being equal, if the residential building footprints within the city contain more residential floor area (an outcome that can only be achieved by building up or digging down), more people will be able to live within each building footprint and the city will have a higher urban density.
The sixth factor is ‘plot coverage,’ measured as the average share of residential plots occupied by residential building footprints:
The denominator of this factor focuses on just the residential area of the city, a part of the urban footprint. All else being equal, a city with a greater share of its residential area occupied by residential buildings can host a greater number of people within its residential area and will have a higher urban density.
The seventh factor is ‘residential share,’ the share of the total area of the city’s urban footprint taken up by residential plots:
Each of these seven factors is a ratio of two averages for the city as a whole.
When multiplying these ratios together, most of these averages cancel. This is
illustrated in the bottom row of
Dwelling unit occupancy × occupancy rate × dwelling unit packing × floor plan efficiency × building height × plot coverage × residential share = urban density.
For the factors that constitute urban density to be useful, they must also be measurable. This paper demonstrates this by calculating average citywide values for each factor. The results of these measurements are preliminary and quite possibly subject to substantial errors, but they are useful in illustrating for the first time that there are important variations in the anatomy of density among cities: different cities get their urban density from different combinations of factors.
To measure the factors that constitute urban density, 10 representative cities
were selected from the global sample of 200 cities in the
Basic data on the 10 representative cities, arranged by their urban density, from the highest (Dhaka) to the lowest (Minneapolis).



CITY  COUNTRY  REGION  CITY GDP PER CAPITA, 2012  SATELLITE IMAGE DATE  URBAN FOOTPRINT AT THE DATE (HA)  POPULATION IN THE URBAN FOOTPRINT (’000s)  URBAN DENSITY (PERSONS/HA) 


Dhaka  Bangladesh  South and Central Asia  US$4,979  1 March 2014  36,541  13,609  372 


Hong Kong  Hong Kong (SAR), China  East Asia and the Pacific  US$50,746  1 October 2013  12,278  4,322  352 


Kinshasa  Congo Democratic Republic  SubSaharan Africa  US$1,849  1 July 2013  45,681  10,226  224 


Bogotá  Colombia  Latin America and the Caribbean  US$15,933  1 January 2010  39,723  7,802  196 


Cairo  Egypt  North Africa  US$12,067  1 May 2013  136,396  15,735  115 


Baku  Azerbaijan  Western Asia  US$13,536  1 August 2014  25,662  1,672  65 


Madrid  Spain  Europe  US$38,069  1 May 2010  84,407  5,256  62 


Bangkok  Thailand  Southeast Asia  US$23,309  1 January 2015  294,462  14,011  48 


Wuhan  China  East Asia and the Pacific  US$17,783  1 September 2013  183,723  8,174  44 


Minneapolis  United States  North America  US$59,082  1 October 2014  251,256  2,627  10 

The measurable metrics that give an insight into the factors of urban density in
each city are defined in
Eight metrics that need to be obtained in a city to calculate urban density and all its factors and their definitions.



METRIC  DEFINITION 


Urban footprint  Total contiguous builtup area of the city and its urbanized open space 


Total population  Total population residing within the urban footprint 


Residential share  Share of the urban footprint occupied by residential buildings/plots 


Plot coverage  Share of the total area of residential plots occupied by residential buildings 


Building height  Average number of residential floors on a unit area of a residential building footprint 


Floor plan efficiency  Average share of the gross residential floor area allocated to living areas in dwelling units 


Occupancy rate  Share of the total number of dwelling units that are occupied 


Persons per dwelling unit  Average number of persons per dwelling unit in the city 

In this section we provide short summaries that explain how the values for each of these eight metrics were obtained. Detailed explanations are provided in the Appendix in the supplemental data online.
The urban footprint and total population were drawn from previous work of the
authors. Several authors (
Residential share, plot coverage and building height estimates were obtained from
Google Earth and Bing satellite imagery using an intraurban spatial sampling
methodology that identified a set of quasirandom points within the urban extent
at a desired point density based on a Halton sequence (
Residential share was measured by determining for each point in the Halton
sequence whether the land use at that point was ‘residential’ or
‘nonresidential’ and calculating the residential share.
Building height was estimated by counting residential floors in the nearest
residential building to a Halton point identified as ‘residential’
earlier. Each building was placed in a typology: (1) single family; (2) noncore
multifamily; and (3) core multifamily, where core buildings were defined as
having centralized elevator shafts and stairwells. Analysts then counted the
stories of that building, excluding floors that were identifiable
nonresidential uses (such as stores or parking).
Plot coverage was estimated by digitizing the boundaries of the blocks surrounding the first few hundred sampled points identified as ‘residential.’ These boundaries could be streets surrounding residential city blocks or intrablock boundaries between ‘residential’ and ‘nonresidential’ land uses. The footprints of all residential buildings within a bounded area defined as ‘residential’ were digitized and their total area was calculated. An average of 460 residential blocks was digitized in each of the 10 pilot cities.
Occupancy rate, floorplan efficiency and persons per dwelling unit were collected from secondary sources.
The occupancy rate of residential units was estimated using three methods, reflecting different levels of data availability. (1) For Cairo, Madrid and Minneapolis national census data provided the occupancy rate directly. (2) For Bangkok, Bogotá, Dhaka, and Hong Kong the census provided ‘households sharing the same housing unit’ and ‘total number of domestic households’ for the city. The former was subtracted from the latter, yielding the number of occupied units (with the assumption that every household occupied a single unit). (3) For Baku, Kinshasa, and Wuhan the same arithmetic was used as in (2), but the total number of dwelling units was calculated by dividing the total square meters of residential floor space in the city by the average dwelling unit size, estimated by multiplying floor area per person and average household size.
Estimating floor plan efficiency required examining architectural drawings of
buildings of varying sizes and heights, grouped by the building typology
identified earlier.
Persons per dwelling unit was typically calculated from national census data using the total population and total number of dwelling units. In some countries it was only available inferentially. In Azerbaijan, for example, the census provided the total residential floorspace in Baku, average square meters per person, and average household size, from which the total number of dwelling units was estimated. The urban extent of the cities used by the respective censuses to collect this information did not usually correspond exactly to the urban footprint of the city. We adopted the empirical value for persons per dwelling unit calculated from census data for the urban footprint as a whole, assuming that it did not vary appreciably from this empirical value.
Datagathering in the 10 cities showed the viability of measuring the factors of
density in a range of different contexts. The empirical findings are shown in
Estimated values for eight metrics obtained from primary and secondary data for the 10 representative cities.



METRICS OBTAINED FROM PRIMARY AND SECONDARY DATA  DHAKA  HONG KONG  KINSHASA  BOGOTÁ  CAIRO  BAKU  MADRID  BANGKOK  WUHAN  MINNEAPOLIS  


a  Population (’000s)  13,609  4,322  10,226  7,802  15,735  1,672  5,256  14,011  8,174  2,627 


b  Urban footprint (ha)  36,541  12,278  45,681  39,723  136,396  25,662  84,407  294,462  183,723  251,256 


c  Building height (stories)  2.5  20.5  1.1  2.8  4.4  2.6  3.4  1.9  5.8  1.4 


d  Plot coverage (%)  53%  22%  20%  52%  43%  35%  26%  44%  32%  11% 


e  Residential share (%)  37%  16%  46%  31%  26%  35%  19%  20%  14%  36% 


f  Persons per dwelling unit  4.2  2.8  5.1  3.6  2.1  3.8  2.3  3.0  2.2  2.4 


g  Occupancy rate (%)  97%  96%  99%  96%  66%  88%  88%  96%  77%  96% 


h  Floorplan efficiency (%)  85%  75%  95%  87%  79%  67%  83%  89%  75%  90% 

Estimated values for six intermediary metrics calculated for the 10 representative cities from metrics obtained from primary and secondary data.



INTERMEDIARY METRICS (CALCULATED)  CALCULATION  DHAKA  HONG KONG  KINSHASA  BOGOTÁ  CAIRO  BAKU  MADRID  BANGKOK  WUHAN  MINNEAPOLIS  


i  Gross residential floor area (ha)  b × c × d × e  17,805  8,643  4,481  17,737  66,310  8,117  13,927  50,264  47,286  13,789 


j  Residential area (ha)  b × e  13,536  1,955  20,812  12,170  35,335  9,102  15,846  59,786  24,911  90,671 


k  Residential building footprints (ha)  b × d × e  7,110  422  4,182  6,314  15,213  3,141  4,112  26,076  8,095  10,179 


l  Dwelling units (’000s)  a/f  3,215  1,527  2,009  2,154  7,405  441  2,321  4,687  3,689  1,077 


m  Occupied dwelling units (’000s)  l × g  3,128  1,467  1,989  2,064  4,920  389  2,045  4,481  2,822  1,029 


n  Area of dwelling units (ha)  i × h  15,140  6,495  4,256  15,378  52,127  5,439  11,519  44,639  35,465  12,377 

Estimated urban densities and their factors calculated for the 10
representative cities from metrics obtained from data presented in



URBAN DENSITY AND ITS FACTORS  CALCULATION  DHAKA  HONG KONG  KINSHASA  BOGOTÁ  CAIRO  BAKU  MADRID  BANGKOK  WUHAN  MINNEAPOLIS  


o  Urban density (persons/ha)  a/b  372  352  224  196  115  65  62  48  44  10 


p  Floorspace occupancy (persons/ha)  a/i  764  500  2,282  440  237  206  377  279  173  191 


q  Floor area density  i/b  0.5  0.7  0.1  0.4  0.5  0.3  0.2  0.2  0.3  0.1 


r  Floor area ratio  i/j  1.3  4.4  0.2  1.5  1.9  0.9  0.9  0.8  1.9  0.2 


e  Residential share (%)  e  37%  16%  46%  31%  26%  35%  19%  20%  14%  36% 


c  Building height (stories)  c  2.5  20.5  1.1  2.8  4.4  2.6  3.4  1.9  5.8  1.4 


d  Plot coverage (%)  d  53%  22%  20%  52%  43%  35%  26%  44%  32%  11% 


s  Dwelling unit occupancy (persons/occupied dwelling unit)  a/m  4.4  2.9  5.1  3.8  3.2  4.3  2.6  3.1  2.9  2.6 


g  Occupancy rate (%)  g  97%  96%  99%  96%  66%  88%  88%  96%  77%  96% 


t  Dwelling unit packing (dwelling unit/ha)  l/n  212  235  472  140  142  81  201  105  104  87 


h  Floorplan efficiency (%)  h  85%  75%  95%  87%  79%  67%  83%  89%  75%  90% 






u  * Floor area per person (m^{2}) [reciprocal of p]  1/p  13  20  4  23  42  49  26  36  58  52 


v  * Dwelling unit size (m^{2}) [reciprocal of t]  1/t  47  43  21  71  70  123  50  95  96  115 


w  * Occupied floor area per person (m^{2})  v/s  11  14  4  19  22  29  19  30  33  45 

The empirical results for the set of representative cities presented here are purely descriptive and cannot be extrapolated to the universe of cities. However, the results are internally valid and reveal large variations in the metrics that are not necessarily correlated with overall urban density. At a minimum, these findings show the value of decomposing density into its constituent factors by confirming the assertion that comparisons of urban density as a composite indicator may hide more than they reveal. They also show that different cities obtain their density from quite different combinations of factors.
The former point is illustrated by graphs showing the variations in urban
density, floorspace occupancy, floor area density and floor area per person (the
reciprocal of floorspace occupancy) in the 10 representative cities
(
Observed variations in urban density, floorspace occupancy, floor area density and floor area per person in the 10 representative cities.
Urban densities of 10 cities represented as volumes of boxes (in grey) in decreasing order from right to left and from top to bottom. The colored cube represents the 10city averages for each of the three factors that make up urban density.
The latter point—that different cities obtain their density from combinations of different factors—is illustrated in the subsequent section.
Section 2.2 focused on urban density as a product of seven factors, an approach that—while yielding a great deal of useful data—is not intuitive or easy to visualize. A simpler way to understand urban density as a product of factors is to focus on the three factors introduced in section 2.1:
Perceiving urban density as a product of three factors as shown above makes it
possible to represent it as a box in threedimensional space. As before, a given
urban density offers no hints as to which factor is responsible for it being
high or low; but representing urban density as a box for each of the 10 cities
begins to reveal its basic anatomy (
The visual representation of urban density as a volume makes the relative
contributions of different factors more apparent than the reliance on a single
number. For example, Dhaka obtained its high density from its aboveaverage
floorspace occupancy and its aboveaverage residential coverage, despite its
floor area ratio being below average. Hong Kong, which had an urban density
similar to that of Dhaka, obtained its high density from its aboveaverage floor
area ratio, while its floorspace occupancy was somewhat below average and its
residential share was far below average. Kinshasa obtained its high density from
its very high floorspace occupancy—more than three times that of
Dhaka—while its floor area ratio was far below average. And Bogotá
obtained its high density from its aboveaverage floor area ratio and its
aboveaverage residential share. At the other end of the spectrum, Wuhan had a
relatively low urban density despite its aboveaverage floor area ratio, largely
because of its very low residential share and its belowaverage floorspace
occupancy. Finally, Minneapolis had the lowest urban density in the group
because of its very low values for two of the three factors. In all,
This article has laid out a new theory for decomposing urban density into measurable
factors, and a rigorous and replicable methodology for calculating these
factors.
This also lays the groundwork for a global study of the factors of urban density. All
the factors of density, as well as urban density itself, are ratios rather than
totals. These ratios are all ‘normalized’,
Such results would advance the study of urban density by providing statistically valid data and internationally comparable data that could be used for hypothesis testing. This work will require an investment of resources, but recent developments in machine learning and the increased availability of large geospatial data sets both promise to reduce projected costs appreciably.
The results of such an exercise would also support planning practice by establishing the distribution of values for different factors, helping to calibrate the expectations of cities seeking to densify through one technique or another.
The true value of the methodology will come with further study of the relationships between the factors. Section 2 established the mathematical relationship between the different factors of urban density, with implications for practice that become evident with the data in hand: policies that seek to increase urban density by focusing on one of the factors, such as floor area density, must also be assessed in terms of their relationship with all of the other factors in order to be effective. For instance, a policy to increase dwelling unit packing without maintaining the occupancy rate and dwelling unit occupancy (which would only be possible with an increase in the population and number of households) would produce a neutral result at great cost.
Such an approach could plausibly be applied in a decisionmaking context to reduce or eliminate these sorts of errors. This fresh look at the anatomy of density affords an opportunity to reconsider plans for cities—and, where appropriate, higher levels of government as well—to establish attainable and measurable densification goals for each factor. This is indeed a challenge, and an effective densification strategy could gain support by joining with existing agendas that seek to minimize greenhouse gas emissions, preserve the countryside, address inequality and promote affordable housing.
Urban planners are experts in understanding the practical difficulties of densification: the cultural and political barriers, the difficulties in revising the regulatory framework, and the budget available for implementation. These are unique to every city and cannot be determined in advance. This paper and the theory of the anatomy of density that it introduces helps urban planners and city leaders retain urban density as the key metric for measuring densification by providing the necessary framework to expose the vital information that urban density contains. The simplicity and transparency of this approach helps distinguish between effective and ineffective policies for densification, providing a way for cities to take rapid and meaningful action on this critical issue in the years to come.
Bourne (
We note at the outset that an ‘average’ ratio of two quantities can
have two distinct meanings (
For a detailed definition of the urban footprint and the method of mapping and
calculating urban footprints using Landsat satellite imagery, see Angel
For example, stairwells, corridors and elevator shafts.
The product of floorspace occupancy and floor area ratio yields the familiar ‘net residential density,’ a common measure of the average number of people in a hectare of net residential area in the city.
An important measure of residential overcrowding (
Occupied floor area per person = dwelling unit size/dwelling unit occupancy = (total living area in occupied dwelling units/total number of occupied dwelling units)/(total population/total number of occupied dwelling units) = total living area in occupied dwelling units/total population. (13)
If, as we suspect, the average size of unoccupied dwelling units is larger than the average size of occupied dwelling units, then a correct estimate of occupied floor area per person may be smaller than that estimated here.
We classified the Landsat imagery into builtup and nonbuiltup pixels. We then
classified the builtup pixels into urban, suburban or rural ones, based on the
shares of builtup pixels within a 1 km^{2} walking distance circle
around them: Those with <25% were classified as rural; those with
25–50% were classified as suburban; and those with ≥50% were
classified as urban. We created urban clusters by grouping contiguous urban and
suburban pixels. We included fringe open spaces that were within 100 m of them,
and captured open spaces that were fully enclosed by urban and suburban pixels
and fringe open spaces, and were <200 ha in area in urban clusters. Urban
clusters that shared buffers surrounding them equal to onequarter of their area
were then combined to form the city’s urban footprint (Figure
Each census enumeration district contains builtup pixels and the population within each enumeration district is assumed to be living within those builtup pixels. It is further assumed that the population is equally divided among those builtup pixels. Only the portion of the population living in pixels that fall within the urban footprint, as defined above, is counted in the population of the city.
This classification was based on a taxonomy developed for Angel
In the majority of cases, it was possible to count the number of floors in highresolution satellite imagery or Google Street View based on window openings and balconies. Occasionally, the number of floors in a building in our sample was estimated by comparing it with an adjacent building of similar height with visible windows, or by comparing the length its shadow with that of buildings with visible windows.
For each architectural floor plan, analysts distinguish living and nonliving areas, with areas that are exclusively within a private dwelling unit categorized as ‘living areas.’ The average ratio of living area to total floor area was calculated for each building type, and then a weighted average ratio was calculated for each city based on the mix of building types identified in the building height measurement.
The simplicity and rigor of the proposed methodology has made it easy to
replicate. For a recent report on the replication of this methodology for
factoring urban density in 10 Japanese cities, see Narro
The authors wish to acknowledge Priam Pillai, Suman Kumar and Sharad Shingade of Mahatma Education Society and Valectus Ltd, and Manuel Madrid of gvSIG Association for their contributions to the measurement of the factors of density.
The authors have no competing interests to declare.
The data sets generated during and/or analysed in the current study are available from the corresponding author on reasonable request.
This research received no specific grant from any funding agency in the public, commercial or notforprofit sectors.
Supplemental data for this article can be accessed at: