Embodied GHG of missing middle: Residential building form and strategies for more efficient housing

This research addresses two critical problems facing communities today: the growing demand for housing and the need to reduce material consumption to mitigate the impacts of climate change. Material production and use accounts for more than 25% of annual global greenhouse gas (GHG) emissions and must be reduced to meet the Paris Climate Agreement's 2°C target. At the same time, increasing urban populations are accelerating the demand for housing and construction materials. Strategies for supplying more materially efficient housing are urgently needed. Here, we quantify the impact of residential form on embodied emissions. Specifically, we look at the reduction potential of missing middle (low‐rise multi‐unit) housing, compare missing middle to single‐family and mid/high‐rise buildings, and identify opportunities for optimizing efficiency within forms. Forty‐two new material quantifications are calculated using an ontology based on MasterFormat and UniFormat. Minimum, maximum, and most likely GHG emissions factors are used to convert material mass to CO2eq. We observe embodied GHG of missing middle buildings varying between 5540 and 39,600 kgCO2eq/bedroom. On average, multi‐unit missing middle buildings have significantly lower embodied GHG per bedroom than single‐family and mid/high‐rise buildings, but variability within forms is greater than between forms, indicating a large potential to reduce embodied GHG through building design. Best‐in‐class design strategies include reducing substructure size and indoor parking, limiting mid/high‐rise slab thickness, and choosing low‐GHG insulation products. Building missing middle homes in the 1st quartile of embodied GHG efficiency with minimum insulation emissions factors could reduce future embodied residential emissions in Ontario, Canada by 46.7%.

tions are accelerating the demand for housing and construction materials.Strategies for supplying more materially efficient housing are urgently needed.Here, we quantify the impact of residential form on embodied emissions.Specifically, we look at the reduction potential of missing middle (low-rise multi-unit) housing, compare missing middle to single-family and mid/high-rise buildings, and identify opportunities for optimizing efficiency within forms.Forty-two new material quantifications are calculated using an ontology based on MasterFormat and UniFormat.Minimum, maximum, and most likely GHG emissions factors are used to convert material mass to CO 2 eq.We observe embodied GHG of missing middle buildings varying between 5540 and 39,600 kgCO 2 eq/bedroom.On average, multi-unit missing middle buildings have significantly lower embodied GHG per bedroom than single-family and mid/high-rise buildings, but variability within forms is greater than between forms, indicating a large potential to reduce embodied GHG through building design.Best-in-class design strategies include reducing substructure size and indoor parking, limiting mid/high-rise slab thickness, and choosing low-GHG insulation products.Building missing middle homes in the 1st quartile of embodied GHG efficiency with minimum insulation emissions factors could reduce future embodied residential emissions in Ontario, Canada by 46.7%.

K E Y W O R D S
bottom-up, concrete, industrial ecology, material efficiency, missing middle, sustainable construction

Material reductions and demand for housing
This research investigates pathways to reduce embodied emissions of residential buildings while increasing housing supply.Action is needed now to accelerate greenhouse gas (GHG) emissions reductions to "net zero" as current climate pathways are likely to overshoot the globally agreed-upon warming limit of 2 • C (IPCC, 2022).Material production and use (primarily in buildings) make up a large portion of humanity's anthropogenic footprint, accounting for a quarter-and growing-share of total GHG emissions (International Resource Panel, 2020).Reductions in material emissions are of equal importance to energy transition in achieving the 2 • C goal (Pauliuk et al., 2021;Röck et al., 2020;Stephan & Crawford, 2016).Beyond climate change mitigation, material reductions are needed to improve ecosystem and human health outcomes (Akenji et al., 2016).
The need to limit material production and use is in tension with the growing need for housing.By 2050, the global urban population is expected to grow by 2.4 billion people (International Resource Panel, 2018), cities are predicted to consume 90 billion tonnes of materials a year (International Resource Panel, 2018), and urban areas will need an extra 40 billion m 2 of living space (Marinova et al., 2020).New construction and associated emissions will be driven primarily by wealth and housing demand in urban areas (Deetman et al., 2020;Moura et al., 2015).Among other growing regions, high-income countries like Canada, the United States, and Australia are currently building large, resource-intensive homes to house their future populations.Single-family homes are the most pervasive houses in these high-income countries, and estimates of their material use can range up to 960 kg of concrete and 50 kg of steel per m 2 (International Resource Panel, 2020; Sprecher et al., 2021).In 2022, Canada started construction of over 82,500 new single-family homes (Statistics Canada, 2022b) and 190,000 other residential units.The country is expected to require an additional 5.7 million homes by 2030 to close its current supply gap (CMHC, 2022).The United States and Australia expect population increases of 71.9 and 9.93 million, respectively, by 2050 and will also need new housing to meet demand (Australian Bureau of Statistics, 2018;Vespa et al., 2020).If growth trends persist without a dramatic change in how we build, emissions from construction material used in housing alone could make meeting climate commitments impossible (Soonsawad et al., 2022).
Material efficiency (ME) is a set of strategies for reducing material demand and emissions without compromising the physical services provided by those materials (Hertwich et al., 2019;Worrell et al., 2016).It includes urban mining (Koutamanis et al., 2018), low-carbon materials and alternatives (Shanks et al., 2019;Vahidi et al., 2021), lifetime extension (Lausselet et al., 2021), lightweighting (Arceo et al., 2023a;Milovanoff et al., 2019), more intensive use, and changes in building form (D'Amico & Pomponi, 2019).ME strategies present a broader opportunity to reduce emissions on top of reductions achieved through the energy transition, which by itself will not be sufficient to meet climate targets (Berrill & Hertwich, 2021).
When applied to residential construction, estimates thus far have shown that ME strategies could reduce the life-cycle emissions of homes by 35% in G7 countries and 60% in China/India by 2050 (International Resource Panel, 2020).These changes, in tandem with materially efficient commercial buildings, could help keep global GHG emissions within a 2 • C budget (Zhong et al., 2021).In general, ME strategies that reduce demand are more effective than supply-side innovations such as low-carbon materials (Zhong et al., 2021).For example, more intense building use is the most important ME strategy in shared socio-economic pathways (SSP) 2 and one of the most important in SSP1 (Pauliuk et al., 2021).
Research has established the importance of ME strategies in reducing embodied emissions, but these strategies are widely modeled in top-down studies as blanket efficiency or percent reductions without specific guidelines that can be applied at an urban planning, architectural, or engineering level (Arceo et al., 2023a).In housing specifically, there is a need for further understanding of how form and design influence embodied GHG to further ME efforts.Further, within the suite of material efficiency tools, research to date on the GHG savings potential of the missing middle has tended to focus on which form is best with less focus on embodied GHG optimization through design changes within forms.This paper addresses these gaps by quantifying the impact of residential housing form on embodied GHG using bottom-up quantifications of recently built (80% newer than 2016) North American buildings and suggesting strategies for embodied decarbonization.Specifically, this paper focuses on changes between and within housing forms and examines the potential for missing middle buildings to deliver materially and embodied GHG-efficient housing.
Section 1.2 provides a background on the term missing middle and lays out the aims of the study.Section 2 describes how building drawings were collected and materials were quantified using building information modeling (BIM) and takeoff software.Section 3 presents an analysis of material use, GHG drivers, and a comparison of residential buildings.Finally, Section 4 discusses the implications of the study.

Missing middle housing
The term "missing middle," first used by architect Daniel Parolek (Opticos Designs, 2022;Webber, 2019), refers to low-rise, typically less than fivestory, residential buildings that contain multiple units.These middle-sized buildings are common in Europe, but in countries such as Canada, the United States, and Australia, middle-sized housing has generally been illegal to build since the early 20th century (hence "missing") due in part to discriminatory zoning practices designed to enforce segregation and protect suburbs from racial and economic diversity (Webber, 2019;Whittemore & Curran-Groome, 2022).Examples of missing middle construction include multiplexes and low-rise apartment buildings (Toronto City Planning Division, 2020).The missing middle has many related or interchangeable terms such as low-rise multi-unit; see Supporting Information S1 Table 1.1 for a more comprehensive list.
Depending on the region, up to 80% of housing stock in Canada and the United States consists of only mid/high-rise (buildings with five or more floors) and single-family homes (Statistics Canada, 2021;United States Census Bureau, 2020).Missing middle has recently become a popular term in planning and architecture, specifically in the context of the housing crisis; in Toronto, Canada, restrictive zoning laws from the early 20th century have led to systematic inequality and unaffordable prices caused in part by a mismatch between desired and available housing types (Bozikovic et al., 2019;Clayton & Petramala, 2019).Large North American cities such as Minneapolis, Portland, Berkeley, and Toronto, and states such as Maine, Massachusetts, and Oregon are changing zoning laws on the basis that allowing missing middle housing will increase density, walkability, and affordability (Droste, 2021;Elgin et al., 2020;Minneapolis City Council, 2020;Toronto City Planning, 2021;Tracy, 2019).
Recent research has suggested that low-rise, high-density (missing middle-like) built environments are the most efficient ways of meeting the "demand for urban space" while also minimizing lifecycle GHG emissions (Pomponi et al., 2021).Planners have long highlighted that dense urban forms can reduce emissions from residential energy use and transportation compared to urban forms dominated by single-family housing (Ewing & Rong, 2008;Ewing et al., 2007;Wegmann, 2020).However, this work examined existing cities rather than planning for future construction and is generally based on a typology approach to building analysis (using one building as a proxy for many), which obscures variability in building forms and uncertainty in results.
This study aims to determine whether, and the degree to which, missing middle provides housing that meets growing demand without compromising emissions targets.The work contributes to research on material use and embodied GHG reductions by: • Quantifying the potential for missing middle housing to reduce the embodied GHG of future residential construction.
• Comparing the material efficiency of missing middle housing to single-family homes and medium/high-rise residential buildings to determine if there is a material or embodied GHG advantage of some housing forms over others.• Comparing different missing middle forms and presenting opportunities for decarbonizing residential building design and construction, such as targeted alternative materials and alternative design practices.
• Adding 42 new entries to a detailed, bottom-up database of construction material intensity in buildings (Guven et al., 2022) and capturing variability within building typologies (Arceo et al., 2021).

METHODS
The methodology for this study can be broken into four steps: collecting design drawings of buildings, quantifying the mass of construction materials from drawings, combining the material quantity takeoffs with an existing database (Guven et al., 2022), and calculating embodied emissions from material emissions factors.This process is illustrated in Figure 1 and explained in detail below.The following sections make use of many buildingdesign terms; Supporting Information S1 Table 1.2 provides definitions of these terms.

Data collection and quantification
Twenty-one missing middle, 1 single-family, and 13 mid/high-rise building drawings were newly quantified for this study using material takeoff and BIM software.In addition, the analysis used material quantifications of 18 missing middle, 40 single-family homes, and 9 mid/high-rise buildings (Arceo et al., 2020;Guven et al., 2022) from a previous study.All buildings were built/to be built between 2009 and 2025 (median built in 2020) in the United States or Canada.Design drawings were collected from over 30 architecture and engineering firms, builders, and building owners (Figure 1a).
All new building drawings were from the end of design development or later (e.g.issued for record drawings) and included floor, foundation, roof, wall, stair, and structural details.The study defines five forms of missing middle buildings (see Table 1).For visualizations of the housing forms, see Supporting Information S1 Figures 1.1-1.7 and page 7 of the report by Toronto City Planning Division (2020).
Thirteen researchers calculated material volumes from design drawings using quality take-off methods after Pratt (2010) (Figure 1b).Twentyfive buildings were quantified through digital measurement on PDF drawings in OnScreen Takeoff (OST) Software.For 10 buildings, BIMs were created in REVIT 2021 and quantities were exported using the program's built-in material schedules.REVIT and OST use the same fundamental approach to calculate material volumes and produce equivalent results (Arceo et al., 2023a).BIM has been used in other studies to improve the detail and speed of material quantification (Miatto et al., 2022).Our experience confirmed that REVIT allowed for a faster and more standardized workflow for material takeoff if users were familiar with the quantification process.Conversely, OST was easier to learn for researchers who were new to quantification.Relevant local/national building codes, expert opinions, and material brochures informed building element volumes if an element's measurements were not specifically given on the drawings.A categorical uncertainty score between 1 and 6 was applied to each building element based on the source of measurements (Guven et al., 2022).For example, a drawing may not give dimensions for slab-on-grade damp proofing, but the Ontario Building Code specifies a minimum thickness of 0.15 mm (Government of Ontario, 2016).In this case, the element volume is Final material volumes were multiplied by their corresponding densities (Supporting Information S1 Table 1.3) and organized into a construction classification system (Guven et al., 2022) based on their MasterFormat (Construction Specification Institute, 2016) and UniFormat codes (Construction Specification Institute, 2010) (Figure 1c).MasterFormat encodes the material of the building element, and UniFormat encodes the location of the element within the building.Both are widely used construction management ontologies in North America.
Descriptive information was collected for each building, including gross floor area (GFA), construction date, and number of stories.GFA was measured as the total area containing external/internal walls, columns, and partitions (ISO, 2017).For most of the analysis, material mass was normalized and compared per bedroom.Measuring efficiency using a per-bedroom functional unit is a better proxy for the function of a home and avoids overweighting buildings with a high GFA that house few people (Arceo et al., 2023a).Data tables and per m 2 equivalents of figures in Section 3 are given in Supporting Information S2.
The detail and scope of material quantification were defined to allow for comparison within missing middle typologies as well as between missing middle and other residential buildings.Materials were quantified for eight MasterFormat categories: concrete (including rebar) (03), masonry (04), metals (05), wood plastics and composites (06), thermal and moisture protection (07), openings (08), finishes (09), and exterior improvements (e.g., aggregates and base courses) (32) (Construction Specification Institute, 2016).Supporting infrastructure, landscaping, HVAC, and other utilities were outside the scope of the study.The study considered base-layer aggregate under basement and at-grade slabs, but it did not consider other types of fills or grouting.Other exclusions include trimming, window/door frame details, handles, structural connections like welded plates, metal hardware, and floor finishes.These exclusions were made as they constitute a small part of building mass and are disproportionately timeconsuming to quantify.Steel and concrete were the only consistently quantified materials in mid/high-rise buildings in Guven et al. (2022) because this form took much more time to quantify than low-rise buildings.Consequently, comparisons between mid/high-rise and other forms are based only on steel and concrete.

Emission factors
Cradle-to-gate GHG emissions factors for common construction materials in Toronto, which were sourced from an aggregation of EPDs and other LCA databases, were used to convert data records from material mass to embodied CO 2 eq mass (Arceo et al., 2023b) (Figure 1d).The database includes a range of factors for each material, capturing variability in published data.Each material was assigned a minimum, maximum (based on the observed min/max), and most likely factor based on the industry average in Toronto (Supporting Information S1 Table 1.4).Results use most likely factors unless otherwise noted.The analysis includes considerations for variability in GHG emissions factors (Supporting Information S3 Figure 3.1).Given the similarity of low-rise construction regulations across Canada and the United States, the study assumes that missing middle buildings outside of Toronto reasonably represent buildings that could be constructed in Toronto; therefore, the analysis applies Toronto emissions factors to all buildings.In cases where an element could be more than one material and the drawings do not specify a material (e.g., sheathing, which could be plywood or oriented strand board), the range of factors from possible materials were combined and the most likely factors were averaged.GHG emissions factors for biogenic materials use the 0/0 approach (Andersen et al., 2021).

RESULTS
Figure 2 summarizes the mass and embodied GHG of the 39 missing middle buildings, partitioned by MasterFormat level 1 code/material and organized by increasing floor area.Figure 2 shows that the embodied GHG efficiency of the missing middle is highly variable across a range of floor areas, with values differing between 5540 and 39,600 kgCO 2 eq/bedroom.Structural concrete dominates mass and is a large contributor to embodied GHG, making up on average 57.6% and 24.3% of each, respectively.Thermal and moisture protection materials have a small mass contribution (4.26%) but a high embodied emission contribution (32.2%).The remaining results are organized as follows: Section 3.1 compares missing middle with single-family and mid/high-rise residential forms.Section 3.2 further examines drivers of embodied GHG in the studied residential buildings, and Section 3.3 quantifies potential embodied GHG savings from missing middle buildings.

Comparing embodied emissions across building forms
Figure 3 breaks down embodied emissions intensity per bedroom by all residential forms described in Table 1 and the materials encoded in MasterFormat level 1. Full results of statistical tests are given in Supporting Information S4 Tables 4.1-4.9.
On average, missing middle buildings have less embodied GHG per bedroom than single-family homes, but this is not true for all missing middle forms.Welch's unequal variance T-test was used to compare the mean embodied GHG of different forms at a 95% confidence interval; the tests show that multi-unit missing middle housing-a grouping of every missing middle form except laneway suites-has significantly lower mean embodied efficiency per bedroom than single-family (p = 0.0061), averaging 12,700 kgCO 2 eq/bedroom compared to single family's 17000 kgCO 2 eq/bedroom.Laneway suites are the least efficient form of missing middle and by themselves are more intense than single family, averaging 17,400 kgCO 2 eq/bedroom.This is moderated by the reality that many laneways dedicate their ground floor to indoor parking, meaning that a large percentage of their materials are related to parking for another dwelling (the primary house on the lot).Per-lot analysis of residential forms could change the efficiency outlook of laneways.When laneway suites are grouped back in with multi-unit missing middle buildings, the mean embodied GHG per bedroom of missing middle remains lower than the single-family mean, but not significantly.Rowhouses and multiplexes are the missing F I G U R E 3 Embodied emissions per bedroom, broken down by building form and MasterFormat level 1 material.The red line indicates the mean of particular box plots.Building types annotated with an * are missing middle forms.Underlying data can be found in Supporting Information S2.
middle forms with the lowest mean embodied GHG intensity, averaging around 11,000 kgCO 2 eq/bedroom.Separate from mean comparisons, there are outliers within residential forms.For example, building #60 is a laneway suite with 7450 kgCO 2 eq/bedroom, 42.8% lower than the mean.Compared to most likely GHG emissions factors, the mean embodied efficiency of the multi-unit missing middle is 33% lower when using all minimum factors and 44% higher when using maximum factors.
From a materials perspective, concrete, thermal, and waterproofing elements drive the emissions in all forms, especially in mid/high-rise buildings and laneway suites.The mean embodied GHG intensity of concrete in mid/high-rise buildings is 9870 kgCO 2 eq/bedroom, which significantly exceeds the mean concrete intensity in every other form (p = 2.5 × 10 −3 to 2.1 × 10 −10 ) and exceeds the total mean intensity in the most efficient missing middle building by 44%.The embodied GHG intensity of the concrete in single-family homes also significantly exceeds the mean in missing middle both with (p = 0.0019) and without laneways (p = 0.0020).An unusually large amount of embodied GHG in laneway suites comes from thermal and waterproofing elements-7210 kgCO 2 eq/bedroom on average-compared to other missing middle forms.This is because most laneway suites contain a garage and lack an attic, both of which increase the insulation required by local building codes (Ontario Building Code, 2016).Laneways without garages have per bedroom GHG efficiency similar to the most efficient single-family homes (Supporting Information S3 Figure 3.2), except for building #70 which has a large concrete basement and GHG-intensive metal finishes.Due to large variability in GHG emissions factors for thermal and waterproofing elements and the heavy use of insulation in laneway suites, the mean embodied GHG in laneways is a less unusual 10,600 kgCO 2 eq/bedroom with minimum factors and an immense 33,600 kgCO 2 eq/bedroom with maximum factors.
Figure 3 illustrates that the observed variability is larger within forms than between them.Per bedroom, the coefficient of variation of embodied GHG within missing middle forms ranged from 29.8% to 51.0% and was 51.0% for the grouping of all missing middle buildings.Conversely, the coefficient of variation between the mean of each form was 19.8%.The least GHG-intensive missing middle building uses 34,100 less kgCO 2 eq/bedroom than the most intensive.This highlights an opportunity for achieving large embodied GHG reductions by optimizing design regardless of form.It also adds caution to the increasing expectation that missing middle forms are inherently more sustainable and that switching to missing middle alone will sufficiently reduce embodied GHG.The results show that missing middle has the potential to greatly reduce embodied GHG-given certain design choices.Major drivers of emissions and opportunities for reductions within forms are discussed in Section 3.2.
Figure 4 plots the per bedroom and per m 2 intensity of concrete in missing middle, single-family, and mid/high-rise buildings against the number of floors above ground.The figure highlights that normalized embodied GHG intensity does not necessarily increase as buildings get taller.
Low-rise single-family and missing middle buildings have a variable intensity that does not increase with the number of floors per m 2 (p = 0.34) or per bedroom (p = 0.19).The mid/high rise buildings see a significant increase of 0.73 kgCO 2 eq/m 2 per floor from concrete (R 2 = 0.279, p = 0.012) (Figure 4a), but the trend is insignificant per bedroom (p = 0.25) (Figure 4b).Taller mid/high-rise buildings have increased slenderness (ratio of base to height), which reduces the building footprint and increases embodied GHG intensity per m 2 with floor count.However, per-bedroom normalization shows that mid/high-rise buildings with more floors are not inherently more GHG intensive, and there are structural concrete buildings that deviate well below the trendline.Also, per-bedroom intensity does not decrease as bedrooms per floor count increase (Supporting Information S3 Figure 3.3).This means that the observed effect is not due to taller buildings having more bedrooms per floor.Instead, best-in-class residential buildings are found to have structural and architectural design choices that reduce their embodied GHG intensity independent of height, bedroom count, or GFA.F I G U R E 5 Embodied greenhouse gas (GHG) per bedroom, organized by building type and split by superstructure and substructure.The horizontal axis shows the unique building ID from the database.The * annotation highlights buildings 54 and 66, which are compared in the text.Underlying data can be found in Supporting Information S2.

Drivers of emissions and opportunities for reductions
Concrete used in basements and parking garages accounts for a large portion of embodied GHG intensity in the studied buildings.Figure 5 plots the embodied GHG per bedroom of each building, grouped by form and split into substructure and superstructure emissions.The substructure accounts for 40.5% of quantified embodied GHG in single-family, 32.6% in missing middle, and 26.6% in mid/high-rise.Structural concrete accounts for 71.0% and 62.6% of these emissions in single-family and missing middle, respectively.In single-family and missing middle, the bulk of substructure concrete emissions is in wall foundations, whereas underground parking slabs dominate in mid/high-rise buildings.The remaining substructure embodied emissions are a mix of waterproofing, insulation, and non-structural concrete elements (e.g., cementitious damp proofing).Substructure construction is more intensive than its superstructure counterpart and adds little livable space to buildings.For example, the mid-high rise building #54 has 44 superstructure floors of residential units accounting for 62% of embodied concrete GHG (see Figure 5 annotation).The other 38% is taken up by five floors of underground parking.In contrast, building #66 has 51 superstructure floors and similar superstructure emissions to #54 but saves 4970 kgCO 2 eq/bedroom of substructure concrete emissions by having only 1 floor of underground parking.Substructures can drive emissions in missing middle forms as well, particularly in laneways and low-rise apartments.Building #76, the most GHG-intensive building in the study, is a laneway suite with 40% of its embodied emissions in the substructure.Several low-rise apartments have one floor of underground parking that accounts for more than a quarter of their embodied GHG.
Wood structural elements in low-rise buildings have lower observed embodied GHG compared to their metal counterparts.Low-rise apartments using structural steel framing add 66.3 to 4310 more kgCO 2 eq/bedroom (26.0% of their structural emission on average) on top of concrete and wood emissions, which they use with a similar intensity to low-rise apartments without steel framing.Rowhouses using structural steel have an order of magnitude higher structural GHG intensity compared to those with just wood framing.Interior structural framing is almost entirely wood and contributes very little to overall embodied emissions, accounting for 136 kgCO 2 eq/bedroom on average (1.94% of emissions from structural elements).
In mid/high-rise buildings made from reinforced concrete, slabs and drop panels make up 69.5% of concrete superstructure embodied emissions on average.Minimizing slab volume offers the greatest chance for reductions in this form.Other embodied emissions can be found in smaller concrete features like elevator shafts and balconies.For example, balcony decks constitute 4.11% of observed concrete embodied GHG in mid/high-rise superstructures on average.
Overall, a few major materials contribute the majority of embodied GHG emissions in most single-family and missing middle buildings, highlighting opportunities for GHG reductions in material design and selection.Figure 6 shows the 15 materials (organized by MasterFormat level 4) that account for the largest share of embodied GHG on average and appear in at least five buildings.Though there is some variation between missing middle and single family, the following materials drive embodied GHG in most low-rise buildings: structural concrete (in the substructure), masonry veneer, insulation, gypsum drywall, and metal framing and finishes (e.g., aluminum finishes and railings).These major materials contribute 40%−60+% of emissions in low-rise residential forms.Results are similar when using minimum GHG emissions factors for all materials, except insulations see a 6.3%-4.9%drop in emissions share, and metal finishes take up an increased share.Insulation dominates emissions under maximum factors (Supporting Information S3 Figure 3.4).
Figure 6 also shows that when material percentages are rank ordered, there is a significant (R 2 = 0.939, 0.945; p = 1.1 × 10 −38 , 2.1 × 10 −27 ) exponential decrease in each subsequent material's share of emissions.Given this, policies and design strategies that allow for even minor reductions in the top three to five materials will be more effective at reducing embodied GHG than strategies targeting materials in the bottom half of the rank order.

Quantifying possible embodied emission reductions from changes in housing form
As of the 2021 Canadian census, Toronto has 270,490 single-detached houses and 542,625 apartment units with five or more floors (Statistics Canada, 2022a).Multiplying by the mean number of bedrooms in Table 1, this equates to 1.07 million single-family and 738,000 mid/high-rise bedrooms.If every single-family bedroom in Toronto had instead been built within a mean, non-laneway missing middle building, the city's current embodied GHG stock would have been reduced by 4.59 MtCO 2 eq.If mid/high-rise bedrooms had instead been built within a mean, non-laneway missing middle, the embodied GHG of concrete would be reduced by 4.85 MtCO 2 eq.Furthermore, if the replacements were with a missing middle building at the 1st quartile of embodied GHG instead of the mean and used minimum thermal and waterproofing emissions factors, savings would have more than doubled to 9.73 MtCO 2 eq for single-family and increased to 6.18 MtCO 2 eq for mid/high-rise concrete.These are lower-bound estimates given the scope of material quantification in the study does not include utilities, landscaping, and other details.Also, the 1st quartile is a conservative estimate of best-in-class that leaves room for further savings from the most efficient missing middle buildings.
Toronto is located in Ontario, the most populated province in Canada.Ontario has committed to build 1.5 million homes by 2030 to meet increasing demand (Government of Ontario, 2022); the difference between providing these homes with business-as-usual construction (maintaining the current proportions of each housing form) and providing them using 1st quartile missing middle buildings with minimum thermal and waterproofing emission factors could be in the order of 4.67 MtCO 2 eq or more a year-equivalent to 46.7% savings over business-as-usual construction.These calculated savings are again conservative given the scope of material quantification.They also exclude potential savings in supporting infrastructure such as roads and water infrastructure (e.g., more kilometers of road are needed in lower-density forms).

Considerations for size and height in GHG efficiency of buildings
Our results show that while low-rise buildings generally have lower embodied GHG intensity than mid/high rise, there is significant variability within forms and nuances to achieving reductions through changes in size and height.The perception of the GHG intensity in low-rise and mid/high-rise buildings varies depending on the functional unit.The relationship between height and embodied concrete GHG is not significant when normalized per bedroom, and we observe a 50+ floor mid/high-rise building that is less embodied GHG intensive per bedroom than many single-family homes.
The embodied GHG of the smallest residential buildings is dominated by shell insulation and is sensitive to small changes in bedroom count.Even within the most GHG-efficient buildings observed-rowhouses and multiplexes with two to six units and two to three floors-there is large variability and care must be taken to limit embodied GHG through more than just form selection.Furthermore, low-rise buildings need a larger urban footprint to house the same number of people as taller buildings.The missing middle is more land efficient than single-family housing but less land efficient than taller buildings.This tradeoff is an important consideration in space-limited cities or when considering space-limited construction proposals.Building out has other environmental impacts not considered here, including embodied GHG of infrastructure (Rousseau et al., 2022), transportation/energy emissions (Norman et al., 2006), and loss of farmland (Bren d'Amour et al., 2017), among others.

Strategy and design implications of results
Multi-unit missing middle buildings have less embodied GHG per bedroom than single-family on average, but reducing emissions just by switching to missing middle misses the large GHG reduction potential of changes within forms.For example, rowhouses are the most GHG-efficient form and have 34.3% lower emissions compared to single-family on average.Despite this, 19 missing middle buildings of other forms and 3 single-family homes were observed to have lower embodied GHG per bedroom than the rowhouse mean.Given there is more variability within forms than between them, strategies for reducing the embodied GHG of housing should emphasize best-in-class construction alongside sustainable form selection.
For single-family and missing middle, best-in-class construction means limiting substructure size, reducing structural steel and aluminum finish use, and lowering drywall mass.Within the data, wooden structural systems have a lower impact than steel or concrete in low-rise buildings.This finding is not dependent on biogenic carbon as this paper uses the 0/0 approach (Anderson & Peters, 2016).That said, the use of wood has implications on land use, forestry management, and questions of how much wood can be sustainably harvested per year that are outside the scope of this paper.Also, single-family homes with smaller GFA generally have lower embodied GHG per bedroom (Supporting Information S3 Figure 3.2) (Arceo et al., 2021).In mid/high-rise, slab volume is a major driver of concrete emissions and could be reduced by building without step backs, which increase concrete load through large transfer slabs while reducing useable space.Indoor parking drives emissions across forms (e.g., laneway suites); reducing its use would limit embodied GHG from insulation and concrete and bring co-benefits from reducing overall parking in cities (Donald Shoup, 2018).Finally, continued legalization of the missing middle will increase opportunities for new, low embodied GHG housing in North America.The above strategies can be implemented immediately in policy and design, maximizing adaptation cost savings compared to strategies that hedge on future changes in material manufacturing to reduce embodied GHG.
Across all forms, there are large opportunities for savings in switching to commercially available, low-embodied GHG thermal and waterproofing elements.Using minimum and maximum GHG emissions factors reduce/increase the calculated embodied GHG of these elements −4000 and +13,600 kgCO 2 eq/bedroom, respectively, from the most likely intensity depending on form (Supporting Information S3 Figure 3.1).The minimum emissions factor insulations are not specialty products but generic mineral fiber (0.885 kgCO 2 eq/kg), meaning savings can be achieved by switching to best-in-market products with comparable R-value.For example, savings can be achieved by replacing high emissions factor materials with similarly functioning alternatives, like swapping superstructure XPS (∼14.0 kgCO 2 eq/kg) for EPS (∼1.51 kgCO 2 eq/kg), two insulations with similar operational performance (Rivera et al., 2021).

Data standardization, limitations, and future work
The study's material quantification technique had time and standardization limitations.Even with the omission of time-consuming elements like metal hardware, material quantifications took between 50 and 200+ h per building.Given the small sample sizes for some housing forms, it is not possible to draw detailed and statistically strong conclusions about some specific forms (e.g., multiplexes) without grouping them under the umbrella of missing middle.The drawings were collected from construction firms rather than from a public database of buildings, so there is an unquantified sampling bias.Other sources of uncertainty are similarly hard to quantify.The dataset contains buildings built/to be built between 2009 and 2025 from different cities in North America, introducing temporal and spatial uncertainty.Takeoffs likely vary slightly depending on which of the 13 researchers completed them, though the quality control review process was used to limit this.The weighted qualitative uncertainty of takeoff data described in Section 2.1 ranged between 2 and 3 for all forms (Supporting Information S3 Figure 3.5).
Material mass and embodied emissions per m 2 found in this paper generally lie between the 1st quartile and the mean of values found in other somewhat older databases and embodied quantification reviews (Röck et al., 2020;Simonen et al., 2017;Sprecher et al., 2021).Differences are to be expected given variation in location and associated construction codes/norms, age of embodied GHG factors (given slow but steady decreases of material embodied GHG), and definition of GFA.As such, direct comparisons between papers are challenging.
Improved integration of BIM with embodied GHG quantification could help address the above limitations.Standardization of public and private building records in software like REVIT, with sufficient detail, could increase the size and independence of samples.This would require detailed labeling of materials and elements in BIMs, which is currently rare, and a standard labeling system for comparability (such as the MasterFormat and UniFormat ontology used here).The field of sustainable construction would also benefit from future research on implementation and barriers to the recommended strategies.

CONCLUSION
This study quantifies the potential of different housing forms, specifically low-rise multi-unit forms often referred to as missing middle, for providing more housing with less embodied GHG emissions.The study adds 42 new material quantifications of North American buildings to the public record and maps material mass to embodied GHG.Like other forms of housing, embodied GHG in missing middle buildings is variable (5540-39,600 kgCO 2 eq/bedroom).On average, multi-unit missing middle buildings have a lower embodied GHG intensity than single-family (12,700 vs. 17,000 kgCO 2 eq/bedroom, p = 0.0061), but laneway suites do not (17,400 kgCO 2 eq/bedroom) because they dedicate a disproportionate amount of space to parking.The building forms with the lowest embodied GHG are two-to three-story multiplexes and rowhouses.Concrete in mid/high buildings is generally more GHG intensive than low-rise per m 2 , but per-bedroom normalization reveals that taller buildings can be less intensive than low-rise due to variability in building design.
Building form and height do not necessarily determine embodied GHG intensity.There is more variability within (29.8%−51.0%)building forms than between (19.8%), with overlap between the embodied GHG of different forms.Design choices can yield large reductions in emissions.Substructures drive emissions in all forms, and limiting basements and interior parking could reduce embodied GHG by 26.6%-40.5%.In low-rise buildings, limiting structural steel, aluminum finishes, and gypsum wallboards could reduce embodied GHG intensity.In mid/high-rise buildings, 69.5% of superstructure embodied concrete GHG is dictated by slab volume, which could be reduced by limiting step backs.Thermal and waterproofing elements (e.g., insulation) in all forms are sensitive to material GHG factor, and their emission may be reduced up to 4000 kgCO 2 eq/bedroom by choosing widely available, low-GHG products.
Study method.(a) Organized drawings and file formats for buildings B 1 → B n .(b) Format of final material volumes organized in the Excel template.(c) Format of the takeoff data table in the material database, with matrix entries for element m in kg.(d) Distribution of min, max, and most likely CO 2 eq mass for each element m in any building B i .calculated using the thickness from the code and is given an uncertainty score of 3. Quantifications were quality reviewed by a secondary researcher for consistency and accuracy.
Per-bedroom intensity of each missing middle building: (a) embodied emissions and (b) material mass.The horizontal axis shows the unique building ID from the database.Buildings are organized from smallest to largest from left to right by gross floor area, which is plotted in black and measured on the right axis.Underlying data can be found in Supporting Information S2.
Floors above ground versus embodied greenhouse gas (GHG) intensity of concrete for the three general residential building forms: (a) per m 2 and (b) per bedroom.Underlying data can be found in Supporting Information S2.
Top 15 materials with the largest average share of embodied greenhouse gas (GHG): (a) materials in the missing middle and (b) in single-family buildings.The embedded plot shows the exponential trend of mean material share when all materials in the given building form are rank-ordered.Only materials used in five or more buildings are shown.Underlying data can be found in Supporting Information S2.
Strategies for reducing embodied GHG in future residential housing should focus on constructing best-in-class buildings while also promoting missing middle construction.A simple calculation shows that constructing missing middle instead of single-family homes could have reduced residential embodied GHG by 4.59 MtCO 2 eq in Toronto, Canada's housing stock.Reductions would have more than doubled to 9.73 MtCO 2 eq if buildings had been in the 1st quartile of embodied GHG and used minimum thermal and waterproofing emissions factors.Building 1st quartile missing middle instead of business-as-usual single-family and mid/high-rise constructions could reduce Ontario, Canada's future embodied residential GHG emissions by 46.7% without requiring changes in material technology.Future work should expand the use of BIM in embodied GHG accounting and further the implementation of material efficiency strategies.