Below is the original analyses and chapter 1.1 of the report. However, since 2018 there are updated figures available for the carbon budget under the 1,5 and 3 degree scenario. These are slightly higher as previously agreed. The special report by IPCC of October 2018 states that the atmosphere can absorb no more than 420 gigatonnes (Gt) of CO2 if we are to stay below the 1.5°C threshold. ( was 200 in 2016) However, since around 42 Gt of CO2 is emitted globally every year—the equivalent of 1332 tonnes per second—this budget is expected to be used up in just over nine years. The budget for staying below the 2°C threshold, for its part, of approximately 1170 Gt, (was 800 in 2016) will be exhausted in about 26 years.
A ticking clock with the new data can be found here: https://www.mcc-berlin.net/en/research/co2-budget.html
1.1 the CO2 budget
The anthropogenic driver of climate change is the increasing concentration of greenhouse gases (GHG) in the atmosphere, chiefly CO2, but also including Methane, Sox and Nox gases, of which a large part is emitted due to human related activities. The cause is mainly burning fossil fuels, and related effects, like the industrial capacity to produce artificial fertilizers, to grow increased yields to feed cattle, that emits NOx. Eliminating fossil fuels would be a direct improvement, which is the main issue for the built environment.
Within the building sector, the most practical strategy is to focus on CO2 emissions.
Scientific research has been able to calculate that there is a kind of maximum emissions budget, which cannot be exceeded without having global temperatures exceed 2ºC, which is considered by IPCC and other researchers to constitute the maximum rise without causing drastic consequences for human life on the planet.[1,2,3] There is also a consensus that 1.5ºC is a safer limit, and attempts should be made to limit global warming close to the 1,5 degree.
The current situation is that we have only 5 years left before the 66% chance to stay below 1.5 degrees is blown. That budget is 204 GtonnesCO2-eq .
For 2 degrees the budget left is 800 Gtonnes CO2-eq (2016) Without any (additional) action, and with current emissions of 40 billion tonnes a year, that budget will be spent in 20 years . See the graph for additional calculations with other chances and with 1.5 , 2 or 3 degrees target 
Figure 1: Carbon Countdown for different scenario (1.5 to 3 degrees) and for different risk consideration (35% to 66% chance to achieve this scenario)(Sce: carbonbrief ).
The actual amount of remaining emissions, is real time documented on a website maintained by the scientific editors from the Guardian Newspaper, and can be found here: https://www.theguardian.com/environment/datablog/2017/jan/19/carbon-countdown-clock-how-much-of-the-worlds-carbon-budget-have-we-spent
After having used this budget, the man caused emissions must remain at zero in the following years. And this situation should be prolonged for as long as the nature has resettled and absorbed CO2, which can take up 50-100 years or more. In this situation, zero does not mean an absolute zero in emissions, but that the emissions needs to be compensated by the naturally captured CO2, this extra budget being related to productive biomass and bio-based materials use, with renewable energy as the driver.
With 0-CO2 being the target for human activities, any new activity or materials investment not complying with 0-CO2 from this moment on, will consume part of the budget, and increasing demand, without being used to be invested for contributing to lowering demand thereafter.
Studies show that building a renewable energy supply system, might even need more materials and related CO2 input as is available in material stocks and GHG budget. [5,6,7]. In other words, the remaining budget should only be used to bringing all our CO2 emitting activities to (near-) 0.
Recently new papers have been published highlighting the urgency of the situation, and the very small time window remaining to bring us on track to the 2 degrees.
Hanssen and 17 colleagues published in a spring 2016 paper further scientific analyses on the GHG consequences, and state:
“We conclude that the message our climate science delivers to society, policymakers, and the public alike is this: “we have a global emergency”. 
Rogelj and colleagues announced in their Nature paper in may 2016 that the Paris Agreement climate proposals need a boost to keep warming well below 2 °C. The paper argues that we are far off the path to two degrees. 
For ease of explorations of emissions in the building sector, which is nearly all CO2 related, we use the 800 Gt Budget for 2 degrees , and 200 Gt budget for 1,5 degrees scenarios. (ie B2 and B1,5)
The 1.5 degrees scenario
The budget is ~200 Gtonnes CO2. Assuming between now and 2050 population will rise to 10 billion, the average for the transition period is 8.5 billion.
Which implies a budget per capita of 23.5 tonnes of CO2 remaining. If we would use the full proposed transition period until 2050, the budget would be 0.7 tonnes of CO2 per capita per year.
As a reference, the total global budget emitted in 2014 was 35.9 Gt CO2 That is per capita-year: (for the current 7.2 billion people) : 5 tonnes. That implies there is only 4.7 years left until we will have passed the threshold for 1.5 degree. 
The 2 degree scenario
The budget is 800 Gtonnes CO2, which implies a budget of 94 tonnes per capita. (the 8.5 billion people-see above). Using the full transition period until 2050, it comes down to 2,5 tonnes CO2/cap-year
With current global average use of 5 ton CO2/cap year, with Business as usual, there are only 19 years to go.
In both cases after 2050 anthropogenic CO2 emissions should be (net) 0.
1 Meinshausen M., Meinshausen N., Hare W., Raper S., Frieler K., Knutti R., Frame D., Allen M., Greenhouse-gas emission targets for limiting global warming to 2C . (2009), Nature, Vol 458 April 2009. CO2 budget: http://www.climatecentral.org/news/two-decades-until-carbon-budget-is-eaten-through-18051
2 Friedlingstein P., Andrew R., Rogelj J., Peters G., Canadell J., Knutti R., Luderer G., Raupach M., Schaeffer M.,Vuuren D. Le Quéré C., (2014) Persistent growth of CO2 emissions and implications for reaching climate target , in Nature Geoscience 7,709–715
3 Carbon budget evaluated :
4 interactive graph for Carbon emissions budgets: https://www.carbonbrief.org/analysis-only-five-years-left-before-one-point-five-c-budget-is-blown
and the datasheet:
5 Kleijn, R. 2012, Materials and energy : a store of linkages, Book, Leiden University, ISBN 978-90-9026938-2
6 Smil V, 2013 Making the Modern World , Materials and Dematerialization, Book ISBN10 1119942535
7 Allwood J., Cullen J., 2012 , Sustainable materials, With Both eyes open
8 Ice melt, sea level rise and superstorms: evidence from paleoclimate data, climate modeling, and modern observations that 2 °C global warming could be dangerous, James Hansen1 , et all Atmos. Chem. Phys., 16, 3761-3812, doi:10.5194/acp-16-3761-2016, 2016.
9 Paris Agreement climate proposals need a boost to keep warming well below 2 °C Joeri Rogelj, Michel den Elzen, Niklas Höhne, Taryn Fransen, Hanna Fekete, Harald Winkler, Roberto Schaeffer, Fu Sha, Keywan Riahi & Malte Meinshausen May 2016, Nature 534, 631–639 doi:10.1038/nature18307