Greenhouse gas emissions from global agriculture are increasing at around 1% perannum, yet substantial cuts in emissions are needed across all sectors 1 . The challenge of reducing agricultural emissions is particularly acute, because the reductions achievable by changing farming practices are limited 2,3 and are hampered by rapidly rising food demand 4,5 . Here we assess the technical mitigation potential offered by land sparingincreasing agricultural yields, reducing farmland area and actively restoring natural habitats on the land spared 6 . Restored habitats can sequester carbon and can offset emissions from agriculture. Using the United Kingdom as an example, we estimate net emissions in 2050 under a range of future agricultural scenarios. We find that a landsparing strategy has the technical potential to achieve significant reductions in net emissions from agriculture and land-use change. Coupling land sparing with demandside strategies to reduce meat consumption and food waste can further increase the technical mitigation potential, however economic and implementation considerations might limit the degree to which this technical potential could be realised in practice.We projected the mitigation potential of land sparing in the United Kingdom with reference to its binding commitment to reduce emissions by 80% by 2050 (relative to 1990 levels) 7 . We began by identifying a technically plausible range in the future yields of all major crop and livestock commodities produced in the UK, based on historic trends and future potential. We define yields as the annual tonnage of production per hectare for crops and the feed conversion ratio (feed consumed per kilogram of production) for livestock. Future yields could vary across a wide range, driven by a number of biophysical, technical and socioeconomic factors [8][9][10][11] . We assessed the likely bounds of this range based on an assessment of technical potential and reflect this in our projections, which span yield declines through to sustained long-term growth averaging 1.3% per annum across all commodities 3 (Table 1; Supplementary Fig. 1; Supplementary Discussion). For the avoidance of doubt, we do not equate our lower yielding scenarios with 'land sharing'.We next projected emissions attributable to UK agricultural production out to 2050, quantifying all sources of emissions that would be affected by a land-sparing strategy. We therefore quantified not only emissions reported under 'Agriculture' in the UK's greenhouse gas inventory 12 , but also emissions related to agriculture but reported in other sectors (e.g. farm energy use, agro-chemical production and land-use change), and emissions arising overseas due to imported feed for livestock (see Supplementary Table 2 for all emissions sources quantified). Our projections assumed that agricultural production increases from present levels in proportion to projected demand growth (Supplementary Table 1). In certain scenarios, projected UK farming capacity does not keep pace with demand growth. In such cases ...