Agriculture directly contributes about 10%-12% of current global anthropogenic greenhouse gas emissions, mostly from livestock. However, such percentage estimates are based on global warming potentials (GWPs), which do not measure the actual warming caused by emissions and ignore the fact that methane does not accumulate in the atmosphere in the same way as CO . Here, we employ a simple carbon cycle-climate model, historical estimates and future projections of livestock emissions to infer the fraction of actual warming that is attributable to direct livestock non-CO emissions now and in future, and to CO from pasture conversions, without relying on GWPs. We find that direct livestock non-CO emissions caused about 19% of the total modelled warming of 0.81°C from all anthropogenic sources in 2010. CO from pasture conversions contributed at least another 0.03°C, bringing the warming directly attributable to livestock to 23% of the total warming in 2010. The significance of direct livestock emissions to future warming depends strongly on global actions to reduce emissions from other sectors. Direct non-CO livestock emissions would contribute only about 5% of the warming in 2100 if emissions from other sectors increase unabated, but could constitute as much as 18% (0.27°C) of the warming in 2100 if global CO emissions from other sectors are reduced to near or below zero by 2100, consistent with the goal of limiting warming to well below 2°C. These estimates constitute a lower bound since indirect emissions linked to livestock feed production and supply chains were not included. Our estimates demonstrate that expanding the mitigation potential and realizing substantial reductions of direct livestock non-CO emissions through demand and supply side measures can make an important contribution to achieve the stringent mitigation goals set out in the Paris Agreement, including by increasing the carbon budget consistent with the 1.5°C goal.