Permafrost, which covers 15 million km(2) of the land surface, is one of the components of the Earth system that is most sensitive to warming(1,2). Loss of permafrost would radically change high-latitude hydrology and biogeochemical cycling, and could therefore provide very significant feedbacks on climate change(3-8). The latest climate models all predict warming of high-latitude soils and thus thawing of permafrost under future climate change, but with widely varying magnitudes of permafrost thaw(9,10). Here we show that in each of the models, their present-day spatial distribution of permafrost and air temperature can be used to infer the sensitivity of permafrost to future global warming. Using the same approach for the observed permafrost distribution and air temperature, we estimate a sensitivity of permafrost area loss to global mean warming at stabilization of 4.0(-1.1)(+1.0) million km(2) degrees C-1 (1 sigma confidence), which is around 20% higher than previous studies(9). Our method facilitates an assessment for COP21 climate change targets(11): if the climate is stabilized at 2 degrees C above pre-industrial levels, we estimate that the permafrost area would eventually be reduced by over 40%. Stabilizing at 1.5 degrees C rather than 2 degrees C would save approximately 2 million km(2) of permafrost.