The decline of Arctic sea ice is one of the most visible signs of climate change over the past several decades. Arctic sea ice area shows large interannual variability due to the numerous factors, but on longer time scales the total sea ice area is approximately linearly related to Arctic surface air temperature in models and observations. Overall, models however strongly underestimate the recent sea ice decline. Here we show that this can be explained with two interlinked biases. Most climate models simulate a smaller sea ice area reduction per degree local surface warming. Arctic polar amplification, the ratio between Arctic and global temperature, is also underestimated but a number of models are within the uncertainty estimated from natural variability. A recalibration of an ensemble of global climate models using observations over 28 years provides a scenario independent relationship and yields about 2°C change in annual mean global surface temperature above present as the most likely global temperature threshold for September sea ice to disappear, but with substantial associated uncertainty. Natural variability in the Arctic is large and needs to be considered both for such recalibrations as well as for model evaluation, in particular when observed trends are relatively short.