In recent decades, the warming in the Arctic has been much faster than in the rest of the world, a phenomenon known as Arctic amplification (AA). Numerous studies report that Arctic is warming either twice, more than twice, or even three times as fast as the globe on average. However, the lack of consensus of AA definition precludes its precise quantification. Here we show, by using several observational datasets which cover the Arctic region and adopting a simple definition of AA, that during the last 40 years the Arctic has been warming almost four times faster than the globe as a whole, which is a higher ratio than generally reported in literature. Furthermore, we compared the observed AA ratio to the ratio simulated by state-of-the-art climate models, and show that the models largely underestimate the present AA, a finding that is not very sensitive to the exact definition of AA. The underestimation of AA by climate models most likely results from their inability to realistically simulate feedback mechanisms between sea ice melt and atmospheric temperatures. Our results imply that the underestimated AA leads to biased projections of climate change both in the Arctic and mid-latitudes.