The soils of the permafrost region are estimated to hold 1100 to 1500 billion tonnes of carbon. As climate change progresses much of this permafrost is expected to thaw and the carbon within it decay. Here we conduct numerical experiments with a climate model to estimate with formal uncertainty bounds the release of carbon from permafrost soils. Our simulations suggest that the permafrost carbon will make a significant but not cataclysmic contribution to climate change over the next centuries.