Recent thinking about the economics of climate change has concerned the uncertainty about the upper bound of both climate sensitivity to greenhouse gases and the damages that might occur at high temperatures. This argument suggests that the appropriate probability distributions for these factors may be fat-tailed. The matter of tail shape has important implications for the calculation of the social cost of carbon dioxide (SCCO2). In this paper a probabilistic integrated assessment model is adapted to allow for the possibility of a thin, intermediate or fat tail for both (i) the climate sensitivity parameter and (ii) the damage function exponent. Results show that depending on the tail shape of the climate sensitivity parameter the mean SCCO2 rises by 2985%. Changes in the mean SCCO2 due to the adjustments to the damage function alone range from a reduction of 7% to a rise of 12%. The combination of both leads to rises of 3315%. Greater rises occur for the upper percentiles of the SCCO2 estimates. Given the uncertainties in both the science and the economics of climate change different tail shapes deserve consideration due to their important implications for the range of possible values for the SCCO2.