Comprehensive global climate models are the only tools that account for the complex set of processes which will determine future climate change at both a global and regional level. Planners are typically faced with a wide range of predicted changes from different models of unknown relative quality, owing to large but unquantified uncertainties in the modelling process. Here we report a systematic attempt to determine the range of climate changes consistent with these uncertainties, based on a 53-member ensemble of model versions constructed by varying model parameters. We estimate a probability density function for the sensitivity of climate to a doubling of atmospheric carbon dioxide levels, and obtain a 5-95 per cent probability range of 2.4-5.4 degrees C. Our probability density function is constrained by objective estimates of the relative reliability of different model versions, the choice of model parameters that are varied and their uncertainty ranges, specified on the basis of expert advice. Our ensemble produces a range of regional changes much wider than indicated by traditional methods based on scaling the response patterns of an individual simulation.