A global carbon cycle model is used to reconstruct the carbon budget, balancing emissions from fossil fuel and land use with carbon uptake by the oceans, and the terrestrial biosphere. We apply Bayesian statistics to estimate uncertainty of carbon uptake by the oceans and the terrestrial biosphere based on carbon dioxide and carbon isotope records, and prior information on model parameter probability distributions. This results in a quantitative reconstruction of past carbon budget and its uncertainty derived from an explicit choice of model, data-based constraints, and prior distribution of parameters. Our estimated ocean sink for the 1980s is 17±7 Gt C (90% confidence interval) and is comparable to the estimate of 20±8 Gt C given in the recent Intergovernmental Panel on Climate Change assessment [Schimel et al., 1996]. Constraint choice is tested to determine which records have the most influence over estimates of the past carbon budget; records individually (e.g., bomb-radiocarbon inventory) have little effect since there are other records which form similar constraints.