The transient global warming event known as the Palaeocene-Eocene Thermal Maximum occurred about 55.9 Myr ago. The warming was accompanied by a rapid shift in the isotopic signature of sedimentary carbonates, suggesting that the event was triggered by a massive release of carbon to the ocean-atmosphere system. However, the source, rate of emission and total amount of carbon involved remain poorly constrained. Here we use an expanded marine sedimentary section from Spitsbergen to reconstruct the carbon isotope excursion as recorded in marine organic matter. We find that the total magnitude of the carbon isotope excursion in the ocean-atmosphere system was about 4%. We then force an Earth system model of intermediate complexity to conform to our isotope record, allowing us to generate a continuous estimate of the rate of carbon emissions to the atmosphere. Our simulations show that the peak rate of carbon addition was probably in the range of 0.3-1.7 Pg C yr-1, much slower than the present rate of carbon emissions.