RADIOCARBON produced naturally in the upper atmosphere or artificially during nuclear weapons testing is the main tracer used to validate models of oceanic carbon cycling, in particular the exchange of carbon dioxide with the atmosphere(1-3) and the mixing parameters within the ocean itself(4-7). Here we test the overall consistency of exchange fluxes between all relevant compartments in a simple model of the global carbon cycle, using measurements of the long-term tropospheric CO2 concentration(8) and radiocarbon composition(9-12), the bomb C-14 inventory in the stratosphere(13,14) and a compilation of bomb detonation dates and strengths(15). We find that to balance the budget, we must invoke an extra source to account for 25% of the generally accepted uptake of bomb C-14 by the oceans(3). The strength of this source decreases from 1970 onwards, with a characteristic timescale similar to that of the ocean uptake. Significant radiocarbon transport from the remote high stratosphere and significantly reduced uptake of bomb C-14 by the biosphere can both be ruled out by observational constraints. We therefore conclude that the global oceanic bomb C-14 inventory should be revised downwards. A smaller oceanic bomb C-14 inventory also implies a smaller oceanic radiocarbon penetration depth(16), which in turn implies that the oceans take up 25% less anthropogenic CO2 than had previously been believed.