Ocean-sediment and weathering interactions exert the primary control on how much anthropogenic-emitted CO2 remains in the atmosphere on timescales longer than about 1 kyr. Analytical theory is presented which predicts, from initial conditions, the remaining atmospheric fraction of emitted CO2 after equilibrium with CaCO3 burial in deep-sea sediments but before silicate weathering removes all excess CO2 on a >100 kyr timescale. The theoretical predictions of final atmospheric CO 2 partial pressure are tested against independent integrations of the GENIE-1 Earth system model and are found to agree to within 10% for total emissions up to about 4000 PgC. The predicted theoretical relationship is linear and is based on the assumptions that ocean carbonate ion concentration is restored when CaCO3 burial reaches a new steady state, and that the steady state change in global ocean CO*2 is proportional to the change in atmospheric CO2; where CO*2 is the combined concentration of aqueous CO2 and carbonic acid. We find that the residual fraction of anthropogenic CO2 in the atmosphere can be determined without explicit use of ocean [CO2-3.], even though this concentration is known to be important in controlling the depth interval over which CaCO3-rich sediments accumulate. The simple theory developed here is particularly suited for efficient assessment of events recorded in the geological record as well as anthropogenic CO2 influences on the long-term stability of ice sheets.