Direct injection of CO2, into the ocean is a potentially effective carbon sequestration strategy. Therefore, we want to understand the effectiveness of oceanic injection and develop the appropriate analytic framework to allow us to compare the effectiveness of this strategy with other carbon management options. Here, after a brief review of direct oceanic injection, we estimate the effectiveness of ocean carbon sequestration using one dimensional and three dimensional ocean models. We discuss a new measure of effectiveness of carbon sequestration in a leaky reservoir, which we denote sequestration potential. The sequestration potential is the fraction of global warming cost avoided by sequestration in a reservoir. We show how these measures apply to permanent sequestration and sequestration in leaky reservoirs, such as the oceans, terrestrial biosphere, and some geologic formations. Under the assumptions of a constant cost of carbon emission and a 4 % discount rate, injecting 900 m deep in the ocean avoids approx. 90 % of the global warming cost associated with atmospheric emission; an injection 1700 m deep would avoid > 99 % of the global warming cost. Hence, for discount rates in the range commonly used by commercial enterprises, oceanic direct injection may be nearly as economically effective as permanent sequestration at avoiding global warming costs.