The ocean contains about 40 times more carbon than the atmosphere, storing 38,000 Pg C as dissolved inorganic carbon (DIC) versus 900 Pg C as carbon dioxide (CO$_2$) in the present atmosphere. The biological carbon pump contributes to ocean carbon storage by moving organic carbon out of the surface ocean into deeper waters in sinking particles, vertically migrating organisms and physical circulation. Century-scale (≥100 years) storage of the resulting biogenic DIC is commonly assumed to occur exclusively in the deep ocean, typically below 1,000 m. However, recent work has shown that carbon can be sequestered at century scales above 1,000 m in many ocean regions, in what we call ‘continuous vertical sequestration’. Here we calculate the century-scale carbon sequestration flux driven by the biological pump throughout the water column by combining previously published estimates of organic carbon flux and modelled values of water-mass sequestration time distributions. We estimate that the flux of organic carbon that is sequestered for ≥100 years in the contemporary ocean by the combined action of various biological pump pathways is 0.9–2.6 Pg C yr$^{−1}$, which is up to six times larger than previous estimates based on the organic carbon flux reaching the deep ocean.