Deforestation has contributed significantly to net greenhouse gas emissions, but slowing deforestation, regrowing forests and other ecosystem processes have made forests a net sink. Deforestation will still influence future carbon fluxes, but the role of forest growth through aging, management, and other silvicultural inputs on future carbon fluxes are critically important but not recognized by bookkeeping and integrated assessment models. When projecting the future, it is vital to capture how management processes affect carbon storage in ecosystems and wood products. This study assesses future forest carbon calculated by global forestry models that manage forests to provide wood products and carbon. The results indicate forests will remain a carbon sink in the future, sequestering 1.2-5.8 GtCO2e/yr under a wide range of drivers and conditions, including increased demand for wood products, agricultural land, and carbon. Improved forest management can jointly increase carbon stocks and harvests without expanding forest area.