Forest growth provides negative emissions of carbon that could help keep the earth's surface temperature from exceeding 2°C, but the global potential is uncertain. Here we use land-use information from the FAO and a bookkeeping model to calculate the potential negative emissions that would result from allowing secondary forests to recover. We find the current gross carbon sink in forests recovering from harvests and abandoned agriculture to be -4.4 PgC/year, globally. The sink represents the potential for negative emissions if positive emissions from deforestation and wood harvest were eliminated. However, the sink is largely offset by emissions from wood products built up over the last century. Accounting for these committed emissions, we estimate that stopping deforestation and allowing secondary forests to grow would yield cumulative negative emissions between 2016 and 2100 of about 120 PgC, globally. Extending the lifetimes of wood products could potentially remove another 10 PgC from the atmosphere, for a total of approximately 130 PgC, or about 13 years of fossil fuel use at today's rate. As an upper limit, the estimate is conservative. It is based largely on past and current practices. But if greater negative emissions are to be realized, they will require an expansion of forest area, greater efficiencies in converting harvested wood to long-lasting products and sources of energy, and novel approaches for sequestering carbon in soils. That is, they will require current management practices to change.