Abstract The international community, through treaties such as the Paris agreement, aims to limit climate change to well below 2 °C, which implies reaching carbon neutrality around the second half of the century. In the current calculations underpinning the various roadmaps toward carbon neutrality, a major component is a steady or even expanding terrestrial carbon sink, supported by an increase of global forest biomass. However, recent research has challenged this view. Here we developed a framework that assesses the potential global equilibrium of forest biomass under different climate change scenarios. Results show that under global warming carbon storage potential in forest aboveground biomass gradually shifts to higher latitudes and the intensity of the disturbance regimes increases significantly almost everywhere. CO2 fertilization stands out as the most uncertain process, with different methods of estimation leading to diverging results by almost 155 PgC of above ground biomass at equilibrium. Overall, assuming that the sum of human pressures (e.g. wood extraction) does not change over time, that total forest cover does not change significantly and that the trend in CO2 fertilisation as it is currently estimated from satellite proxy observations remains, results show that we have reached (or are very close to reaching) the peak of global forest carbon storage. In the short term, where increased disturbance regimes are assumed to act quicker than increased forest growth potential, global forests might instead act as a carbon source, that will require even more effort in decarbonization than previously estimated. Therefore, the potential of forests as a nature-based solution to mitigate climate change brings higher uncertainties and risks than previously thought.