<p>Uncertainty in future CO₂ emissions and the geophysical response to emissions drives variability in future sea-level rise. However, the relative contributions of emissions and geophysical dynamics (for example, Antarctic Ice Sheet (AIS) tipping points) to future sea-level projections are not well understood. Here we disentangle their relative importance by propagating an ensemble of CO₂ emissions trajectories through a calibrated carbon cycle–climate–sea-level model chain. Without negative emissions, the CO₂ emissions trajectory, particularly the timing of when emissions are reduced, becomes the primary driver of sea-level variability between 2065 and 2075. Accelerated AIS melting greatly influences the sensitivity of global mean sea-level rise to time-averaged and integrated temperature changes. The most important geophysical uncertainties associated with the risk of exceeding sea-level thresholds are the threshold corresponding to accelerated AIS melting and equilibrium climate sensitivity. Our results highlight the need for both adaptation and rapid decarbonization to manage the risks posed by SLR.</p>