Mass loss from the ice sheets contributes substantial uncertainty to global mean sea-level rise under future warming.  The ice sheets have correlated uncertainties, amplifying the combined uncertainty.  However, the strength of the correlation is unknown.  Here, we aim to determine the correlation.  We begin by considering the idealized cases of independence and perfect correlation among the East Antarctic, West Antarctic, and Greenland ice sheet components of sea-level rise.  We find that correlation influences the 95th percentile of the total ice sheet contribution by up to 50% at the end of the 21st century.  We then explore three alternative approaches for determining the correlation: (i) shared dependence on global mean surface temperature, (ii) correlation derived from structured expert judgement, and (iii) correlation derived from model ensembles.  For each approach, we quantify the correlation by fitting copulas to published projections for the 21st century.  Shared dependence on global mean surface temperature produces only weak correlation among the ice sheet components, approximating the idealized case of independence.  In contrast, structured expert judgment and model ensembles suggest the East Antarctic component correlates strongly with the West Antarctic component.  We should include this correlation when summing the components.  To do this, we recommend using a copula derived from model ensembles.  Alternatively, we can approximate the correlation by assuming perfect correlation between the East and West Antarctic components.  This ‘Antarctic correlation’ increases the 95th percentile of the total ice sheet contribution by approximately 12%.  If we neglect this correlation, we will underestimate the combined uncertainty.