In this work, the miscibility gap of hydrogen-helium mixtures is calculated under conditions relevant for the gas giants Jupiter and Saturn. Density functional theory coupled to classical molecular dynamics simulations is used to obtain the equations of state for 29 helium concentrations. The entropy is calculated using a combination of thermodynamic integration of the equation of state and coupling-constant integration. New planetary profiles for Jupiter and Saturn are derived giving strong indications that there is demixing in Saturn but possibly not in Jupiter.<eng>
