Accurate constraints on the light element composition of the Martian core are required for models of the Martian core dynamo, the conditions under which the Martian core formed (i.e. the existence and extent of a magma ocean) and the overall volatile inventory of Mars. Here, we present a synthesis of geochemical constraints on the abundances of light elements S, C and O in the Martian core using mass balance calculations combined with published expressions that predict their high-pressure metal–silicate partitioning behaviour. We incorporate recently proposed bulk S Martian mantle abundances and find that the Martian core must be S-rich, virtually independent of the type of bulk composition considered and the P-T conditions during core-mantle differentiation of Mars. The core contains at least 7 wt % S and may be up to stoichiometric FeS in composition, depending on which P-T conditions (and bulk compositions) are assumed. If bulk Mars was formed from chondritic building blocks, the core S content is constrained to 13.5 ± 3.5 wt.%, in good agreement with geophysical models of the Martian interior and with measured siderophile element depletions in SNC meteorites. Our calculations yield O contents for the Martian core of < 4 wt.%, with the highest concentrations for the highest P-T conditions of Martian core formation. Carbon contents in the Martian core are expected to be low (< 1.4 wt.%) given the abundance of C in chondritic meteorite groups. The calculated solubility limit for C in Fe-Ni-S alloys is higher than calculated core C contents in virtually all cases, suggesting the Martian primitive mantle is not graphite saturated if the bulk Mars C budget is (close to) chondritic. The estimated depletions of volatile elements Se and Te in the Martian interior can be reconciled easily with formation of a Martian S-rich core. This implies that these volatile elements may not have been lost from Mars by degassing in Mars early history. The calculated Martian core S contents cannot be used to distinguish between the two different proposed modes of core crystallization, but do suggest the Martian core may still be fully liquid today.