The capacitance of arrays of vertical wrapped-gate InAs nanowires is analysed. With the help of a Poisson-Schrödinger solver, information about the doping density can be obtained directly. Further features in the measured capacitance-voltage characteristics can be attributed to the presence of surface states as well as the coexistence of electrons and holes in the wire. For both scenarios, quantitative estimates are provided. It is furthermore shown that the difference between the actual capacitance and the geometrical limit is quite large, and depends strongly on the nanowire material.