The remarkably high open-circuit voltage of methylammonium lead iodide perovskite solar cells is investigated. Both the theoretical maximum and the real open-circuit voltage are predicted from electroluminescence and photovoltaic external quantum efficiency spectra. Radiative and non-radiative recombination are quantified, where a source of non-radiative recombination is found in the mesoscopic structure, independent of the Al2O3 or TiO2 scaffold. Without a hole-transport layer, non-radiative recombination is strongly enhanced, which reduces the open-circuit voltage. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.