For applications to harvest solar energy, it is essential to characterize upconverter materials under broad-band excitation at reasonable irradiance levels achievable by concentration of solar radiation. We present a method to determine the absolute upconversion quantum yield (UCQY) under broad-band excitation by photoluminescence measurements. We introduce a spectral mismatch correction that allows calculating the UCQY that can be expected under illumination with the solar spectrum with a certain solar concentration. Applying these methods to β-NaYF4 doped with 25%Er3+, we determine an external UCQY of 2.0% in the spectral range from 1450 nm to 1600 nm under a comparatively low solar concentration of only 50 suns. This value corresponds to a potential increase of the short-circuit current density of 3.89 mA/cm2. Subsequently, we measure the external quantum efficiency due to upconversion of sub-band-gap photons for a bifacial silicon solar cell with upconverter attached to its rear side under the same broad-band excitation. We determine an additional short-circuit current density due to upconversion of 4.03 mA/cm2 for a solar concentration of only 77 suns. This value agrees very well, with the expected additional short-circuit current density due to upconversion, calculated from the external UCQY values as determined by the photoluminescence measurements, by considering the transmittance of the solar cell for sub-band-gap photons and the external quantum efficiency of the solar cell for photons emitted by the upconverter. Finally, a comparison with different literature values based on a set of figures of merit shows that our results currently constitute the largest enhancement of the short-circuit current density due to upconversion.