UV-Vis absorption spectroscopy is frequently used to characterize the size and shape of gold nanoparticles. We present a full-spectrum model that yields reliable results for the commonly encountered case of mixtures of spheres and rods in varying proportions. We determine the volume fractions of the two populations, the aspect ratio distribution of the nanorods (average value and variance) and the interface damping parameter. We validate the model by checking the fit results against small-angle X-ray scattering and transmission electron microscopy data and show that correctly accounting for the polydispersity in aspect ratio is essential for a quantitative description of the longitudinal plasmon peak.