Photon-number-resolving (PNR) single-photon detectors are an enabling technology in many areas, such as photonic quantum computing, nonclassical light-source characterization, and quantum imaging. Here, we demonstrate high-efficiency PNR detectors using a parallel superconducting nanowire single-photon-detector (P-SNSPD) architecture that does not suffer from crosstalk between the pixels and that is free of latching. The behavior of the detector is modeled and used to predict the possible outcomes given a certain number of incoming photons. We apply our model to a four-pixel P-SNSPD with a system detection efficiency of 92.5%. We also demonstrate how this detector allows reconstructing the photonnumber statistics of a coherent source of light, which paves the way towards the characterization of the photon statistics of other types of light source using a single detector.