We demonstrate and verify quantum detector tomography of a superconducting nanowire single-photon detector (SNSPD) in a multiplexing scheme which permits measurement of up to 71 000 photons per input pulse. We reconstruct the positive operator valued measure (POVM) of this device in the low photon-number regime, and use the extracted parameters to show the POVMs spanning the whole dynamic range of the device. We verify this by finding the mean photon number of a bright state. Our work shows that a reliable quantum description of large-scale SNSPD devices is possible, and should be applicable to other multiplexing configurations.