We present the calibration and background model for the Large Area X-ray Proportional Counter (LAXPC) detectors on board AstroSat. The LAXPC instrument has three nominally identical detectors to achieve a large collecting area. These detectors are independent of each other, and in the event analysis mode they record the arrival time and energy of each photon that is detected. The detectors have a time resolution of 10 s and a dead-time of about 42 s. This makes LAXPC ideal for timing studies. The energy resolution and peak channel-to-energy mapping were obtained from calibration on the ground using radioactive sources coupled with GEANT4 simulations of the detectors. The response matrix was further refined from observations of the Crab after launch. At around 20 keV the energy resolution of the detectors is 10%-15%, while the combined effective area of the three detectors is about 6000 cm2.