The DArk Matter Particle Explorer (DAMPE), a satellite-based cosmic ray and gamma-ray detector, was launched on December 17, 2015, and began its on-orbit operation on December 24, 2015. In this work we document the on-orbit calibration procedures used by DAMPE and report the calibration results of the Plastic Scintillator strip Detector (PSD), the Silicon-Tungsten tracKer-converter (STK), the BGO imaging calorimeter (BGO), and the Neutron Detector (NUD). The results are obtained using Galactic cosmic rays, bright known GeV gamma-ray sources, and charge injection into the front-end electronics of each sub-detector. The determination of the boundary of the South Atlantic Anomaly (SAA), the measurement of the live time, and the alignments of the detectors are also introduced. The calibration results demonstrate the stability of the detectors in almost two years of the on-orbit operation.
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