The PADME experiment at the LNF Beam Test Facility searches for dark photons produced in the annihilation of positrons with the electrons of a fixed target. The strategy is to look for the reaction e+ + e− → γ + A0, where A0 is the dark photon, which cannot be observed directly or via its decay products. The electromagnetic calorimeter plays a key role in the experiment by measuring the energy and position of the final-state γ. The missing four-momentum carried away by the A0 can be evaluated from this information and the particle mass inferred. This paper presents the design, construction, and calibration of the PADME’s electromagnetic calorimeter. The results achieved in terms of equalisation, detection efficiency and energy resolution during the first phase of the experiment demonstrate the effectiveness of the various tools used to improve the calorimeter performance with respect to earlier prototypes.