The Antikythera Mechanism, the technologically advanced Greek computer of around 150–100B.C., was found in 1900. In the almost 110years since his recovery, the Mechanism has been largely investigated. It is now known that 30 gears have survived and that others are still missing. The construction of a working model of the Antikythera Mechanism would serve to investigate the accuracy of its predictions. Such a construction would though need determination with high precision of the geometrical characteristics of its gears. In this paper the geometrical dimensions of the gears needed for an operational model of the Antikythera Mechanism are being investigated. ► We investigate the Antikythera Mechanism. ► We determined the geometrical characteristics for the construction of a working model. ► We used the measurements of all gears found in the fragments of the Mechanism. ► We determined the root angle, the module and the chord length of all gears. ► We calculated the axial distances of all cooperating gears.