Magnetic monopoles with masses up to 1014 GeV can be accelerated to relativistic velocities in Galactic and intergalactic magnetic fields. The cosmic flux of relativistic monopoles is constrained by various experiments, with the limits given as functions of the monopole velocity (Lorentz factor) at the detectors. The velocity, however, is usually treated as a free parameter due to the ambiguity in the computation of the acceleration before the monopoles arrive at Earth. We explicitly evaluate the velocity by exploiting recent studies on cosmic magnetic fields and the monopole acceleration therein, to recast experimental limits in terms of the mass of monopoles. By applying our method to various terrestrial experiments, including the Pierre Auger Observatory, IceCube, MACRO, and the upcoming Cherenkov Telescope Array Observatory, as well as to astrophysical constraints, we report limits on the flux of monopoles for a wide range of monopole masses. We also highlight the role of monopoles as messengers of cosmic magnetic fields, and discuss the possibility of using monopole experiments to probe intergalactic magnetic fields.
