Resonance in a ferromagnetic sphere, known in the body of literature as the mode of uniform precession, has recently been proven to be magnetic plasmon resonance (MPR). This finding has prompted research which is presented in this paper on the relation between the Q-factor at the MPR and the ferromagnetic resonance (FMR) linewidth ΔH, which is a parameter of magnetized gyromagnetic materials. It is proven in this paper that ΔH can be unequivocally determined from the Q-factor measured at the MPR, if all losses in the resonance system are properly accounted for. It can be undertaken through a rigorous but simple electrodynamic study involving the transcendental equation, as proposed in this paper. The present study also reveals that electric losses have a substantially reduced impact on ΔH due to the large magnetic to electric energy storage ratio at the MPR. Theoretical results are supported by measurements of the Q-factors on a monocrystalline yttrium iron garnet (YIG) sphere.