We present a state estimation scheme for spins using a modified setup of the Stern-Gerlach experiment in which a beam of neutral spin-1/2 point particles interacts with a quadrupolar magnetic field. The proposed estimation procedures, based either on a quadrant or a continuous intensity distribution detection, require a suitable initial spatial state of the beam. The statistical characterization of the estimators of the initial spin state allows us not only to associate an error to the estimated parameters, but also to define a measure for comparing estimation procedures corresponding to different Stern-Gerlach setups.