An exemplary stage apparatus has a motor, stage, and position-measuring device. The motor has a planar stator and moving-coil mover (planar motor). The stator is a checkerboard magnet array extending in an x-y plane and producing a magnetic field having a field period of 2π in a u-v coordinate system rotated 45° from the x-y coordinate system of the plane. The stage, coupled to the mover, moves with corresponding motions of the mover relative to the stator. The position-measurement device includes a first group of four magnetic-field sensors that are movable with the stage. The sensors are situated at integer multiples of π/2 from each other in u- and v-directions of the u-v coordinate system. The sensors produce respective data regarding a respective component of the magnetic field at, and hence the position of, the respective sensor within the period of the magnetic field.