We have studied the magnetic switching behavior of arrays of Co ring elements as a function of film thickness (2 ⩽ t ⩽ 32 nm), ring width (0.15 ⩽ w ⩽ 0.7 μm), and external diameter (0.5 ⩽ D ⩽ 2.0 μm), using magneto-optical Kerr effect magnetometry. For thick rings, two stable magnetic states are observed, a high remanence state (called the “onion” state) and a low remanence state (called the vortex state). The switching field for the transition from the onion to the vortex state increases with increasing thickness t and external diameter D, and with decreasing width w. In particular, for thin rings, the switching occurs between the two oppositely magnetized onion states, i.e., no vortex states develop during the reversal process. The transition between these two regimes depends on the diameter and width of the rings, and phase diagrams for the dependence of the switching behavior on the geometric parameters are presented. The switching behavior is discussed in terms of the competition between the exchange and magnetostatic energy terms. © 2003 American Institute of Physics.