We have investigated the effects of particle size and aspect ratio on the hysteresis in controlled arrays of small magnetic particles. The arrays of permalloy particles were fabricated via electron-beam lithography. Each array consists of ∼ 106 identical, uniformly spaced particles. Hysteresis loops measured with an alternating-gradient magnetometer for particles ∼5-0.1 μm are presented. We find an increase in the coercive force as the particle width decreases below 0.3 μm due to a change in the switching mechanism from domain-wall nucleation and wall motion to vortex nucleation and vortex motion. A novel angular dependence of the loops is described in detail. Results from ab initio micromagnetic calculations on isolated rectangular Permalloy particles are compared, where applicable, with the measurements. We find excellent qualitative and, in selected cases, quantitative agreement between the experiments and calculations.