Traditionally, field-aligned current densities calculated from gradients in the perturbation magnetic field measured from low-altitude spacecraft have been based on the assumption that the current regions are infinite in length. However, many measurements clearly indicate that this assumption is invalid. We have performed model calculations of the magnetic field produced by finite current regions that would be measured by a spacecraft-borne magnetometer. These calculations serve two purposes: (1) to assess the extent to which an infinite current sheet approximation is applicable in calculating field-aligned current densities by comparing the current density computed from the model perturbation magnetic field assuming an infinite length current region to the model current density; and (2) to assist in the interpretation of the magnetometer signals when the infinite sheet current approximation is clearly inapplicable. For current regions with various aspect (length to width) ratios, we find that the perturbation magnetic fields within the current region more than one current element width from an end produce a calculated current density with less than a 10% departure from the model current density. Certain nonlinear patterns (e.g., V-shaped signatures) in the correlation plots of the two horizontal components of the perturbation magnetic field can be explained in terms of the end field effects of field-aligned current regions. Such signatures can be used to determine the configuration of the satellite track through the current region.