A Finite-Difference, Time-Domain (FDTD) analysis of a square Archimedean spiral antenna is performed to calculate antenna gain and scattering patterns. The spiral is mounted in a large, conducting ground plane and is backed by an air-filled or absorber-filled cavity. The effects of resistive sheets placed over the spiral are also evaluated for both radiation and scattering. Total-field FDTD calculations are used to compute the gain patterns, while a specially-modified scattered-field approach for aperture antennas in infinite ground planes is used for the scattering results. Comparisons are made with calculations done with a Finite Element method and excellent results are obtained.