The spatial arrangement of preferred directions (PD) in the primary motor cortex has revealed evidence for columnar organization and short range-order. We investigated the large-scale properties of this arrangement. We recorded neural activity at sites on a grid covering a large region of the arm area of the motor cortex while monkeys performed a 3D reaching task. Sites were projected to the cortical surface along anatomically defined cortical columns, and a PD was extracted from each site with directionally tuned activity. We analyzed the resulting two-dimensional surface map of PDs. Consistent with previous studies, we found that any particular reaching direction was re-represented at many points across the recorded area. In particular, we determined that the median radius of a cortical region required to represent the full complement of reaching directions is at most 1 mm. We also found that for the majority of regions of this size, the distribution of PDs within them exhibits an enrichment for the representation of forward and backward reaching directions (see companion paper). Finally, we found that the error of a population vector estimate of reaching direction constructed from neural activity within these regions is small on average, but varies significantly across different sections of the motor cortex, with the highest levels of error sustained near the fundus of the central sulcus, and lowest levels achieved near the crown. We interpret these findings in the context of two well-known features of motor cortex, namely, its highly distributed anatomical organization, and its behaviorally-dependent plasticity.