Spatial terms in the world’s languages appear to reflect both universal conceptual tendencies and linguistic convention. A similarly mixed picture in the case of color naming has been accounted for in terms of near-optimal partitions of color space. Here, we demonstrate that this account generalizes to spatial terms. We show that the spatial terms of 9 diverse languages near-optimally partition a similarity space of spatial meanings, just as color terms near-optimally partition color space. This account accommodates both universal tendencies and cross-language differences in spatial category extension, and identifies general structuring principles that appear to operate across different semantic domains.