The vast majority of research on the spatial nature of numerical representation has focused on the horizontal axis, highlighting the left-to-right orientation of increasing values. Recent evidence points to spatial organization along the vertical (bottom-to-top) axis as well, but these findings are better characterized as generalized magnitude mappings between number and other magnitude dimensions (e.g., near-far spatial extent). Here we replicate generalized magnitude mappings for number (Exp. 1A) and show that they take precedence over left-to-right orientation (Exp. 1B). In contrast, we find no evidence of spontaneous organization along the true vertical axis (Exp. 2A) and show that left-to-right orientation trumps bottom-to-top orientation when the two are inconsistent (Exp. 2B). Reliable bottom-to-top orientation was evident only after priming of magnitude relations among numbers (Exp. 3). Together, these findings demonstrate that number is more strongly represented horizontally than vertically. We suggest that experience with cultural tools may drive this asymmetry.