According to the OED, ax is the more etymologically correct spelling of the two. Common usage has, however, preferred axe for multiple centuries, rendering the etymologically-preferred spelling unbalanced and archaic to modern eyes. Curiously, ax has regained popularity in American English throughout the last century and appears in print only slightly less frequently than its three-lettered rival. Nonetheless, the standard spelling remains axe, which both American and British English prefer. The same goes for its compound uses (e.g., pickaxe, poleaxe, axeman).