stadium (n.)

mid-14c., stadie, "a foot race, a racecourse;" early 15c., "ancient measure of distance," from Latin stadium (plural stadia) "a measure of length" (variously reckoned, commonly one-eighth of a Roman mile or a little over 600 standard English feet; translated in early English Bibles by furlong); also "a stage, a station; a course for foot-racers;" from Greek stadion "a measure of length; a race-course, a running track," especially the track at Olympia, which was one stadion in length.

"Originally the distance between successive stations of the shouters and runners employed to estimate distances," extended to the course itself [Century Dictionary].

According to Barnhart, the notion in the Greek word might be "fixed standard of length, that which stands fast" (from stadios "firm, fixed," from PIE root *sta- "to stand"). Beekes does not seem to connect them, however, and allows rather that stadion is "Perhaps an original folk-etymological transformation" of Greek spadion "race-track," which is a derivative of span "to draw up, pull" (compare spasm), perhaps on the notion of "the lengthy one." If so, the form might be influenced by stadios.

The form in English has been re-Latinized from early modern stade. The meaning "running track" in English is recorded from c. 1600 and was extended to mean "large, open oval structure with tiers of seats for viewing sporting events" (1834). The classical sports stadiums had sloping banks of seats for spectators along two sides and one end.