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late 14c., "a foot race, an ancient measure of length," from Latin stadium "a measure of length, a race course" (commonly one-eighth of a Roman mile; translated in early English Bibles by furlong), from Greek stadion "a measure of length, a running track," especially the track at Olympia, which was one stadium in length.
The Greek word might literally mean "fixed standard of length" (from stadios "firm, fixed," from PIE root *sta- "to stand"), or it may be from spadion, from span "to draw up, pull," with form influenced by stadios.
The meaning "running track," recorded in English from c.1600, was extended to mean in modern-day context "large, open oval structure with tiers of seats for viewing sporting events" (1834).