"Stadium" comes from the Greek word "stadion" (στάδιον), a measure of length equalling the length of 600 human feet. As feet are of variable length the exact length of a stadion depends on the exact length adopted for 1 foot at a given place and time. Although in modern terms 1 stadion = 600 ft (180 m), in a given historical context it may actually signify a length up to 15% larger or smaller.
A Roman stadium was defined somewhat differently to be a distance of 125 passus (double-paces), equal to about 185 m (607 ft).
Although most dictionaries provide for both "stadiums" and "stadia" as valid plurals, etymological sticklers sometimes apply "stadia" only to measures of length in excess of 1 stadium. (That the "stadium" measurement is used only in historical contexts perhaps explains the sustained use of the archaic plural.)
The English use of stadium comes from the tiered infrastructure surrounding a Roman track of such length.
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