In Olympic and International competition, the distances are in meters (usually either 25 "short course" or 50 meter "long course" pools). A mile is 1609 meters. 1650 is the first 50 meter multiple over a mile, so that's the distance used for the race. The races are all the same digit of measurement (100, 200, 400, 800, 1650) regardless of yards or meters.
A true "olympic size pool" measures 50 meters long and 25 meters wide (this way, the pool can be either short course or long course depending on how the lane lines are strung) which is as big as you're probably ever gonna see. However, the term "Olympic sized" seems to be thrown around a lot and can generally mean any pool big enough to do laps in (which is 25 yards (short course) in length minimal). So when asking how big a pool is one should probably find out if it's long or short course and yards or meters.
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