It's 90 feet along each edge of the diamond, so a home run would be 360 feet.
If you're asking how far you have to hit a ball for it to be considered a home run, there's no answer. Anything beyond the rear fence, but the position of the rear fence varies in different parks... in fact, the distance often varies considerably within a park, with the distance just inside the foul line on either side being not the same as the distance to the center of center field. Often the left field and right field distances aren't even the same.
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Most ballparks vary in distance to the outfield fence, but with a 90-foot basepath field, one would be hard-pressed to find a fence shorter than 300 feet from home plate.
360 feet! - yoceb3
507 feet by prince fielder
The longest home run that can be verified was hit by Babe Ruth. It went an estimated 575 feet. Many hitters have hit home runs that may be longer, but the distance was not or could not be verified.
Ted William's longest home run in Fenway Park was 502 feet, but I don't know if that was his longest home run ever.
663 feet high by Mr.notreal,in 19never