I recently had the entrance bar clang on a 6'8" garage entrance at a hospital, so I exited and parked in a surface lot. The bar may have been hanging a bit low though, at least it didn't look level as I drove by after the fact. My crossbars are on and the best I could measure it is about 6'6" in height to the top of them. The spec height is listed at 6' 4.5" but that is probably with the crossbars off. I have been considering taking them off, they are almost to high to use regularly, might as well take them off and eliminate the drag.
Edit: just went out and remeasured using a straight board across the side rails and the tallest part of the rails was 76". The crossbars put it at 78". The sharkfin is lower than the side rails according to my level. It was pretty much empty inside and gas was nearly full, so your measurements may vary.