Gross tonnage is a measure of volume, not mass, it simply means the Constitution class has an internal volume of 100,000,000 cubic feet or about 2,831,684.66 m3 (which gets into Discovery tier ship interiors, given st-v-sw.net estimates the Galaxy-class at having a volume of 5,820,983 m3 and the baseline Excelsior as being 873,287 m3*).Yeah but the same canon thinks the Constitution is a million tons so, you know. Take it with a grain of salt. The Galaxy-class massing only 2.5 times as much an Excelsior is unlikely.
The million gross ton quote was also given in an episode, whereas the Excelsior mass (and my mistake, it was 3.35 million tonnes) was given in the DS9 technical manual, which is not canon (or is beta canon, if you prefer). Furthermore the DS9 technical manual is rather infamous for getting ship sizes wildly wrong, whereas the 4,960,000 tonne Galaxy value is given in the TNG technical manual, which unfortunately only really focuses on the Galaxy-class.
You are correct, though, the masses are rather out of whack.
*and the TOS Connie (which it annoyingly refers to as the Constitution A, with the refit being the B) is 211,248 m3.
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