gauge has 9 distinct synonyms spread across 4 of its 11 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
determine the capacity, volume, or contents of by measurement and calculation
“gauge the wine barrels”
measure precisely and against a standard
“the wire is gauged”
adapt to a specified measurement
“gauge the instruments”
mix in specific proportions
“gauge plaster”
a measuring instrument for measuring and indicating a quantity such as the thickness of wire or the amount of rain etc.
Synonyms, antonyms and the broader and narrower relations for gauge come from Princeton University’s WordNet. Full sources and licences.
accepted or approved instance or example of a quantity or quality against which others are judged or measured or compared
the distance between the rails of a railway or between the wheels of a train