measure has 25 distinct synonyms spread across 11 of its 13 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.
how much there is or how many there are of something that you can quantify
the act or process of assigning numbers to phenomena according to a rule
“the measurements were carefully done”
a basis for comparison; a reference point against which other things can be evaluated
“the schools comply with federal standards”
(prosody) the accent in a metrical foot of verse
musical notation for a repeating pattern of musical beats
“the orchestra omitted the last twelve bars of the song”
measuring instrument having a sequence of marks at regular intervals; used as a reference in making measurements
a container of some standard capacity that is used to obtain fixed amounts of a substance
determine the measurements of something or somebody, take measurements of
“Measure the length of the wall”
Synonyms, antonyms and the broader and narrower relations for measure come from Princeton University’s WordNet. Full sources and licences.