about has 16 distinct synonyms spread across 7 of its 8 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.
(of quantities) imprecise but fairly close to correct
“lasted approximately an hour”
used of movement to or among many different places or in no particular direction
“wandering about with no place to go”
1 of the 8 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for about.
Synonyms, antonyms and the broader and narrower relations for about come from Princeton University’s WordNet. Full sources and licences.