An Etymological Dictionary of the German Language/genau

by Friedrich Kluge

genau, ‘accurate, precise, strict, parsimonious,’ from late MidHG. (MidG.) nouwe, ‘careful, exact,’ akin to nouwe, genouwe, adv., ‘scarcely’; comp. Du. naauw, ‘narrow, exact, punctual.’ Probably these cognates, in their Goth. form *ga-nêws, are to be connected with Goth. nêhws, HG. nahe. Others refer them to a root nau, ‘to narrow,’ in Not and its cognates.