'invertibility' originates from Latin, specifically the verb 'invertere' (in- + vertere), where 'in-' meant 'in, into' and 'vertere' meant 'to turn'; the adjective form 'invertible' (from Latin 'invertibilis') combined with the noun-forming suffix '-ity' (from Latin '-itas' via Old French) produced the English noun 'invertibility'.

'invert' comes from Latin 'invertere' which passed into Late Latin/Medieval Latin as 'invertĕre' and into Old French/Norman forms before entering Middle English as 'invert'; the adjective 'invertible' was formed in English from these elements and later the abstract noun 'invertibility' was created by adding the suffix '-ity'.

Initially, related forms meant 'to turn or turn over'; over time the derived abstract noun came to be used not only for physical turning but also for technical senses such as the existence of an inverse in mathematics, the predominant modern usage in technical contexts.