'inequivalence' originates from English formation by adding the prefix 'in-' (not) to 'equivalence', where 'equivalence' comes from French 'équivalence' and ultimately from Late Latin 'aequivalentia'; the Latin elements 'aequus' meant 'equal' and 'valēre' meant 'to be strong, to be worth'.

'inequivalence' was formed in modern English by prefixing 'in-' to the existing noun 'equivalence' (from Middle French 'équivalence' and Late Latin 'aequivalentia'); over time the Latinate roots produced the English noun 'equivalence', and the negative form 'inequivalence' followed by regular word-formation.

Originally the components conveyed the idea of 'not equal in value or status'; over time the compound has come to be used broadly for 'lack of equivalence' in general contexts and more technically in logic and mathematics for 'not equivalent' relations.