'non-converting' originates from the prefix 'non' (from Latin 'non') meaning 'not', combined with the present participle 'converting', ultimately from Latin 'convertere' where 'con-' meant 'together' and 'vertere' meant 'to turn.'

'converting' developed from Latin 'convertere' → Old French/Medieval Latin forms (e.g. 'convertir') → Middle English 'convert', with the present-participle form 'converting' in Modern English; the prefix 'non-' was later attached in Modern English to form the compound adjective 'non-converting'.

Originally 'convert' had a basic sense of 'to turn' or 'to change (literally)', and over time came to mean 'to change form, function, belief, or state'; 'non-converting' therefore came to mean 'not undergoing that change' or 'not producing the desired change'.