late 14c., "interchangeable," from Old French convertible "interchangeable" (13c.) and directly from Late Latin convertibilis "changeable," from Latin convertere "to turn around; transform," from assimilated form of com "with, together" (see con-) + vertere "to turn" (from PIE root *wer- (2) "to turn, bend").
Meaning "capable of being changed in form, substance, or condition" is from 1530s. Of paper money, etc., "capable of being converted into gold of a similar amount," from 1834. The noun is recorded from 1610s; meaning "automobile with a fold-down top" is from 1916. Related: Convertibility.