Origins
The word 'convert' entered English in the mid-thirteenth century from Old French 'convertir,' itself from Latin 'convertere,' a compound of 'con-' (together, completely — here used as an intensifier) and 'vertere' (to turn). The literal meaning was 'to turn around completely' — a transformation, a reversal of direction. This spatial metaphor proved powerful enough to generate meanings spanning religion, chemistry, mathematics, finance, sports, and everyday life.
The Latin verb 'vertere' is one of the great root verbs of English vocabulary, comparable to 'trahere' (to pull) or 'facere' (to do) in its productivity. Through its various prefixed compounds, 'vertere' generated an enormous family of English words: 'convert' (turn completely), 'invert' (turn in/upside down), 'revert' (turn back), 'divert' (turn aside), 'pervert' (turn thoroughly wrong), 'subvert' (turn from below), 'avert' (turn away from), and 'extrovert/introvert' (turned outward/inward). The past participle stem 'vers-' produced 'verse' (a turning of the plow, hence a line of poetry), 'version' (a turning, a translation), 'versatile' (able to turn easily), and 'versus' (turned against).
The PIE root behind 'vertere' is *wert- (to turn), which was remarkably productive across the Indo-European family. In Germanic, it produced Old English 'weorþan' (to become — literally 'to turn into'), which survives in modern German 'werden' (to become) and in the archaic English suffix '-ward' (toward, in the direction of — as in 'homeward,' 'upward'). The English word 'worth' may also be related, from the sense of 'turning out to be' of a certain value. The connection makes 'convert' and '-ward' distant cousins.
Latin Roots
The religious sense of 'convert' was present from the beginning of the word's English life and reflects Latin Christian usage. In Christian Latin, 'conversio' was the spiritual turning of the soul toward God — Augustine's 'Confessions' describes his famous 'conversio' in the garden at Milan. This sense entered all the Romance languages and was the word's most culturally significant meaning throughout the medieval period. The noun 'convert' (a person who has changed faith) appeared in English by the fourteenth century.
In modern English, 'convert' has expanded far beyond its religious origins. One converts currencies (turns one into another), converts units of measurement, converts a try in rugby (turns it into additional points), converts a file from one format to another, converts an attic into a bedroom, or converts skeptics into believers. The underlying metaphor in every case is the same: turning one thing into another.
The noun-verb stress distinction follows the standard English pattern for Latinate words: the verb stresses the second syllable (/kənˈvɜːt/), while the noun stresses the first (/ˈkɒn.vɜːt/). This pattern is shared with other '-vert' words like 'pervert' and demonstrates one of the most regular morphological processes in English phonology.
Legacy
In chemistry, 'conversion' refers to the transformation of one substance into another, particularly the percentage of reactant that is transformed into product. In computing, 'conversion' encompasses any transformation of data from one format or type to another. In real estate, 'conversion' means transforming a building's use (a warehouse conversion into apartments). Each specialized sense preserves the etymological core: complete turning, transformation.