Origins
The word 'value' rests on a metaphor so fundamental it is almost invisible: worth is strength. The word descends from Old French 'value' (worth, price), the feminine past participle of 'valoir' (to be worth), from Latin 'valēre' (to be strong, to be well, to have force, to be worth). The PIE root is *walh₂- (to be strong), which may also be connected to Old Church Slavonic 'vladěti' (to rule) and Lithuanian 'valdyti' (to govern) — suggesting an ancient semantic cluster linking strength, power, and authority.
The equation of strength with worth runs through the entire family of 'valēre' derivatives in English. 'Valid' means 'strong enough to hold' — a valid argument stands firm, a valid ticket has force. 'Valor' is strength of character in the face of danger. 'Valiant' is having the strength to be brave. 'Avail' (from 'ad-' + 'valēre') means 'to be of force or use.' 'Prevail' (from 'prae-' + 'valēre') means 'to be stronger than.' 'Equivalent' (from 'aequi-' + 'valēns') means 'of equal strength or force.' 'Convalescent' (from 'con-' + 'valēscere') means 'growing strong together' — recovering health. 'Ambivalent' (from 'ambi-' + 'valēns') means 'strong in both directions' — pulled equally toward two options.
In Latin, 'valēre' had a remarkably broad semantic range. It meant 'to be strong physically,' 'to be healthy,' 'to be effective,' 'to have force,' and 'to be worth a certain amount.' The Roman farewell 'valē' (plural 'valēte') was the imperative form — 'be strong,' 'be well' — and the letter-closing formula 'si valēs, bene est; ego valeō' (if you are well, that is good; I am well) used the same verb. Health, strength, and worth were linguistically inseparable.
French Influence
The narrowing to a specifically financial sense occurred during the medieval period, as Latin 'valēre' passed through Old French 'valoir' and its nominal form 'value.' In English, the word arrived in the early fourteenth century carrying both monetary and moral senses, and it has retained both ever since. 'Value' can mean 'how much money something costs' (the value of a house) and 'how much something matters' (family values, the value of education). The philosophical discipline of 'axiology' (the study of values) treats both senses as related aspects of a single question: what is worth having?
The verb 'to value' appeared shortly after the noun, meaning both 'to estimate the monetary worth of' and 'to regard as important.' 'Evaluate' (from French 'évaluer') added a prefix meaning 'out' — to bring the value out, to make the implicit worth explicit. 'Devalue' (to reduce in value) and 'overvalue' (to estimate too highly) followed.
The tension between monetary value and moral value has been a persistent theme in Western thought. Aristotle distinguished between 'use value' (a thing's usefulness) and 'exchange value' (what it can be traded for). Adam Smith and Karl Marx returned to the same distinction. Oscar Wilde's famous quip — 'a cynic is a man who knows the price of everything and the value of nothing' — depends on the distinction between 'price' (monetary cost) and 'value' (true worth), a distinction embedded in the language itself: 'price' comes from Latin 'pretium' (price), while 'value' comes from 'valēre' (to be strong). Different roots, different emphases, and a culture that has always sensed they are not quite the same thing.