From Latin 'aequus' (equal) + 'valere' (to be strong) — literally 'equally strong' or 'of equal worth.'
Equal in value, amount, function, or meaning; a thing that is equal to or corresponds with another.
From Late Latin aequivalens (of equal value), the present participle of aequivalere (to be of equal worth), a compound of aequus (equal, even) + valere (to be strong, be worth). Aequus traces to PIE *h2eyk-w- (even, equal), while valere derives from PIE *walh2- (to be strong), which also produced Old English wealdan (to wield, rule), Gothic waldan (to govern), and Old Church Slavonic vlasti (to rule). The compound literally means "equally strong" or "equally powerful" — equivalence is not mere sameness but matched force. Medieval scholastic
The 'val-' in 'equivalent' is the same root as in 'value,' 'valid,' 'valiant,' and 'prevail' — all from Latin 'valēre' (to be strong). The idea that something's worth is tied to its strength reflects a worldview where power and value were practically synonymous.