'undervalue' originates from the Old English prefix 'under-' combined with the word 'value', which ultimately derives from Latin 'valere' meaning 'to be strong, to be worth'.

'value' entered English via Old French 'valoir' (from Latin 'valere'); 'under-' is an Old English element. The compound 'undervalue' was formed in English by joining 'under-' + 'value' to mean assigning less worth.

Initially it carried the literal sense of assigning less monetary or intrinsic worth; over time it has kept that core sense and extended to broader senses such as underestimating importance, ability, or contribution.