'evenhandedly' originates from English, specifically the word 'evenhanded' + suffix '-ly', where 'even' meant 'level' or 'equal' and 'hand' meant 'hand'.

'evenhanded' developed in Early Modern English as a compound of 'even' + 'handed' (literally 'having an even hand') and the adverb 'evenhandedly' was later formed by adding the adverbial suffix '-ly' in modern English.

Initially, it could be understood more literally as 'with an even (steady) hand'; over time it shifted to the abstract sense 'in an impartial or fair manner', which is the current dominant meaning.