'normal-eyed' originates from English as a compound of 'normal' and 'eye'; 'normal' ultimately comes from Latin 'normalis' (from 'norma'), where 'norma' meant 'carpenter's square' or 'rule', and 'eye' comes from Old English 'eage' meaning 'eye'.

'normal' passed into English via Medieval Latin 'normalis' (and Old French influence) and became 'normal' in Modern English; 'eye' developed from Old English 'eage' to Middle English 'eye', and the compound 'normal-eyed' is a modern English formation combining the two elements.

Initially the components referred to 'rule/square' (for 'normal') and the anatomical 'eye'; over time the compound simply came to mean 'having eyes or vision that are normal' (i.e., not impaired).