'concavity' originates from Latin, specifically the word 'concavus', where 'con-' (an assimilated form of 'com-') functioned as an intensifier or 'together' and 'cavus' meant 'hollow'.

'concavus' passed into Medieval Latin and Late Latin as 'concavus/concavitas', then into Middle French/Medieval English as 'concave' and 'concavity', eventually becoming the modern English 'concavity' (plural 'concavities').

Initially it referred simply to 'hollowness' or 'a hollowed place'; over time it retained that core sense while also expanding into technical uses (e.g., geometry and analysis) to mean the property of curving inward.