The word is a modern English compound, built entirely from native Germanic elements. "Three" derives from Old English þrīe, from Proto-Germanic þrīz, ultimately from Proto-Indo-European tréyes. "And" comes from Old English and, ond, meaning "thereupon, next." "Half" originates from Old English healf, meaning "side, part," from Proto-Germanic halbaz. "Hour" entered Old English as ōra or ūre from Latin hōra and Greek hōra, meaning "season, time of day." The compound's logic is purely additive and literal, following the standard English pattern for specifying durations. Its formation reflects the analytic nature of English, where precise, multi-word concepts are often lexicalized into single hyphenated modifiers, especially before a noun, such as in "a three-and-a-half-hour meeting."

This is a compound adjective formed by combining the cardinal number "three", the conjunction "and", the indefinite article "a", the fraction "half", and the unit of time "hour" with hyphens. Each component is a free morpheme of Old English origin, and their functional role is to create a single, fixed descriptive unit modifying a noun.