"space above the head," 1851, from head (n.) + room (n.).
Entries linking to headroom
head n.
Old English heafod "top of the body," also "upper end of a slope," also "chief person, leader, ruler; capital city," from Proto-Germanic *haubid (source also of Old Saxon hobid, Old Norse hofuð, Old Frisian haved, Middle Dutch hovet, Dutch hoofd, Old High German houbit, German Haupt, Gothic haubiþ "head"), from PIE root *kaput- "head."
Modern spelling is early 15c., representing what was then a long vowel (as in heat) and remained after pronunciation shifted. Of rounded tops of plants from late 14c. Meaning "origin of a river" is mid-14c. Meaning "obverse of a coin" (the side with the portrait) is from 1680s; meaning "foam on a mug of beer" is first attested 1540s; meaning "toilet" is from 1748, based on location of crew toilet in the bow (or head) of a ship.
Synechdochic use for "person" (as in head count) is first attested late 13c.; of cattle, etc., in this sense from 1510s. As a height measure of persons, from c. 1300. Meaning "drug addict" (usually in a compound with the preferred drug as the first element) is from 1911.
To be over (one's) head "beyond one's comprehension" is by 1620s. To give head "perform fellatio" is from 1950s. Phrase heads will roll "people will be punished" (1930) translates Adolf Hitler. Head case "eccentric or insane person" is from 1966. Head game "mental manipulation" attested by 1972.
room n.
Middle English roum, from Old English rum "space, extent; sufficient space, fit occasion (to do something)," from Proto-Germanic *ruman (source also of Old Norse, Old Saxon, Old High German, Gothic rum, German Raum "space," Dutch ruim "hold of a ship, nave"), nouns formed from Germanic adjective *ruma- "roomy, spacious," from PIE root *reue- (1) "to open; space" (source also of Avestan ravah- "space," Latin rus "open country," Old Irish roi, roe "plain field," Old Church Slavonic ravinu "level," Russian ravnina "a plain").
Old English also had a frequent adjective rum "roomy, wide, long, spacious," also an adverb, rumlice "bigly, corpulently" (Middle English roumli).
The meaning "chamber, cabin" is recorded by early 14c. as a nautical term; applied by mid-15c. to interior division of a building separated by walls or partitions; the Old English word for this was cofa, ancestor of cove. The sense of "persons assembled in a room" is by 1712.
Make room "open a passage, make way" is from mid-15c. Room-service is attested from 1913; room-temperature, comfortable for the occupants of a room, is so called from 1879. Roomth "sufficient space" (1530s, with -th (2)) now is obsolete.