From Late Latin 'cappa' (cloak, hood), likely from Latin 'caput' (head), from PIE *kaput-.
A soft, close-fitting head covering, typically with a visor; a protective lid or cover for the end of something.
From Old English 'cæppe' (a hood, a head-covering, a cap worn by monks or ecclesiastics), from Late Latin 'cappa' (a cloak with a hood, a cape, a head covering), of disputed origin: possibly derived from Latin 'caput' (head) via a diminutive or derived form, connecting it to PIE *kaput- (head) — the same root that gives 'capital,' 'captain,' 'chapter,' and 'decapitate' — or possibly of pre-Indo-European, Celtic, or Germanic substrate origin, with the Latin form representing a borrowing rather than a native development. The saint's relic most famously associated with the Latin 'cappa' is the cloak of St. Martin of Tours, which became so important a sacred object that the priests who guarded it were called 'capellani' (chaplains) and the portable shrine
The words 'cap,' 'cape,' 'captain,' 'capital,' and 'chapter' all trace back to Latin 'caput' (head). A captain is a 'head' person, a capital is a 'head' city, a chapter is a 'heading,' and a cap covers the head itself. Even 'escape' derives from this root — literally 'out of the cape,' referring to slipping out of a cloak when seized.