'apeirophobia' originates from Greek roots used in modern coinage: specifically from Greek 'apeiros' (ἄπειρος), where 'a-' meant 'not' and 'peiros' related to 'finite/limited' (thus 'without limit'), combined with Greek 'phobos' (φόβος) meaning 'fear'.

'apeirophobia' is a modern English formation combining the ancient Greek elements 'apeiros' and 'phobos'; the individual Greek words date to Classical Greek and were adapted into Neo-Latin/modern English coinage for psychological terminology.

Initially the Greek elements literally denoted 'without limit' + 'fear'; in modern English the compound has retained that literal sense and is used specifically to denote 'fear of infinity.'