According to Apollodorus as quoted by Philodemus, Cleanthes was born in Aristophanes' archonship (331/0 BC) and died in Jason's Archonship (230/29 BC).
Ifølge Apollodorus der citeres af Philodemus, blev Kleanthes født i Aristophanes' periode som archont(331/0 f.Kr.) og døde da Jason var archont (230/29 f.Kr).