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Callias was one of the wealthiest men in Athens in the later part of the Vth century : he is presented by Socrates at Apology, 20a as "a man who spent more money with the sophists than all others taken together", and it is in his house, termed "the greatest and most prosperous in town" (Protagoras, 337d), where he hosted all visiting sophists, that the Protagoras takes place. He was born somewhere between 455 and 450 in one of the richest families of Athens, the Ceryces, who, besides owning silver mines in Laurium that were at the root of its fortune, was one of the families in charge of the celebration of the Eleusinian mysteries, where it provided the torch-bearers. His father was Hipponicus, "the richest man in Greece" (Andocides' On the Mysteries, 130), and his grandfather was the Callias who negociated the peace that bears his name, which put an end to the second Persian War in 449 (see Herodotus ' Histories, VII, 151). Another Callias, the grandfather of the peace negociator, is also mentioned by Herodotus for his successes at the Olympic games, his wealth and huge expenditures, and his hate of tyranny (Histories, VI, 121-122). Callias' mother later married Pericles (Protagoras, 314e ; Plutarch's Life of Pericles, 24, 5), so that he was the half-brother of Xanthippus and Paralus, the two sons of Pericles mentioned in the Alcibiades (118e), the Protagoras (314e-315a ; 320a ; 328c-d) and the Meno (94b). And his sister Hipparete married Alcibiades (Plutarch's Life of Alcibiades, 8).
Callias was married several times. Andocides, in his speech On the Mysteries, delivered in 399 to answer accusations of impiety brought forth against him by Callias and a few others, tells the jury how Callias married a girl and, within a year, made the girl's mother his mistress, living eventually with both mother and daughter, only to abandon them both later, and how he had a son from the mother, born after he had left her, that he initially repudiated but later recognized, after he had fallen in love again with the mother and welcomed her back in his house (On the Mysteries, 117-131).
Callias is most likely the father of the Protarchus staged as the interlocutor of Socrates in the Philebus (see Philebus, 19b). Hermogenes, his less wealthy youger brother (Cratylus, 391b-c) plays a leading role in the Cratylus.