Calippus is a small lunar impact crater that is located on the eastern edge of the rugged Montes Caucasus mountain range in the northern part of the Moon. It was named after Greek astronomer Callippus of Cyzicus. It lies to the southwest of the crater remnant Alexander, to the northwest of the Mare Serenitatis. To the southeast of this crater, on the edge of the Mare Serenitatis, is an arcing rille designated Rima Calippus. This cleft follows a path to the northeast for a length of about 40 kilometers.