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 lies to the southwest of the crater remnant Alexander, to the northwest of the Mare Serenitatis.

The outer rim of Calippus has an irregular appearance, with outward bulges to the northeast and particularly to the west where there is an interior shelf of slumped material. The rim along the north to east edges has an altitude of over 2 km. The exterior has a slight rampart that is surrounded by the rugged terrain of the mountain range. Within the sharp-sided interior walls is a rough and irregular interior floor.

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. A pyroclastic deposit has been identified in this area based on its low strength radar signature.

This crater was named after Greek astronomer Callippus of Cyzicus. Its name was adopted by the International Astronomical Union in 1935.

By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Calippus.