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.

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 exterior has a slight rampart that is surrounded by the rugged terrain of the mountain range.

To the southeast of this crater, on the edge of the Mare Serenitatis, is an arcing rille designated Rima Calippus.

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.