Cleomedes est un cratère de 126 Km et profond de 2600 m. Situé dans la partie du nord-est de la lune, au nord de la mer des Crises (Mare Crisium). Cleomedes est entouré par un terrain tourmenté avec des impacts multiples de cratère. Le cratère irrégulier Tralles (43 Km) est incrusté dans le mur nord-ouest. Le mur externe de Cleomedes est fortement érodé, particulièrement le long de la partie méridionale du mur qui porte le cratère Cleomedes C (14 Km). Le fond du cratère est  presque  plat,  inondé  par  la  lave, avec une petite crête centrale au nord du point médian. Il y a  plusieurs   craterlets   notables sur  le fond. Une rainure longue de 30 Km, appelé Rima Cleomedes va du nord-ouest vers le sud-est et s'évase en fourchette après avoir traversé la moitié du cratère.

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Cleomedes is a prominent lunar crater located in the northeast part of the visible Moon, to the north of Mare Crisium. It is surrounded by rough ground with multiple crater impacts. The irregular Tralles crater is intruding into the northwest rim. To the east is the Delmotte crater. North of Cleomeses is a triple-crater formation with Burckhardt crater occupying the center.

The outer wall of this crater is heavily worn and eroded, especially along the southern part of the wall. The 'Cleomedes C' crater lies across the south-southwest rim. The crater floor is nearly flat, with a small central peak to the north of the mid-point, forming a linear ridge toward the north-northeast. There are several notable craterlets on the floor, including a pair of overlapping craters just inside the northwest rim.

A rille named the Rima Cleomedes crosses the northern floor, running southeast from the northwest rim. This rille branches in a fork after crossing the crater mid-line. Smaller clefts lie in the southeast part of the floor.