Cleostratus is a lunar impact crater near the northwest limb of the Moon. It lies to the northeast of the crater Xenophanes, and west-southwest of the prominent Pythagoras. From the Earth this crater appears highly elongated due to foreshortening.
The rim of this crater has become soft-shouldered due to steady impact erosion, and the formation is now just a depression in the surface surrounded by an eroded rise. A pair of small craters lie across the southwest rim, forming part of a short chain of craters leading to the west. Along the crest of the southern rim is a linear ridge. The satellite crater Cleostratus E is attached to the northwest rim, and intrudes slightly into the inner wall. The interior floor of this crater is flat and nearly featureless, having only a few tiny craterlets marking the surface.
thumb|Cleostratus (center) in a telescopic photograph
Satellite craters
By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Cleostratus.
{| class="wikitable"
!width="25%" style="background:#eeeeee;" |Cleostratus
!width="25%" style="background:#eeeeee;" |Latitude
!width="25%" style="background:#eeeeee;" |Longitude
!width="25%" style="background:#eeeeee;" |Diameter
|-
|align="center"|A
|align="center"|62.7° N
|align="center"|77.3° W
|align="center"|35 km
|-
|align="center"|E
|align="center"|60.9° N
|align="center"|79.6° W
|align="center"|21 km
|-
|align="center"|F
|align="center"|61.5° N
|align="center"|80.4° W
|align="center"|50 km
|-
|align="center"|H
|align="center"|61.2° N
|align="center"|81.9° W
|align="center"|13 km
|-
|align="center"|J
|align="center"|61.3° N
|align="center"|83.8° W
|align="center"|20 km
|-
|align="center"|K
|align="center"|62.0° N
|align="center"|81.1° W
|align="center"|17 km
|-
|align="center"|L
|align="center"|62.2° N
|align="center"|79.3° W
|align="center"|11 km
|-
|align="center"|M
|align="center"|61.5° N
|align="center"|74.9° W
|align="center"|9 km
|-
|align="center"|N
|align="center"|60.6° N
|align="center"|73.1° W
|align="center"|4 km
|-
|align="center"|P
|align="center"|59.6° N
|align="center"|72.9° W
|align="center"|7 km
|-
|align="center"|R
|align="center"|58.9° N
|align="center"|72.9° W
|align="center"|6 km
|}