A control system controls a construction machine having a work machine including a tilting bucket. The control system includes: a first acquisition unit configured to acquire dimension data; a second acquisition unit configured to acquire external shape data of the bucket; a third acquisition unit configured to acquire target excavation landform data indicating a target excavation landform that is a two-dimensional target shape of an excavation object on a work machine operation plane perpendicular to a bucket axis; a fourth acquisition unit configured to acquire work machine angle data; a fifth acquisition unit configured to acquire tilt angle data indicating a turning angle of the bucket; and a calculation unit configured to obtain two-dimensional bucket data indicating an external shape of the bucket on the work machine operation plane on the basis of the dimension data, the external shape data, the work machine angle data, and the tilt angle data.