A deformable display device is provided. The deformable display device includes a deformable display, a sensor which senses a deformation located in a first area of the deformable display and a second area of the deformable display and a controller which receives deformation information corresponding to the deformation, determines whether to identify one of only the first area and only the second area as a deformation area of the deformation based on the deformation information, and identifies i) only the first area as the deformation area if it is determined to identify only the first area and ii) only the second area as the deformation area if it is determined to identify only the second area.