The center of Center Township is located at (38.8275111, −98.6786868) at an elevation of 1,742 feet (531 m). The township lies in the Smoky Hills region of the Great Plains. The western third of Wilson Lake lies in northeastern Center Township. Elm Creek, which drains into the lake, flows north through the northeast part of the township. Cedar Creek, a tributary of the Saline River, runs northeast through the northwest part of the township. In the south, the Smoky Hill River flows generally east through the township, joined by one of its tributaries, Beaver Creek, which runs northeast.