A surgical instrument having opposed jaws that can be selectively moved between open and closed positions. Various embodiments include components for measuring the thickness of tissue clamped between the opposed jaws. Some embodiments are configured to ascertain the amount of compressive force that is being applied to the tissue while the thickness of the tissue is being determined. The tissue thickness data is displayed on the instrument itself and/or on a display that is remote from the instrument. The various embodiments may comprise different types of surgical instruments such as surgical staplers and graspers. A jaw arrangement with jaws shaped to define a cradle that corresponds to a cross-sectional shape of an object is also disclosed. The components that generate the thickness data may be electrically or mechanically actuated.