Metacentric height is a measurement of the initial static stability of a floating body, such as a ship. It is calculated as the distance between the center of gravity of the ship and its metacentre. A larger metacentric height implies greater initial stability against overturning. The metacentric height also influences the natural period of rolling of a hull, with very large metacentric heights being associated with shorter periods of roll which are uncomfortable for passengers. Hence, a sufficiently high metacentric height is considered ideal for passenger ships, but not excessively high.
The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel. Beyond that range, the stability of the vessel is dominated by what is known as a righting moment. Depending on the geometry of the hull, naval architects must iteratively calculate the center of buoyancy at increasing angles of heel and then calculate the righting moment at this angle.
The vertical distance between the center of gravity and the initial metacentre is referred to as the metacentric height. The relative positions of the vertical center of gravity and the initial metacentre are extremely important with regard to their effect on the ships stability. The ship is in stable equilibrium if the center of gravity is below the metacentre, in neutral equilibrium if the vertical center of gravity and the metacentre are coincident, and in unstable equilibrium if the vertical center of gravity is above the metacentre. If the metacentric height of a ship is small, the righting arms that develop will be small, and such a ship is "tender" and will roll slowly. However, if the metacentric height of a ship is large, the righting arms that develop at small angles of heel will be large. It is advisable to avoid excessive values of metacentric height, since these might lead to acceleration forces that could be dangerous to the ship, its equipment, and cargo.
