Metacentric Height Calculator
Metacentric height, GM, is the single most important measure of a vessel's initial stability. It is the gap between the center of gravity and the metacenter: a positive GM means the ship rights itself after a small heel, while a negative GM means it is unstable. You compute GM by subtracting the center of gravity height (KG) from the metacenter height above the keel (KM), then applying a free surface correction for slack tanks. Enter KM, KG, and the free surface correction and this calculator returns solid GM and corrected (fluid) GM with a stability verdict.
Metacentric height formula
Solid GM = KM - KG
Fluid KG = KG + free surface correction
Corrected GM = KM - fluid KG = solid GM - free surface correction
GM > 0: stable | GM = 0: neutral | GM < 0: unstable
KM is read from the ship's hydrostatic tables at the current draft. KG comes from the loading condition. The free surface correction accounts for liquids shifting in slack tanks, which always reduces effective stability.
Stability notes
- Corrected (fluid) GM, not solid GM, is the value compared against stability criteria.
- A very small positive GM gives a tender ship with a slow, deep roll.
- A very large GM gives a stiff ship with a violent, short-period roll that can damage cargo.
- Press tanks up or empty them to cut the free surface correction.
- Always confirm GM lies within the limits in the approved stability booklet.
Metacentric height: frequently asked questions
What is metacentric height (GM)?
Metacentric height, GM, is the distance between a vessel's center of gravity (G) and its metacenter (M). It is the primary measure of initial transverse stability. A positive GM means the vessel is stable and returns upright after a small heel; a negative GM means it is unstable and may capsize or loll.
How is GM calculated?
GM equals KM minus KG, where KM is the height of the metacenter above the keel and KG is the height of the center of gravity above the keel. KM comes from the ship's hydrostatic tables at the current draft, and KG comes from the loading condition. So GM = KM - KG.
What is a good GM value?
GM must be positive and within the range set in the ship's stability booklet. Too small a GM gives a tender, slow-rolling ship with poor stability; too large a GM gives a stiff, fast, uncomfortable and potentially damaging roll. The acceptable range depends on the vessel type and applicable stability criteria.
What is the free surface correction?
Liquid in a partly filled tank shifts as the ship rolls, raising the effective center of gravity and reducing stability. The free surface effect is added to KG as a correction, giving a corrected fluid KG. Enter your free surface correction in this calculator to get the corrected GM.
What does negative GM mean?
A negative GM means the metacenter lies below the center of gravity, so the vessel is unstable in the upright position. It will heel to an angle of loll and may capsize. Negative GM must be corrected by lowering KG, for example by ballasting low tanks, before the vessel proceeds.
Official sources
- International Maritime Organization: IMO.
- U.S. Coast Guard: Navigation Center.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.