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Metacentric Height

Stability measure; positive GM means the ship rights itself.

Formula

GM=KM−KGGM = KM - KG

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Variables

GMMetacentric height (m)
KMMetacentre above keel
KGCentre of gravity above keel

Example

KM=8 m, KG=6.5 m: GM = 1.5 m

How it works

Metacentric height, GM, is a quick indicator of a ship’s initial stability after a small heel. It is found by comparing two vertical positions measured from the keel: the metacentre (M), which represents how the buoyant force shifts for a slight tilt, and the centre of gravity (G), which is where the ship’s weight acts. If M lies above G, the buoyant and weight forces create a restoring couple, so the vessel tends to return upright; if G is above M, the couple can overturn it further.

When to use it

Use this when checking the initial stability of a floating vessel, barge, pontoon, or loaded ship, especially after changes in cargo, ballast, fuel, or passenger distribution. It is also used in naval architecture and marine operations to assess whether a vessel is stiff, tender, or dangerously unstable.

Worked example, step by step

Given: KM = 10.4 m Given: KG = 9.1 m Formula: GM = KM - KG Substitute: GM = 10.4 - 9.1 Calculate: GM = 1.3 m Interpretation: The metacentre is 1.3 m above the centre of gravity, so the vessel has positive initial stability and will tend to right itself after a small heel.

Common mistakes to avoid

  • Subtracting in the wrong order and reporting a negative GM when it should be positive
  • Using the waterline or deck height instead of the keel as the common reference datum
  • Assuming a large GM always means complete safety, even though cargo shift, flooding, or large angles of heel can still make the vessel unsafe

Did You Know?

Too small a GM makes a ship roll dangerously slowly; too large makes it snap back so sharply it's uncomfortable.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026