Metacentric Height

MARITIME – HULL & NAVAL ARCHITECTURE CALCULATOR Metacentric Height A precise tool.
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What is the Metacentric Height & How does it work?

The metacentric height (GM) is a key indicator of a vessel’s initial static stability. It represents the distance between the centre of gravity (G) and the metacentre (M), the point about which the vessel heels for small angles of inclination.

GM can be expressed as the sum of the keel‑to‑centre of buoyancy distance (KB) and the metacentric radius (BM) minus the keel‑to‑centre of gravity distance (KG): GM = KB + BM – KG. A positive GM indicates that the vessel will right itself after a small heel, while a negative value signals instability.

The metacentric radius BM is derived from the geometry of the waterplane: BM = I / V, where I is the second moment of area of the waterplane about its centreline and V is the displaced volume of the hull.

GM = K_{B} + B_{M} – K_{G}
GM = Metacentric height (m)  |  KB = Keel‑to‑centre of buoyancy (m)  |  BM = Metacentric radius (m)  |  KG = Keel‑to‑centre of gravity (m)
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Parameters
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Frequently Asked Questions
What is metacentric height in naval architecture?
Metacentric height (GM) is the distance between the center of gravity (G) and the metacentre (M), indicating a vessel’s stability.
How do I calculate metacentric height?
Use the formula GM = KB + BM – KG, where KB is keel-to-center of buoyancy distance, BM is metacentric radius, and KG is keel-to-center of gravity distance.
Why is a positive GM important for a vessel?
A positive GM indicates that the vessel will right itself after a small heel, ensuring stability.
What does a negative metacentric height mean?
A negative GM means the center of gravity is below the metacentre, making the vessel unstable and prone to capsizing.
Can you explain the components of the GM formula?
KB is the distance from the keel to the center of buoyancy, BM is the distance from the keel to the metacentre, and KG is the distance from the keel to the center of gravity.
How does metacentric height affect a vessel’s stability?
Metacentric height directly affects a vessel’s stability; a higher GM indicates greater stability for small angles of inclination.
What are the units used for calculating metacentric height?
Metacentric height is typically measured in meters (m) or feet (ft), depending on the regional standards and vessel specifications.

Results are for informational purposes only and do not constitute professional advice.