What is metacentric height (GM)?

GM is the distance from the center of gravity (G) to the metacenter (M). A positive GM means G is below M, and the vessel will return upright after a small heel — it is stable. A negative GM means G is above M, and the vessel will capsize or list to a new equilibrium. GM is the fundamental measure of initial stability.

What is the metacenter (M)?

The metacenter is the point about which a vessel rotates when heeled by a small angle. For small angles it is approximately fixed. Its height above the keel (KM) equals KB + BM, where BM (the metacentric radius) depends on waterplane geometry and displaced volume.

How is BM calculated for a rectangular waterplane?

For a rectangular waterplane of length L and breadth B, the second moment of area I = L × B³ / 12 = Aw × B / 12. Since B = Aw / L, exact BM requires knowing both dimensions. This tool uses the simplified approximation BM ≈ Aw² / (12 × V), valid when the waterplane is approximately square or when L ≈ B. For non-square waterplanes, supply I directly or use a dedicated hydrostatics program.

What is a healthy GM value?

IMO guidelines suggest a minimum GM of 0.15 m (0.5 ft) for most cargo ships. Passenger vessels require higher margins, often 0.30–0.50 m. Very high GM (over 2–3 m) can make a vessel too stiff, causing rapid uncomfortable rolling. The ideal range balances stability and crew comfort.

KB is the vertical distance from the keel (K) to the center of buoyancy (B) — the geometric centroid of the submerged volume. For simple rectangular hulls KB ≈ draft / 2. KG is the vertical distance from the keel to the vessel's center of gravity, which depends on the distribution of all weights on board.

Why does moving weight upward reduce stability?

Raising KG reduces GM = KM − KG. If KG rises to meet or exceed KM, GM becomes zero or negative and the vessel becomes neutrally stable or unstable. This is why deck cargo, heavy machinery high up, and free-surface liquids in tanks all reduce stability margins.

Metacentric Height Calculator

Name: Metacentric Height Calculator
Availability: InStock
Author: Nham Vu

Enter waterplane area, displaced volume, KB, and KG to compute the metacentric height GM and assess vessel stability.

Vessel Parameters

Waterplane Area (Aw) (m²)

Horizontal cross-section area at the waterline

Displaced Volume (V) (m³)

Volume of water displaced at design draft

Center of Buoyancy Height (KB) (m)

Vertical distance from keel to center of buoyancy

Center of Gravity Height (KG) (m)

Vertical distance from keel to center of gravity

Enter vessel parameters and click Calculate GM

GM Stability Reference

GM Range	Assessment
< 0 m	Unstable — vessel will capsize or list
0 – 0.15 m	Marginally stable — below IMO minimum for cargo ships
0.15 – 0.50 m	Acceptable — meets IMO minimum; typical cargo ships
0.50 – 1.50 m	Good — comfortable rolling, suitable for most vessels
> 1.50 m	Very stiff — short, snappy roll period; may stress cargo

Summary

Enter waterplane area, displaced volume, KB, and KG to compute the metacentric height GM and assess vessel stability.

How it works

Enter the waterplane area (Aw) — the horizontal cross-section area at the waterline.
Enter the displaced volume (V) — the volume of water the vessel displaces.
Enter KB — the height of the center of buoyancy above the keel.
Enter KG — the height of the center of gravity above the keel.
The tool computes BM = Aw² / (12 × V) for a rectangular waterplane, then KM = KB + BM, and finally GM = KM − KG.
A positive GM means the vessel is stable; a negative GM means it is unstable.

Use cases

Assess initial stability of a barge or ship during early design.
Check whether loading or shifting cargo changes the stability margin.
Validate hydrostatic tables from a stability booklet.
Support naval architecture coursework on ship stability theory.
Estimate the stiffness of a vessel before conducting an inclining experiment.
Compare stability margins across hull variants with different waterplane areas.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu