Navisailor Learning CentreAMSA Examiner
Log in

Stability

Ship stability fundamentals: GM, GZ and what the numbers mean

By Navisailor Learning Centre · Published 7 October 2026 · Updated 7 October 2026

Stability is one of the subjects candidates fear most, partly because it looks like a wall of formulas. It is easier when you hold a small number of ideas clearly and can explain them in plain language: what makes a ship return upright, what makes her stop doing so, and what an officer can do about it.

This guide covers those core ideas with a worked example. It is a study aid for understanding. For real loading decisions always use the ship’s approved stability information, and for the exact criteria that apply use the current text of the relevant code or regulation.

The points and what they mean

Four points describe a ship’s initial stability. Learn what each one is and how it moves.

  • G, the centre of gravity: the point through which the weight of the ship acts downwards. It moves when weights are loaded, discharged or shifted.
  • B, the centre of buoyancy: the centre of the underwater volume, through which the buoyant force acts upwards. It moves as the ship heels because the shape of the underwater volume changes.
  • M, the transverse metacentre: the point where the vertical line through B at a small angle of heel meets the ship’s centreline. For small angles it behaves as a fixed point.
  • K, the keel: the reference point from which heights are measured. KG is the height of G above the keel and KM the height of M above the keel.

Metacentric height and the righting lever

The metacentric height, GM, equals KM minus KG. When M is above G the ship has positive GM. At a small angle of heel the weight acting down through G and the buoyancy acting up through B form a couple that tries to return the ship upright. The horizontal distance between those lines is the righting lever, GZ, and for small angles GZ equals GM multiplied by the sine of the angle of heel.

Three conditions of equilibrium follow from the sign of GM. With G below M, the ship is in stable equilibrium and returns upright. With G at M the equilibrium is neutral. With G above M the ship is unstable and will not return upright. A large GM gives a stiff ship that returns quickly and may roll violently. A small positive GM gives a tender ship that rolls slowly and has less margin.

What changes G

Loading and discharging

Adding a weight moves G towards it, and removing one moves G away. Loading high raises G and reduces GM, so a plan that loads heavy cargo low is a stability decision as well as a stowage one.

Shifting a weight

Moving a weight w through a distance d in a ship of displacement W moves G through a parallel distance equal to w multiplied by d, divided by W. A transverse shift causes a list. A worked example: shifting 100 tonnes by 12 metres across a ship of 8,000 tonnes moves G sideways by 0.15 metres. If GM is 1.20 metres, the tangent of the list angle equals 0.15 divided by 1.20, which is 0.125, giving a list of about 7 degrees.

Suspended weights

A weight hanging from a derrick or crane acts as though it is concentrated at the point of suspension from the moment it is lifted clear. Lifting a heavy load can therefore raise the effective centre of gravity and reduce GM, even though the weight has not moved far.

Free surface effect

A tank that is partly filled lets liquid move to the low side as the ship heels, shifting the weight in the same direction as the heel. The effect is a virtual rise of G, which reduces the effective GM. The loss is greater for wide tanks, because it depends on the breadth of the free surface cubed, and it is not reduced by the liquid’s depth. It is reduced by keeping tanks either full or empty where possible, and by dividing tanks longitudinally with a centreline bulkhead.

Free surface is a classic oral question. Be ready to explain it in words, state what it depends on and say what you would do about a slack tank on a stability-critical voyage.

List and loll

A list is a heel caused by a transverse shift or an uneven distribution of weight with a positive GM. The ship is stable and sits at an angle to the upright. A loll is a heel in a ship with a negative GM. She is unstable upright and flops over to one side until the righting lever begins to act again at the angle of loll.

The distinction matters because the corrective action is different. Correcting a list means moving weight to the high side. Doing the same to a ship that is lolling may cause her to flop to the other side, so the first priority with a loll is to lower G by, for example, filling slack tanks low in the ship, starting with the lowest tanks on the low side. Be ready to describe how you would tell the difference and the cautious steps you would take.

The GZ curve

For larger angles GM alone is not enough, so stability is shown with a curve of the righting lever against the angle of heel. Learn what each feature tells you.

  • The initial slope of the curve is related to GM.
  • The maximum GZ and the angle at which it occurs show how large a heeling moment the ship can resist and how far she can heel before her resistance begins to fall.
  • The angle of vanishing stability and the range of stability show how far the ship can be heeled before she would capsize in still water.
  • The area under the curve represents the energy the ship can absorb from waves and wind.

Intact stability criteria

International rules set minimum requirements for the shape of the curve and for GM. The International Code on Intact Stability, 2008, which is mandatory under SOLAS and the Load Lines Protocol, includes general criteria for the initial GM, the area under the GZ curve to specified angles, the maximum righting lever and the angle at which it occurs. It applies to ships of 24 metres in length and above, and it also includes a weather criterion for severe wind and rolling. Know where the criteria are in the ship’s stability booklet, and check the exact values in the current Code.

How to practise

  1. Draw a ship section and mark K, G, B and M. Explain, aloud, what each one is and how each moves when the ship heels.
  2. Work three short numerical problems: a weight shift causing a list, a loading that changes GM, and a free surface correction. Say what each answer means in practical terms.
  3. Sketch a GZ curve and label every feature. Then explain what changes if G rises.
  4. Explain list versus loll to a colleague, including the first action you would take in each case and why.

Official sources

This guide was written from the following sources. Requirements change, so confirm the current position with the source before relying on it.

Related certificate guides

Independence note

Independent AMSA exam preparation platform by Navisailor Learning Centre. Not affiliated with or endorsed by the Australian Maritime Safety Authority. This guide is general study material. It is not legal advice, it is not official AMSA exam content, and it does not replace AMSA’s checklists, syllabi or the current legislation.

Share:WhatsAppLinkedInFacebook

Prepare with structured study tools

Create an account to see the study topics, practice questions and readiness tools currently available for your rank.

Start preparing with AMSA Examiner Log in