What is the GZ righting lever?

GZ is the horizontal distance between the lines of action of buoyancy and gravity when a vessel heels. It is the lever that rights the ship, so the GZ curve against heel angle shows how strongly the vessel resists capsize at each angle.

How is GM estimated here?

GM equals KM minus KG. KM is KB plus BM, where KB uses the Morrish approximation, BM is the waterplane inertia divided by the displaced volume, and KG is the centre of gravity you enter. A positive GM of at least 0.15 metres is the IMO minimum.

What is the wall-sided formula?

The wall-sided formula, GZ equals GM plus half BM times tan squared of the heel, all times the sine of the heel, gives a good GZ estimate while the hull sides stay vertical. It loses accuracy once the deck edge immerses, so treat the larger angles as indicative only.

Which IMO criteria does it check?

It checks the core intact-stability rules from the IMO 2008 IS Code: minimum initial GM, minimum GZ at 30 degrees, the areas under the GZ curve to 30 and 40 degrees and between them, and the angle of maximum GZ. All values are derived from the simplified curve.

Can I use this for a real loading condition?

No. This is a teaching and first-pass estimator using box-like approximations. A real assessment needs the vessel's measured hydrostatics, cross curves of stability, free-surface corrections, and the approved stability booklet. Never base an actual loading decision on this tool.

What is the GZ Stability Curve Basic Estimator?

Use simplified stability formulae for KB, BM, and GM from breadth, depth, and block coefficient to sketch a basic GZ curve and flag IMO intact-stability criteria pass or fail. Naval architecture students and small-vessel operators use this for first-pass checks. It runs free in your browser on Gera Tools, with nothing uploaded.

GZ Stability Curve Basic Estimator

Name: GZ Stability Curve Basic Estimator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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The GZ curve is the heart of ship stability: it shows how much righting lever a vessel develops as it heels, and whether that is enough to satisfy the regulations. This estimator builds a basic curve from a handful of hull parameters so students and small-craft operators can see how breadth, draught, and centre of gravity drive stability and intact-criteria compliance.

How it works

The tool first estimates the metacentric height, then sweeps the wall-sided righting lever across heel angle:

KB ≈ d × (5/6 − Cb / (3·Cw))        (Morrish approximation)
BM = k·B² / (Cb·d)                  (waterplane inertia ÷ volume)
KM = KB + BM ,  GM = KM − KG
GZ(θ) = (GM + ½·BM·tan²θ)·sinθ      (wall-sided, to moderate heel)

The areas under the GZ curve are integrated by the trapezium rule and compared with the IMO intact-stability minimums for the 0–30°, 0–40°, and 30–40° ranges, along with the GZ-at-30° and angle-of-maximum-GZ checks.

What the IMO 2008 IS Code criteria check

The IMO Intact Stability Code (IS Code 2008, Part A, Regulation 2.2) sets minimum mandatory criteria for the GZ curve of most passenger and cargo vessels. The five key checks are:

Criterion	Minimum
Initial metacentric height GM	0.15 m
Righting lever GZ at 30° heel	0.20 m
Area under GZ curve, 0° to 30°	0.055 m·rad
Area under GZ curve, 0° to 40°	0.090 m·rad
Area under GZ curve, 30° to 40°	0.030 m·rad

There is also a criterion that the maximum GZ shall occur at a heel angle not less than 25°. Failing any single criterion means the loading condition is non-compliant and the vessel should not proceed in that configuration.

These are minimum thresholds, not targets. Well-designed vessels typically exceed them significantly, particularly in normal displacement loading conditions.

Why GM alone is not enough

A vessel with a high initial GM feels very stiff and rights quickly from small angles, but that does not mean it will survive large angles. The critical question is how far up the heel angle the GZ curve remains positive and how much area sits under it. Some vessel forms develop a large initial GM but then have a GZ curve that falls rapidly beyond 40°, giving little reserve in a severe wave. Conversely, a vessel with a modest GM may have a broad, sustained GZ curve that gives excellent survival capability.

This is why the area criteria exist alongside the GZ value and GM criteria — they capture curve shape, not just the initial slope.

Example and notes

An 80 m × 14 m vessel at 5 m draught with Cb = 0.70, Cw = 0.80, and KG = 5.5 m gives a GM of roughly 1.0 m and a healthy GZ curve that clears the basic IMO criteria. Raise KG toward KM and the GM collapses, the curve flattens, and the checks start to fail — a vivid illustration of why keeping weight low matters. Treat every number as a learning estimate: the wall-sided assumption breaks down once the deck edge dips, and a real ship needs full hydrostatics, free-surface corrections, and its approved stability booklet.