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.

GZ Stability Curve Basic Estimator

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.

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.