Stability GZ Curve Calculator

GM measures initial transverse stability -- the height of the metacenter above the vessel's center of gravity. A positive GM means that when the vessel heels slightly, the shifting center of buoyancy creates a righting moment that pushes it back upright; a zero or negative GM means the vessel is neutrally or unstably balanced at small heel angles and may not return upright on its own. It's the single most basic stability check in naval architecture, though it only describes behavior near zero heel, not the full range captured by the GZ curve.

The wall-sided righting-arm formula (GZ = sin(theta) x [GM + 0.5 x BM x tan^2(theta)]) assumes the hull's underwater and topside shape stays roughly vertical-sided through the heel angle -- an assumption that ends once the deck edge immerses or the bilge emerges. Published naval-architecture guidance puts that breakdown point around 20-30 degrees of heel for typical hull forms, and as low as roughly 10 degrees for full-form hulls like bulk carriers and tankers. Since this calculator has no freeboard or hull-fullness input to distinguish those cases, it uses a single 30 degree cap -- a reasonable upper bound for moderate hull forms, but potentially still optimistic for a very full hull -- and does not compute, chart, or search for a peak past it, to avoid reporting a physically meaningless value from the formula's tan^2 term growing unbounded at higher angles.

It means the GZ curve was still rising, or still positive, when this calculator's 30 degree formula-validity cap was reached, so the true angle of maximum GZ or the true vanishing angle lies somewhere past 30 degrees -- a real value this calculator cannot determine without full hydrostatic data for the actual hull. That's a distinct, honest result from a specific numeric angle within the 0-30 degree range: it tells you the vessel is not showing a stability problem within the range this formula can compute, without pretending to know exactly how far the good behavior extends.

KB = 0.53 x draft is a commonly used rule-of-thumb approximation for typical hull forms, not a precise calculation from the vessel's actual underwater volume distribution -- the real value depends on hull shape (block coefficient and section shape) and is normally taken from a vessel's hydrostatic tables or computed via integration (e.g., the Morrish formula) for an actual design. Treat this calculator's KB, and the GM and GZ values that depend on it, as an estimate for a typical hull form rather than a substitute for a vessel-specific hydrostatic calculation.

Not by itself -- this calculator computes the same kind of GZ curve that regulatory frameworks like the IMO Intact Stability Code evaluate, but it doesn't check your results against any specific regulatory threshold, since required minimums for maximum GZ, angle of maximum GZ, area under the curve, and range of positive stability vary by vessel type, size, and flag-state requirements. A formal stability assessment requires comparing actual hydrostatic data against the applicable regulation for your specific vessel.