Metacentric Height (GM)
Calculates the metacentric height GM of a vessel by adding the centre of buoyancy height to the metacentric radius (waterplane moment of inertia divided by displaced volume) and subtracting the centre of gravity height. A positive GM means stable equilibrium; negative means a heeled hull will not right itself. Enter the moment of inertia, displaced volume, KB and KG.
Result
—
The number that says whether a heeled hull comes back
Every inclining experiment ends at GM, and every skipper course trips over it. Someone who has just loaded weight onto the deck feels nothing while the vessel sits upright: the loss of stability only surfaces once she is already heeled and the hull takes its time returning, or fails to return at all. GM catches that on the spreadsheet, before the weight ever goes aboard. It remains the first figure any maritime authority asks for in a loading review.
Two steps: BM = I_T / ∇, then GM = KB + BM − KG. I_T means the transverse moment of inertia of the waterplane in m⁴, ∇ the displaced volume in m³, KB the height of the centre of buoyancy above the keel and KG the height of the centre of gravity, both in metres. With the values on screen, I_T of 4200 m⁴, ∇ of 1850 m³, KB at 2.1 m and KG at 3.8 m, BM comes to 2.270 m and GM to 0.570 m. Merchant ships commonly run between 0.3 and 1.5 m, while the IMO IS Code sets a floor of 0.15 m for corrected GM in the intact condition.
GM holds only for small angles, something like 7 to 10 degrees; beyond that the GZ righting arm curve takes over, and a comfortable GM can sit alongside a short range of stability. What this page returns is solid GM: it takes no account of the free surface correction from slack tanks, worth i×ρ/Δ per tank, which eats effective GM without a single tonne moving. Note how much weight I_T carries — for a rectangular waterplane, I_T = L×B³/12, with beam cubed. That is why widening a hull improves initial stability far more than lengthening it.
Frequently asked questions
GM came out negative. Is that a typing error or a real result?
How much GM counts as good? Is more always better?
Does the tool apply the free surface correction?
Related Tools
Ship Roll Period (IMO IS Code)
Computes the natural roll period of a ship using the empirical formula of the IMO International Code on Intact Stability (IS Code 2008), used in the weather criterion and in the inclining experiment. The period is T = 2 × C × beam ÷ square root of GM, with the coefficient C = 0.373 + 0.023 × (beam ÷ draught) − 0.043 × (length ÷ 100), so that rolling gets faster as the metacentric height grows. The number indicates comfort and safety: short periods, below some 8 seconds, reveal a stiff ship that rolls with high acceleration and punishes cargo and crew; long periods indicate a tender ship, with little stability reserve. The IMO empirical form was adopted rather than the pendulum expression T = 2π × radius of gyration ÷ square root of (g × GM), because the roll radius of gyration is rarely known on board — which is exactly what the coefficient C estimates from hull geometry. Enter the beam, the draught, the waterline length and the metacentric height GM.
Crane Load Moment
Calculate a crane's load moment, M = W·R, from the load weight W (N) and the operating radius R (m, the horizontal distance from the crane's rotation center to the load). The load moment is the product of the load weight and its distance to the crane's rotation axis, and it GOVERNS the TIPPING stability — the most feared and catastrophic crane failure mode. A crane tips when the load moment (tending to overturn it forward, toward the load) exceeds the STABILIZING moment (the crane's own weight and counterweight, acting backward). The genius — and danger — is in the RADIUS: the SAME load generates a much larger moment when far (boom extended) than near (boom retracted). So a crane's capacity is NOT a single number, but a LOAD CHART that drops drastically as the radius grows — a crane lifting 50 tonnes at 5 m radius may lift only 5 tonnes at 30 m. Exceeding the maximum load moment (the 'load curve') is the main cause of crane tipping, so cranes have load moment indicators (LMI) locking operation near the limit. Computing the load moment and comparing it with the allowable moment for that radius is the fundamental safety check in every crane operation. Enter the load weight and the operating radius.
Block Coefficient (Cb)
Compute a ship's block coefficient (Cb), Cb = ∇/(L·B·T), the ratio of the displaced (carene) volume to the enclosing box (length × beam × draft). It measures how 'full' the hull is: slow cargo ships have a high Cb (~0.8); fast, fine vessels a low Cb (~0.5). It is one of the central parameters of naval architecture. Enter the displaced volume, the length, the beam and the draft.
Hydrostatic Thrust on Dam
Calculate the horizontal hydrostatic thrust per metre of length on a dam face, E = ½·γ·H², from the unit weight of water γ (≈ 9.81 kN/m³) and the water depth H (m) at the upstream face. Since hydrostatic pressure grows linearly with depth (p = γ·h), its diagram is triangular and the resultant is its area, ½·γ·H², applied at one third of the height from the base. This thrust is the main action tending to overturn and slide the dam, and the starting point of gravity dam stability analysis: it generates the overturning moment (about the downstream toe) and the horizontal force resisted by base friction. Dam stability depends on its self-weight (providing the stabilizing moment and normal friction force) exceeding these with adequate margin, also accounting for foundation uplift. Enter the unit weight of water and the depth.
Tropical Tree Height by Years
Estimates the height of a tropical tree in meters by age in years.
NR-17 Ergonomic Bench Height
Suggests a workbench height based on stature for standing work per Brazilian NR-17.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.