GM stability estimator

The metacentric height (GM) is the primary indicator of initial transverse stability. A positive GM means the vessel will right herself when heeled; a negative GM means she is unstable and will loll or capsize. This tool calculates the key stability parameters using a rectangular box approximation.

The calculation

BM = B² ÷ (12 × d) — distance from centre of buoyancy to the metacentre (transverse). Derived from second moment of the waterplane area divided by the displaced volume.
KB = d ÷ 2 — height of centre of buoyancy above keel (rectangular box: centroid of displaced volume).
KM = KB + BM — height of the metacentre above the keel.
GM = KM − KG — metacentric height. Positive = stable; negative = unstable.

The block coefficient (C_b) for a real ship is typically 0.55–0.85 and the waterplane coefficient (C_w) is typically 0.70–0.90. Using a box (C_b = C_w = 1.0) overestimates BM and therefore KM, which means estimated GM will be higher than the actual value.

Vessel dimensions (box approximation)

L — length (m)B — breadth (m)d — mean draft (m)KG — vert. CoG (m)

Enter all four dimensions to compute.

Caution — estimation only. This uses a rectangular box approximation (Cb = 1.0). Real ships have block coefficients typically 0.55–0.85, and a non-rectangular waterplane area. Results are for cadet study and conceptual understanding only. Never use this for operational loading or stability calculations — use the vessel's approved stability instrument and loadicator.

When to use this tool

Quick sanity-check before cargo loading — is the intended cargo distribution going to leave the vessel with adequate GM? Also for training purposes to build intuition about the drivers of transverse stability (beam-squared dominates BM, so wide vessels are naturally more stable; loaded KG must not exceed KM). NOT a substitute for the ship's stability booklet or approved loading computer.

Worked example

Scenario: Panamax bulker B = 32 m, drought d = 12 m, KG (from loading computer) = 8.5 m.

Calculate: BM = 32² ÷ (12 × 12) = 1024 ÷ 144 = 7.11 m. KB = 12 ÷ 2 = 6.00 m. KM = 6.00 + 7.11 = 13.11 m. GM = 13.11 − 8.5 = 4.61 m.

Interpretation: Well-positive GM. However this is box-approximation; real bulker Cb ≈ 0.85 + Cw ≈ 0.88, so actual BM ~15% lower, actual GM ~4.0 m. Still comfortable. On a real voyage, verify against the loading computer output.

Regulatory basis

IMO Res. A.749(18) as amended by MSC.75(69) — Code on Intact Stability for All Types of Ships. IMO 2008 IS Code (Res. MSC.267(85)) revised the criteria for cargo ships. Vessel-specific criteria vary by type + service. Modern bulker + tanker CSR (Common Structural Rules) integrate stability + strength considerations at design.