About this calculator
GM (metacentric height) measures a ship's initial stability: the distance between the ship's centre of gravity G and the metacentre M. The larger the GM, the harder the ship returns upright after heeling — but too much GM gives violent rolling and higher forces on lashings. Too little or negative GM is dangerous: the ship may lie over by itself (angle of loll) or capsize.
This calculator follows the stability booklet steps. Start from the displacement and KG of the initial condition, then add load, discharge or shift lines with the weight and the height of its centre of gravity above the keel. New KG = Σ(weight × height) ÷ Σ weight. Take KM from the hydrostatic table at the final draft, so solid GM = KM − KG. Slack tanks create free surface: the liquid moves when the ship heels and virtually raises G. The correction is FSC = Σ free surface moments ÷ displacement; for a rectangular tank the moment = ρ × length × breadth³ ÷ 12. Corrected GM = solid GM − FSC.
A transverse moment from cargo off the centreline gives a list angle of tan⁻¹(TCG ÷ GM). The calculator also estimates the natural roll period with the IS Code 2008 formula T = 2·C·B ÷ √GM. The IS Code general criteria ask for an initial GM of at least 0.15 m, besides the GZ curve criteria. This is an education/estimation tool using small-angle theory; loading decisions use the ship's approved loading computer.
Worked example
Initial condition Δ 8,000 t, KG 6.90 m; load 300 t at KG 9.5 m; final KM 7.80 m; one 12 × 10 m tank half full; 50 t shifted 8 m to starboard:
- New KG = (8,000 × 6.90 + 300 × 9.5) ÷ 8,300 = 6.994 m → solid GM 7.80 − 6.994 = 0.806 m
- Free surface moment 1.025 × 12 × 10³ ÷ 12 = 1,025 t·m → FSC 1,025 ÷ 8,300 = 0.123 m
- Corrected GM 0.683 m (meets the 0.15 m minimum)
- TCG 400 ÷ 8,300 = 0.048 m → list 4.04° to starboard
- Roll period (B 20 m, d 7 m, L 120 m): C = 0.3871 → T = 2 × 0.3871 × 20 ÷ √0.683 = 18.7 s
How to use it
Enter the initial condition
Enter the displacement and KG of the initial condition from the loading condition or stability booklet.
Add weight changes
Fill load/discharge lines with weight, KG and TCG, or shift lines with the vertical and transverse distance moved.
Enter KM and free surface
Enter KM at the final draft from the hydrostatic table, then the free surface moments or the sizes of slack tanks.
Read GM and list
See solid GM, FSC, corrected GM, list angle and roll period, including a warning below 0.15 m.