Ship stability calculator
What this calculates: metacentric height (GM), roll period, wall-sided righting arm (GZ), and free-surface loss from a slack tank, for a car carrier, tanker, or container ship.
What it assumes: hydrostatic coefficients estimated from length, breadth, draught, and block/waterplane coefficients — no real hull offsets or hydrostatics tables.
What it ignores: large-angle stability beyond about 15° of heel, downflooding, damage stability, and anything needing an actual hydrostatics model.
Vessel
KG rises fast as deck stacks fill - moderate by default, tender when stacked high.
Cargo loaded: low ↔ high
Sweeps the vertical centre of gravity from a low, stiff loading condition to a high, tender one, holding the hull fixed. Watch GM (effective) above respond live.
Free surface demo: slack ballast tank
A representative double-bottom ballast tank near midships. At 0% it is pressed full (no free surface); at 100% it is fully slack. Free-surface loss grows with the cube of the liquid's breadth, so a wider or slacker tank costs disproportionately more GM than the tank's size alone would suggest.
Stability figures
| Quantity | Value | Note |
|---|---|---|
| KB (height of buoyancy) | 7.22 m | Morrish's approximation |
| BM (metacentric radius) | 11.09 m | I_T / ∇, waterplane-coefficient estimate |
| KM (= KB + BM) | 18.31 m | |
| KG (this loading) | 15.83 m | 55% of the way from stiff to tender |
| GM, solid (no free surface) | 2.48 m | |
| Free surface correction | −0.00 m | 0% slack ballast tank |
| GM, effective (fluid) | 2.48 m | GM solid − free surface correction |
Wall-sided GZ curve (righting arm)
| Heel | GZ | |
|---|---|---|
| 5° | 0.220 m | |
| 10° | 0.461 m | |
| 15° | 0.745 m | edge of valid range |
Heel in a steady turn
Heel angle: 2.61°
Honest limits
• This is a tier-1 hydrostatic estimate from waterplane and block coefficients, not real hull offsets or a hydrostatics model
• The wall-sided GZ formula is only valid to roughly 15 degrees of heel - it says nothing about large-angle stability
• Downflooding angle and progressive flooding are not modelled at all
• Damage stability (compartment loss) is out of scope - this tool assumes an intact hull throughout
• The free-surface demo uses one representative tank; real ballast/cargo plans involve many tanks with different liquids and geometries
• Roll period and turn heel use standard rule-of-thumb formulas, not a full seakeeping or manoeuvring model
How it works
The calculator estimates the metacentric radius (BM) from a waterplane-coefficient approximation to the transverse moment of inertia, and the height of the centre of buoyancy (KB) from Morrish's approximation. Combined with a user-supplied KG, that gives GM. A slack tank's free surface subtracts from GM in proportion to the cube of its breadth, which is why a barely-slack tank barely matters and a wide, mostly-empty one costs disproportionately more stability than its size alone suggests. Roll period and turn heel use standard rule-of-thumb formulas built on top of GM.