Ship stability calculator
What this calculates: displacement, metacentric height (GM) checked against the IMO minimum of 0.15 m, roll period, small-angle wall-sided righting arm (GZ), free-surface loss from a slack tank, and heel in a steady turn, 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. Displacement is the moulded volume CB·L·B·T in seawater, so it always agrees with the hull form.
What it ignores: large-angle stability beyond about 15° of heel (and so the IMO GZ-area, GZ-at-30°, maximum-GZ-angle and weather criteria), deck-edge immersion, 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 rectangular double-bottom ballast tank near midships, 0.15L long and 0.45B wide. Pressed full, it has no free surface. Once slack, the loss is the same whether it is nearly full or nearly empty, because it depends on the breadth of the liquid surface, not its depth. That loss grows with the cube of the breadth, so splitting the tank with n longitudinal bulkheads into n + 1 equal compartments cuts it by a factor of (n + 1)².
Stability figures
| Quantity | Value | Note |
|---|---|---|
| Displacement | 103,935 t | ∇ = Cb·L·B·T (moulded), seawater 1.025 t/m³ |
| KB (height of buoyancy) | 7.22 m | Morrish's approximation |
| BM (metacentric radius) | 9.95 m | I_T / ∇, I_T from Cw (Dudszus & Danckwardt) |
| KM (= KB + BM) | 17.17 m | |
| KG (this loading) | 15.83 m | 55% of the way from stiff to tender |
| GM, solid (no free surface) | 1.35 m | |
| Free surface correction | −0.00 m | Pressed full (no free surface) |
| GM, effective (fluid) | 1.35 m | GM solid − free surface correction; IMO minimum 0.15 m |
Wall-sided GZ curve (righting arm)
| Heel | GZ | |
|---|---|---|
| 5° | 0.121 m | |
| 10° | 0.261 m | |
| 15° | 0.441 m | edge of valid range |
GZ = sin φ (GM + ½ BM tan² φ). Exact for a box until the deck edge immerses or the bilge emerges; this tool has no depth input, so it cannot check deck-edge immersion.
Heel in a steady turn
Heel angle: 4.81°
Honest limits
• This is a tier-1 hydrostatic estimate from waterplane and block coefficients, not real hull offsets or a hydrostatics model
• Displacement is the moulded volume Cb·L·B·T in seawater; shell plating and appendages are ignored
• The wall-sided GZ formula is only valid to roughly 15 degrees of heel - it says nothing about large-angle stability
• Only the initial-GM criterion of the IMO 2008 Intact Stability Code (Part A 2.2.4) is checked; the GZ-area, GZ-at-30° and maximum-GZ-angle criteria and the weather criterion need a large-angle GZ curve
• 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 uses the IMO IS Code empirical formula and turn heel a steady-turn, small-angle moment balance - not a seakeeping or manoeuvring model
How it works
The calculator estimates the metacentric radius (BM = IT/∇) from Dudszus and Danckwardt's waterplane-coefficient approximation to the transverse moment of inertia, and the height of the centre of buoyancy (KB) from Morrish's formula. 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; in a wall-sided tank the loss is the same whether the tank is nearly full or nearly empty. The cures are to press it full or divide it with longitudinal bulkheads; topping it up part-way does not help. Roll period uses the IMO Intact Stability Code formula T = 2CB/√GM, and turn heel balances the centrifugal heeling moment, acting on the lever KG − T/2, against the small-angle righting moment.