Marine ballast changes a vessel’s mass distribution and displacement. Weight placed low can lower the combined center of gravity, but the resulting stability also depends on hull geometry, loading and liquid free surfaces. This animation explains transverse initial stability using metacentric height and a small-angle righting-arm estimate. It does not approve a ballast plan or calculate capsize probability.
Ballast Metacentric Height Interactive Calculator
Vary KB, BM, KG and heel angle to compare metacentric height and the small-angle righting arm on a rolling hull section.
Equation Used
For ship ballast stability, metacentric height is calculated as GM = KB + BM - KG. KB is the buoyancy-center height above the keel, BM is the metacentric radius, and KG is the gravity-center height. This calculator also estimates the small-angle righting arm as GZ ~= GM sin(theta).
- GM = KB + BM − KG; dimensions share the keel datum.
- GZ ≈ GM sin θ is a small-angle relation, not a complete righting-arm curve.
- Free-surface effects, loading cases and actual hull hydrostatics are not solved.
- The 0.15 m reference and normalized shortfall index are comparisons only.
GM and GZ are initial-stability estimates. The 0.15 m comparison does not establish compliance with a vessel-specific stability standard. The shortfall index is not a probability of capsize.
How Ship Ballast Changes Stability
Ballast changes the vessel’s displacement and mass distribution. Weight placed low in the hull can lower the combined centre of gravity. The buoyancy force shifts as the hull heels, and the horizontal separation between buoyancy and weight produces a restoring or overturning moment.
This illustration focuses on transverse initial stability. It does not simulate the hull’s submerged volume or a ballast-water transfer operation.
Marine ballast and loading conditions
A vessel may use permanent ballast, variable water ballast or both to achieve its designed loading conditions. Added water also changes displacement, draft and potentially the center of buoyancy and metacentric radius. Those changes must be evaluated for the actual hull.
Partly filled tanks introduce free-surface effects as liquid shifts with heel. Their contribution depends on tank geometry and loading. Moving ballast through intermediate tank states can create conditions different from both the starting and final arrangements.
The word ballast is also used for railway aggregate and lamp current-control equipment. Those are different physical systems; the ship-stability equations on this page do not describe either one.
Metacentric Height and Righting Arm
Using one keel datum, GM = KB + BM − KG. KB is the initial centre-of-buoyancy height, KG is the combined centre-of-gravity height, and BM is the metacentric radius. For small heel angles, GZ ≈ GM sin θ. Positive GM indicates initial restoring tendency; it is not by itself proof of stability over a complete operating range.
The 0.15 m comparison in this calculator is only a reference. Compliance, free-surface corrections, damage cases and large-angle stability require the applicable vessel criteria and hydrostatic data.
Worked example: interpreting the reference comparison
For a hypothetical initial condition, enter KB = 4.2 m, BM = 3.0 m and KG = 6.8 m using the same keel datum. GM = 4.2 + 3.0 − 6.8 = 0.4 m. At 5° heel, GZ ≈ 0.4 sin 5° = 0.03486 m.
The margin to the calculator’s 0.15 m reference is 0.25 m, and the shortfall index is zero. That zero means only that GM is at or above the chosen fixed reference; it does not mean zero capsize risk.
If KG is instead 7.1 m with the other inputs held fixed, GM = 0.1 m, GZ ≈ 0.00872 m at 5°, the reference margin is −0.05 m and the shortfall index is 33.33%. That percentage describes a normalized numerical shortfall, not a probability.
At KG = 7.3 m, GM = −0.1 m and the model gives GZ ≈ −0.00872 m at 5°. It indicates an initial overturning tendency. The actual subsequent heel, downflooding or capsize behavior cannot be determined from this small-angle relation.
Separately, if a justified free-surface correction of 0.18 m applied to the first condition, its corrected initial GM would be 0.22 m. The calculator has no separate free-surface input and does not compute that correction. These examples are not vessel loading instructions or a departure assessment.
Ballast and roll stabilization have different roles
| Approach | Principal effect | Separate consideration |
|---|---|---|
| Fixed ballast | Changes mass distribution permanently. | Displacement, structure, draft and payload consequences. |
| Water ballast | Allows loading conditions to be varied within the vessel design. | Tank geometry, free surfaces, transfer sequence and approved limits. |
| Fins or gyroscopic stabilizers | Can reduce roll motion in their operating conditions. | They do not substitute for adequate hydrostatic stability or reserve buoyancy. |
The response to waves also depends on inertia, damping, speed and the full righting-arm curve. A larger positive GM is not automatically the most comfortable condition, and a preferred roll period cannot be inferred without a vessel model.
Reference-index arithmetic
Margin = GM − 0.15 m. Shortfall index = 100(0.15 − GM)/0.15, limited to the range 0–100%. The clamp gives 100% for GM at or below zero and zero for GM at or above 0.15 m. These are comparison conventions only.
Actual stability assessment uses the vessel’s applicable criteria, approved information and loading condition. A single fixed GM reference does not determine legal compliance or seaworthiness.
Ship-ballast questions
No. Its position affects the combined center of gravity, while displacement changes affect hull hydrostatics. Liquid free surfaces and intermediate transfer conditions also matter.
KB and KG are heights from the same keel datum. BM is the distance from the initial center of buoyancy to the transverse metacenter; KB plus BM gives KM in this initial model.
It indicates an initial restoring tendency in the small-angle model. It does not establish the full range of positive righting arm, downflooding limits, damage stability or behavior in waves.
Not as a general vessel prediction. Use the actual hull’s righting-arm data and loading condition beyond the range where the initial-metacenter approximation is appropriate.
No. It is a clamped numerical comparison of GM with 0.15 m. It contains no probability model.
No. It takes supplied KB, BM and KG and applies the stated equations. Any required correction must be established separately with the actual tank and loading data.
The diagram cannot prescribe a transfer. Use the vessel’s approved stability information, loading procedures and competent assessment of each stage.
Reducing roll motion is different from establishing adequate hydrostatic stability. The vessel must still satisfy its applicable stability and loading requirements.
Stability references
- IMO: Ship Design and Stability: the broader intact-stability framework, including righting levers, free surfaces and watertight integrity.
- UK Maritime and Coastguard Agency: fishing-vessel stability guidance: practical explanations and links to vessel-specific guidance.
Consult the requirements that apply to the actual vessel; this teaching comparison is not a substitute for its approved stability information.
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