Enter Ship Condition Data
Use hydrostatic booklet values where available. This calculator estimates initial transverse stability and should support, not replace, approved marine stability documents.
Example Data Table
Example operating cases below illustrate how corrected GM can change with weight distribution, density, and free surface effects.
| Condition | ∇ (m³) | Density | Beam | LWL | Draft | Cwp | KG | FSC | Heel | Corrected GM | Class |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Harbor departure | 12,550 | 1,025 | 22.4 | 128.0 | 7.2 | 0.84 | 8.15 | 0.18 | 10 | 0.985 | Serviceable |
| Full cargo leg | 13,100 | 1,025 | 22.4 | 128.0 | 7.5 | 0.85 | 8.42 | 0.24 | 12 | 0.812 | Serviceable |
| Ballast return | 10,980 | 1,000 | 22.4 | 128.0 | 6.3 | 0.81 | 7.76 | 0.15 | 8 | 1.146 | Very stiff |
Formula Used
This calculator applies a practical initial transverse stability model for small heel angles. It is suitable for quick engineering checks, voyage planning reviews, and loading sensitivity studies.
1. Displacement mass: Δmass = ρ × ∇ ÷ 1000
2. Buoyancy force: Fb = ρ × g × ∇ ÷ 1000
3. Waterplane area: Aw = LWL × B × Cwp
4. Approximate transverse waterplane inertia: IT = LWL × B³ × Cwp ÷ 12
5. Metacentric radius: BMt = IT ÷ ∇
6. Metacentric height: KMt = KB + BMt
7. Uncorrected GM: GM = KMt − KG
8. Corrected GM: GMcorr = KMt − KG − FSC
9. Righting arm at small heel: GZ ≈ GMcorr × sin(θ)
10. Righting moment: MR = W × GZ
11. Wind heeling arm: lH = MH ÷ W
12. Net lever: lnet = GZ − lH
Engineering note: The waterplane inertia and KB treatment here are simplified. For final decisions, use approved hydrostatic curves, cross curves, tank correction tables, and the vessel’s official stability booklet.
How to Use This Calculator
Enter the active loading condition name first so reports remain traceable.
Provide operating vessel weight and underwater displacement volume for the same condition.
Select a density preset or type a measured water density manually.
Enter beam, waterline length, draft, and waterplane coefficient from drawings or hydrostatic records.
Type KG from the loading computer or weight estimate sheet.
Enter free surface correction from slack tanks. Use zero only when justified.
Leave KB blank for a quick estimate or enter a manual KB from hydrostatic data.
Set the heel angle to inspect the estimated righting arm and moment.
Add an optional wind heeling moment to compare available righting energy against an external overturning effect.
Submit the form. Review corrected GM, GZ, righting moment, balance difference, and advisory notes shown above the form.
Frequently Asked Questions
1. What does corrected GM tell me?
Corrected GM estimates initial transverse stability after subtracting free surface effects. Positive values usually indicate a restoring tendency at small heel angles.
2. Why is free surface correction important?
Slack liquids shift as the vessel heels. That movement raises effective KG and reduces available stability, sometimes enough to change a safe condition into a risky one.
3. Is this suitable for large heel angles?
No. The GZ relationship here is a small-angle approximation. Large-angle stability should use approved cross curves, KN data, and statutory criteria from the vessel booklet.
4. What if I do not know KB?
The calculator can estimate KB as 0.53 times draft. That is a quick placeholder, but hydrostatic booklet data is preferred for operational accuracy.
5. Why compare vessel weight with hydrostatic displacement?
The comparison helps identify mismatches in cargo figures, tank contents, or density assumptions. Large differences usually mean the input condition needs rechecking.
6. What does a very stiff classification mean?
Very stiff vessels may have strong initial stability, yet they can also roll quickly and create uncomfortable or damaging accelerations. More GM is not always better.
7. Can I use freshwater or brackish water?
Yes. Density presets are included for quick scenario switching, and a custom density field allows local measurements or special harbor conditions.
8. Does this replace a stability booklet?
No. It is a fast engineering estimator for planning and sensitivity checks. Official stability approval must still come from the vessel’s approved documentation.