This tool is for preliminary engineering review and learning. Final vessel stability decisions should always use approved hydrostatic data, cross-curves, loading conditions, and the governing rules for the craft.
Calculated Result
The summary appears here above the form after calculation.
Calculation Details
Engineering Notes
Righting Arm Input Form
Use the small-angle GM method, the KN approach, or hydrostatic inputs using KB, BM, and KG. The form stays in one page section, while the input grid adapts across screen sizes.
Plotly Graph
The chart shows the GZ curve across the chosen angle range.
Formula Used
1) Small-Angle GM Method
GZ = GM × sin(θ)
Use this when metacentric height is already known for the loading condition. It is a practical approximation at small and moderate heel angles.
2) KN Method
GZ = KN(θ) − KG × sin(θ)
This approach uses cross-curve data. A KN table across angles gives a more realistic large-angle curve than one constant KN value.
3) Hydrostatic Method
GM = KB + BM − KG
BM = I / ∇
GZ = GM × sin(θ)
Additional Output Relationships
Righting Moment (kN·m) = Displacement (tonnes) × 9.81 × GZ
Area under GZ curve is estimated numerically with the trapezoidal rule in m·rad over the selected angle range.
How to Use This Calculator
- Select the calculation method that matches the data you have.
- Enter the vessel name, displacement, and the selected heel angle.
- Define the angle range and step size for the GZ curve.
- For the GM method, enter the known GM value.
- For the KN method, enter KG and either one KN value or a KN table.
- For the hydrostatic method, enter KB and KG, then choose direct or derived BM.
- Press Calculate Righting Arm to show the result above the form.
- Review the summary cards, engineering notes, graph, and exports.
Example Data Table
| Method | Selected Angle | Key Inputs | Computed GZ | Approx. Righting Moment |
|---|---|---|---|---|
| GM Method | 20° | GM = 1.35 m, Displacement = 6500 t | 0.462 m | 29,450 kN·m |
| KN Method | 25° | KN = 1.28 m, KG = 2.10 m, Displacement = 7200 t | 0.392 m | 27,730 kN·m |
| Hydrostatic Method | 30° | KB = 1.10 m, BM = 1.90 m, KG = 2.30 m, Displacement = 5000 t | 0.350 m | 17,170 kN·m |
Frequently Asked Questions
1) What is a righting arm?
A righting arm, usually called GZ, is the horizontal distance between the lines of action of buoyancy and weight at heel. It indicates the lever that tends to restore the vessel toward upright.
2) When should I use the GM method?
Use the GM method when a reliable GM value is already known for the loading case and you need a quick estimate. It is most suitable at small to moderate heel angles.
3) Why is the KN method often better for larger angles?
KN varies with heel angle. A KN table reflects geometry changes as the hull heels, so it can represent larger-angle behavior better than a simple constant-GM approximation.
4) What does a negative GZ mean?
A negative GZ means the vessel develops an overturning lever instead of a restoring lever at that angle. That is a warning sign and may indicate unstable or unsafe equilibrium.
5) Why does the calculator ask for displacement?
Displacement is used to estimate righting moment from the righting arm. GZ shows lever length, while righting moment shows the restoring effect scaled by vessel weight.
6) What units should I keep consistent?
Enter all lengths in meters, angles in degrees, displaced volume in cubic meters, and waterplane inertia in fourth-power meters. Keep displacement in tonnes for the moment output shown here.
7) What does the area under the GZ curve mean?
The area under the GZ curve summarizes available dynamic stability over the chosen angle range. Larger positive area generally indicates stronger energy resistance to heeling within that range.
8) Can this replace an approved stability booklet?
No. Use it for study, checks, and preliminary engineering work. Final decisions should rely on approved stability documentation, verified hydrostatics, and applicable regulatory criteria.