Metacentric Height

Calculate GM = KB + BM − KG to assess the small-angle stability of a floating vessel. Positive GM means the vessel is stable and will self-right after a small heel.

Fluid Properties & Statics

Hull Cross-Section

Vessel presets

Inputs

Beam (breadth) B (m)

Transverse width of waterplane.

Length L (m)

Draft D (m)

Depth of submersion below waterline.

Centre of gravity above keel KG (m)

Measured from keel (bottom of hull) to overall centre of gravity.

Water density (optional) ρ (kg/m³)

Used to compute displacement force.

Theory

Key points and formula:

KB = D / 2 (centroid of submerged rect. section)

BM = I / V (metacentric radius)

KM = KB + BM (metacentre above keel)

GM = KM − KG (metacentric height)

GM = KB + BM − KG

BM for common cross-sections:

Section	I (waterplane)	BM formula
Rectangle (B×L)	L B³ / 12	BM = B² / (12D)
Circle (dia. B)	π B⁴ / 64	BM = B² / (16D)

Stability classification:

Condition	GM	Behaviour
Stable	GM > 0	Restoring moment; returns to upright after small heel
Neutral	GM = 0	Indifferent — stays at any heel angle
Unstable	GM < 0	Overturning moment; capsizes under small disturbance

Practical GM guidelines:

Cargo ships: GM ≈ 0.15–1.0 m (too large → stiff, uncomfortable roll)
Passenger ferries: GM ≈ 0.3–1.5 m
Stability can be increased by lowering KG (move cargo down, add ballast) or widening the beam
Free-surface effect: liquid in partially filled tanks reduces effective GM — add solid GM correction