Metacentric Height and Ship Stability Calculator

Calculate metacentric radius and initial metacentric height for a rectangular waterplane.

BM = I/V; GM = KB + BM − KG

Waterplane length L (m)

Waterplane width B (m)

Displacement volume V (m³)

Keel-to-buoyancy-center KB (m)

Keel-to-gravity-center KG (m)

Enter valid values in all required fields.

What this formula means

Metacentric height is a first-order measure of a floating body’s initial stability at small heel angles. BM comes from waterplane geometry and displaced volume; GM is the vertical distance from the center of gravity to the metacenter.

Use preliminary GM calculations for ships, barges, pontoons, floating platforms, and laboratory stability models. The result should be interpreted with consistent units and with the assumptions of the underlying model in mind.

Worked example

For the default rectangular waterplane, BM ≈ 1.333 m and GM ≈ 0.333 m, indicating positive initial stability.

Applications

Use preliminary GM calculations for ships, barges, pontoons, floating platforms, and laboratory stability models. It is also useful as an independent check when comparing hand calculations, laboratory measurements, simulations, or preliminary engineering estimates.

Assumptions and common mistakes

Important: The rectangular-waterplane approximation and small-angle interpretation are simplified. Real vessel stability requires hydrostatic curves, free-surface corrections, loading conditions, and regulatory criteria.

Use SI units unless the field label states otherwise. Keep significant figures appropriate to the accuracy of the inputs, and do not treat a simplified calculator as a replacement for codes, detailed design standards, or professional review.

Frequently asked questions

What equation does this calculator use?BM = I/V; GM = KB + BM − KG. The calculator evaluates the displayed relationship using the values entered above.

Are the results unit-sensitive?Yes. The input labels use SI units so the displayed output follows the corresponding SI unit.

Can I use this for engineering design?Use it for learning and preliminary checks. Final designs require validated data, applicable standards, safety factors, and professional judgment.