Metacentric Height (GM) First-Principles Estimator
GM built from its parts — KB + BM − KG — with the waterplane-inertia estimate for BM: the naval architecture taught in one calculator.
The decomposition is the lesson: buoyancy's height (KB) plus the waterplane's leverage (BM, where beam enters SQUARED) minus gravity's height (KG). Beam is the cheap stability lever — and the reason wide boats can carry tall rigs with shallow ballast.
Formula
⚠️ For planning and education only — verify with your vessel's documentation, naval-architecture data and official sources. Not for navigation or stability decisions on real voyages without professional data.
GM built from its parts — KB + BM − KG — with the waterplane-inertia estimate for BM: the naval architecture taught in one calculator.
About Metacentric Height (GM) First-Principles Estimator
GM isn't a mystery constant — it's three measurable heights in a tug-of-war: the center of buoyancy (KB) plus the metacentric radius the waterplane's inertia provides (BM, with beam entering squared) minus the center of gravity (KG). This calculator assembles GM from those parts using standard approximations for the form coefficients, making visible WHY beam is the cheapest stability and high weight the dearest enemy.
How to use Metacentric Height (GM) First-Principles Estimator
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula GM = KB + BM − KG; KB ≈ T(0.9 − 0.3·C_b); BM = I_waterplane/∇ ≈ C_wp²·B²/(11.4·C_b·T) substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Metacentric Height (GM) First-Principles Estimator?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula GM = KB + BM − KG; KB ≈ T(0.9 − 0.3·C_b); BM = I_waterplane/∇ ≈ C_wp²·B²/(11.4·C_b·T) with sources cited on the page
- ✓The decomposition is the lesson: buoyancy's height (KB) plus the waterplane's leverage (BM, where beam enters SQUARED) minus gravity's height (KG). Beam is the cheap stability lever — and the reason wide boats can carry tall rigs with shallow ballast.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
Why does beam enter the stability squared?+
BM = I/∇, and the waterplane's transverse moment of inertia I grows with beam CUBED (length × beam³/12 for a rectangle) while displaced volume grows only linearly with beam — net effect B². Ten percent more beam buys ~21% more BM: this is why modern cruisers carry apartment-like interiors and tall rigs on shallow ballast, and why narrowboats are so spectacularly tender.
Where do I get KG — the input that matters most?+
It's the hardest number aboard: formally from an inclining experiment (shift known weights, measure heel, back-calculate), or from the builder's stability documentation. Estimates: 0.6–0.7 × hull depth for typical small craft, lower with deep ballast, higher with flybridges and gear aloft. Every pound added above the current G raises KG proportionally — the running ledger that stability letters on commercial vessels exist to track.
What are KB and the Morrish approximation doing?+
KB locates the upward force: the centroid of the underwater volume, somewhere between half-draft (box barge) and ~0.63 × draft (fine yacht sections). Morrish's 19th-century formula — still in every mate's exam — interpolates by block coefficient. Errors here are small compared with KG uncertainty, which is why the approximation has survived 140 years.
How does this connect to the roll-period test?+
Two routes to one number: this page builds GM from geometry (design-stage thinking); the roll test measures its consequence (T ∝ B/√GM) on the actual boat with its actual loading. Agreement validates both; disagreement usually convicts the KG estimate — gear creep aloft that the geometry method didn't know about. Surveys of working boats use exactly this cross-check.
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