Metacentric Height Calculator
A floating body is stable when the metacentre lies above its centre of gravity: a 4 × 2 × 1 m block of specific gravity 0.6 has GM = 0.355556 m, so it is stable.
0.355555555555556 m
Full answer, then cut to fewer decimals (not rounded):
- 0.355555555555556 m
- 0.35555555555555 m
- 0.3555555555555 m
- 0.355555555555 m
- 0.35555555555 m
- 0.3555555555 m
- 0.355555555 m
- 0.35555555 m
- 0.3555555 m
- 0.355555 m
- 0.35555 m
- 0.3555 m
- 0.355 m
- 0.35 m
- 0.3 m
- Stability
- stable (M above G)
- Metacentric radius BM = I/V
- 0.555556 m
- BG
- 0.2 m
- Draft (depth immersed)
- 0.6 m
- Centre of buoyancy above the base KB
- 0.3 m
- Centre of gravity above the base KG
- 0.5 m
- Buoyant force ρgV
- 47.088 kN
Step-by-step solution
- BM = I/V = 2.66667 ÷ 4.8 = 0.555556 m
- GM = BM − BG = 0.555556 − 0.2 = 0.355556 m
Metacentric Height Formula
GM = BM − BG = I/V − BG
I second moment of the waterplane, V displaced volume, BG distance from B to G
Worked Example
A 4 m × 2 m × 1 m block with specific gravity 0.6 floating in water:
- BM = I/V = 2.66667 ÷ 4.8 = 0.555556 m
- GM = BM − BG = 0.555556 − 0.2 = 0.355556 m
Metacentric radius BM = I/V: 0.555556 m · BG: 0.2 m · Draft (depth immersed): 0.6 m · Centre of buoyancy above the base KB: 0.3 m · Centre of gravity above the base KG: 0.5 m · Buoyant force ρgV: 47.088 kN
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Frequently asked questions
When is a floating body stable?
When GM > 0, with the metacentre M above the centre of gravity G. A larger GM means a stiffer, faster roll.
What is the buoyant force?
The weight of the displaced liquid, ρgV (Archimedes’ principle).
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Metacentric Height Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/metacentric-height-calculator/
IEEE
Scientific Converters, "Metacentric Height Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/metacentric-height-calculator/