What is the formula for calculating the metacentric height

What is the formula for calculating the metacentric height

The metacentric height (GM) is calculated as the distance between the center of gravity (G) and the metacenter (M) of a ship[1][4]. The formula for calculating the metacentric height is GM = KM - KG, where KM is the height of the metacenter above the keel and KG is the height of the center of gravity above the keel[4]. The metacentric height can also be calculated by dividing the metacentric radius by the roll or pitch angle[2]. The metacentric radius is the distance between the center of buoyancy and the metacenter[2]. The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel[1]. The height of the intersection above the base (YZ), when measured on the GZ scale, will give the initial metacentric height[6]. The formula for calculating the metacentric radius is BM = I / V, where I is the moment of inertia of the waterplane area of the ship around the axis of rotation under consideration, and V is the volume of the underwater part of the ship[5].

Citations:

[1] Metacentric height - Wikipedia https://en.wikipedia.org/wiki/Metacentric_height

[2] How do you calculate the metacentric height of a ship with a complex hull shape? - LinkedIn https://www.linkedin.com/advice/1/how-do-you-calculate-metacentric-height-ship

[3] Determination of Metacentric Height of a Floating Body - The Constructor https://theconstructor.org/practical-guide/metacentric-height-floating-body/30000/?amp=1

[4] LESSON TOPIC: 4 https://man.fas.org/dod-101/navy/docs/swos/dca/stg4-01.html

[5] Formula of metacentric height - Physics Forums https://www.physicsforums.com/threads/formula-of-metacentric-height.860585/

[6] Initial Metacentric Height - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/initial-metacentric-height

By Perplexity at https://www.perplexity.ai/search/42cd622a-5dfe-4aa4-8c25-bfe03c2bb0bc?s=m