What is the formula for calculating the metacentric radius

What is the formula for calculating the metacentric radius

The metacentric radius (BM) is the vertical distance between the center of buoyancy and the metacenter of a ship[2][4][5][6]. The metacentric radius can be calculated using the formula 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[4][5]. The metacentric radius is used to compare the stability of different vessels[2][5]. The metacentric height (GM) is calculated as the distance between the center of gravity (G) of a ship and its metacenter (M)[1][4][6]. 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][6]. The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel[1][6]. The metacentric height and the metacentric radius are both important parameters for a ship's stability, and they are used together to determine the stability of a ship[6].

Citations:

[1] 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

[2] Metacentric Radius - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/metacentric-radius

[3] Lecture 21 -Derivation of Metacentric Radius (BM) - YouTube https://youtube.com/watch?v=37PdV1ySoO4

[4] Naval architecture - Metacentric Stability, Buoyancy, Stability - Britannica https://www.britannica.com/technology/naval-architecture/Metacentric-stability

[5] FORMULAE AND DEFINITIONS https://pms2004.tripod.com/formulae_and_definitions.html

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

By Perplexity at https://www.perplexity.ai/search/837d939e-2b18-4d05-9bea-3baa8bfaff2b?s=m