When a body is partially or totally immersed in water, the volume of displacement of water can be determined by integrating over its submerged surface:

(3–1)

where is the wetted surface of the body in still water, is the unit normal vector of the body surface pointing outwards and is the vertical coordinate of a wetted surface point with reference to the fixed reference axes (FRA).

The buoyancy of a submerged body is the vertical upthrust due to displacement of water:

(3–2)

where is the water density and is gravitational acceleration.

and the center of buoyancy can be calculated by

(3–3)

where is the location of a point on the submerged body surface in the FRA.

More generally, the hydrostatic force and moment are referred to as the fluid loads acting on a body when placed in still water. The hydrostatic force can be calculated by integrating the hydrostatic pressure over the wetted surface of the body, up to the still water level. The hydrostatic moments are taken about the center of gravity of the body. The expressions for hydrostatic force and moment are:

(3–4)

where and represents the hydrostatic pressure and and represents the position vector of a point on the hull surface with respect to the center of gravity in the FRA. The vertical component of the hydrostatic force vector in Equation 3–4 is the buoyancy of submerged body, which is defined by Equation 3–2.