If we know the mass density of the water, , in which a ship is floating, we can calculate the weight of the displaced fluid, or the displacement weight, W,

By Archimedes' principle this weight is equal to the weight of the ship and its contents. In inch-pound (or "English") units, W is in long tons if is in and in salt water (SW); i.e.,

in FW or SW, respectively.

In SI (Systeme International), the above expression for displacement weight (Eq. 1) applies if units of force are newtons (with ) or kilonewtons (with ). In FW the value of is approximately and in SW is . Such units are common in resistance and propulsion calculations.

However, adherance to the SI system obliges one to think of ship displacement, , in mass units, rather than weight (force) units, with the unit of mass being a multiple of grams, such as a kilogram (1000 grams), or a metric ton (1000 kilograms) t, sometimes written as "tonne." 3 Hence, in the SI system, mass displacement,

where is in metric tons, is in , (equal to kg / L) in FW and in SW. For the above relationship to be true in inch-pound units, would have to be expressed in or in the seldom-used slugs and

Since the mass density of fresh water is 1.0 kg / L or , density is numerically the same in SI units as specific gravity, ' (at standard temperature). Hence, it may be more convenient when using SI units to use,

Again this is true in inch-pound units only if is in or in slugs.

Sometimes naval architects prefer to make use of the reciprocal of density, or specific volume, (volume per unit mass), in their calculations. For fresh water, of course, ; for salt water

We shall in general consider ship displacement in units of metric tons of mass, where one metric ton is equal to the mass of one cubic meter of fresh water (at standard temperature), i.e., . It should be noted that one of fresh water in inch-pound units. is 2204 lb or 0.9839 long ton (2240 Ib/ton). Hence, it can be seen that one SI ton is roughly equivalent to a long ton of weight (1.6 percent error) in the inch-pound system. The term weight will often be used loosely to mean either weight in tons (Ib) or mass in metric tons (kg.).

The centroid of the underwater portion of a vessel may be calculated by the principle of moments, using methods also outlined. The centroid is called the center of buoyancy. It represents a point through which the vertical buoyant vector is considered to pass, i.e.

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