Around 246 B.C., the Greek scientist Archimedes discovered that an object totally or partially immersed in a fluid, experiences an upward buoyant force FBequal to the weight of the fluid it displaces. This makes sense because that same volume of fluid was in equilibrium with its surroundings before the object was placed in the fluid (see Figure 1).

If the submerged volume of the object is Vsubm, the mass of fluid it displaces is given by fluid density · submerged volume, i.e. mdisp = ρfluid · Vsubm, and therefore the weight of the fluid displaced is mdisp · g. So we can write:

Buoyant force FB = mdisp · g = ρfluid · Vsubm · g

It is important to note that the only object property that affects the buoyant force is its volume - not what it is made of or its shape. For example, a solid metal ball and a hollow plastic ball, of the same volume, both held underwater experience equal buoyant forces.

Of course, as long as there is gravity (g), the object in the fluid always has the weight force pulling down on it, and the buoyant force pushing up on it. How these two forces compare determines whether the object sinks or floats.

This image shows on the left a tank filled up with water with an imaginary boundary around a volume of fluid. In this case, the buoyant force balances the weight of the fluid volume. On the right, there is the same tank where, this time, a real object with the same size and shape of the fluid volume represented on the left, is immersed. The buoyant force on the submerged object stays the same because the surrounding fluid is unaffected.

Figure 1: Archimedes Principle