Archimedes’ principle: definition and formula

Definition

Archimedes’ buoyancy is the force exerted by a fluid (liquid or gas) on an object that is partially or completely submerged in it. This force is always vertical and directed upwards.

The formula

The value of this buoyancy, denoted by Pi, is calculated as follows:

Pi = rho × V × g

where:

• rho: density of the fluid, in kg/m³
• V: volume of fluid displaced (= the submerged volume of the object), in m³
• g: acceleration due to gravity, approximately 10 N/kg at secondary school level

Example calculation

A cube with a side length of 10 cm (V = 0.001 m³) is completely submerged in water (ρ_water = 1000 kg/m³).

Pi = 1000 × 0.001 × 10 = 10 N

This force pushes the cube upwards with a magnitude of 10 N, regardless of the cube’s material (wood, iron, plastic, etc.).

A common pitfall to avoid

Note: Archimedes’ buoyancy depends on the submerged volume, not on the weight or nature of the object. Two objects of the same volume but made of different materials (one made of cork, one made of iron) experience exactly the same buoyant force if they are fully submerged. What differs is their weight, which determines whether they float or sink.

Also bear in mind that if the object is only partially submerged (such as a boat), V represents only the volume below the surface, not the object’s total volume.