Archimedes' Principle Calculator

Archimedes' principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This principle explains why objects float or sink and is fundamental to naval architecture, hydrostatics, and many engineering applications.

The buoyant force is calculated using F_B = ρ × g × V, where ρ (rho) is the density of the fluid in kg/m³, g is the gravitational acceleration (9.81 m/s² on Earth), and V is the volume of the fluid displaced (i.e., the submerged volume of the object) in m³. The result is expressed in Newtons (N).

To find an object's density, weigh it in air (m_air) and then weigh it while submerged in a fluid of known density (m_fluid). The object density is calculated as: ρ_object = ρ_fluid × m_air / (m_air − m_fluid). The difference in mass readings equals the mass of fluid displaced, which gives you the volume and thus the density.

The law of floatation is a special case of Archimedes' principle. It states that a floating object displaces a volume of fluid whose weight equals the total weight of the object. An object floats when its average density is less than or equal to the density of the fluid it is placed in, and sinks when its density is greater.

If a coin displaces 200 g (0.2 kg) of water, the buoyant force equals the weight of that displaced water: F_B = m × g = 0.2 kg × 9.81 m/s² = 1.962 N. This upward force acts on the coin regardless of whether it ultimately floats or sinks.

Archimedes' principle has countless practical applications: designing ships and submarines (buoyancy control), hot air balloons and blimps (buoyancy in air), hydrometers (measuring fluid density), determining the purity of metals (as Archimedes did with the king's crown), medical imaging (underwater weighing to measure body fat), and hydraulic lifts.

When an object is submerged, the upward buoyant force partially counteracts gravity, making the object appear lighter. The apparent weight in fluid equals the true weight in air minus the buoyant force: W_apparent = W_air − F_B. The difference is the apparent weight loss, which equals the weight of the displaced fluid.

The buoyant force depends on the volume of fluid displaced, not on the depth. If an object is fully submerged, moving it deeper does not change the buoyant force (assuming fluid density is constant). However, if the object is only partially submerged, increasing depth increases the submerged volume and therefore the buoyant force.