Archimedes' Principle states that a body wholly or partially immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the body. The principle applies to liquids and gases and follows from the pressure distribution in a fluid under a body force such as gravity. If the displaced volume is V and fluid density is rho, the buoyant force magnitude is rho g V under the usual uniform gravity assumptions. The principle provides a direct relationship between fluid statics and the forces acting on immersed bodies and is one of the foundational results of hydrostatics.
The physical basis of Archimedes' Principle is the hydrostatic pressure gradient. Pressure increases with depth, so the lower parts of an immersed body's surface experience greater pressure than corresponding higher parts. Integrating these pressure forces over the entire surface produces a net upward resultant. The displaced volume represents the volume of fluid that would occupy the region occupied by the immersed part of the body. The weight of that hypothetical displaced fluid is therefore equal to the resultant pressure force. This derivation shows that buoyancy does not require the fluid to exert a single upward force at one particular point; it emerges from the distributed pressure field.
Archimedes' Principle explains three basic equilibrium outcomes. If the weight of an object exceeds the maximum buoyant force available when it is fully submerged, the object sinks. If the object's weight equals the buoyant force while fully submerged, it can be neutrally buoyant under suitable conditions. If its weight is less than the buoyant force available for full submergence, it can rise until only enough of the object remains submerged for the displaced fluid weight to equal the object's weight. A floating body's submerged volume therefore adjusts according to its weight and the density of the surrounding fluid rather than simply according to the object's material density.
The principle has a major role in determining density and volume. If an object is weighed in air and then immersed in a fluid, the apparent reduction in measured weight can be related to the buoyant force. With appropriate corrections, this allows density to be determined when either mass or displaced volume is known. Archimedes' Principle is historically associated with the use of buoyancy to determine whether a crown was made from the expected material without melting it, although the exact historical details of that story are uncertain. Modern hydrometers, displacement measurements and buoyancy experiments provide more controlled applications of the same physical principle.
Archimedes' Principle applies to gases as well as liquids. A body immersed in air displaces a volume of air and receives an upward buoyant force equal to the weight of that displaced air. This effect is often small compared with the weight of dense objects but becomes decisive for balloons and airships. For a balloon to rise, the buoyant force from displaced ambient air must exceed the combined weight of the envelope, payload and lifting gas or heated air. Atmospheric density changes with altitude and meteorological conditions, so the available buoyant force changes as a balloon rises.
The principle is closely connected with the concepts of centre of buoyancy and displaced volume. For a homogeneous static fluid, the buoyant force can be considered to act through the centre of volume of the displaced fluid, commonly called the centre of buoyancy. The object's centre of gravity determines where its weight acts. For simple vertical equilibrium, the magnitudes of the forces are sufficient, but rotational stability requires consideration of their lines of action and the resulting moments. In ships and other floating structures, this leads to additional concepts concerning metacentres and restoring moments.
Archimedes' Principle assumes the relevant fluid is in hydrostatic equilibrium and that the buoyant force can be obtained from the surrounding pressure distribution. If the fluid is accelerating, strongly nonuniform, moving relative to the body or affected by other dynamic effects, additional forces may occur and the simple hydrostatic expression may not describe the complete force. A moving body can experience drag, lift, added mass effects and other hydrodynamic forces. The principle nevertheless remains applicable to the hydrostatic component when its assumptions are appropriate. Distinguishing static buoyancy from the total hydrodynamic force is essential in dynamic fluid problems.
Archimedes' Principle remains important in physics, engineering, metrology and everyday technology because it provides a general explanation for displacement, floating and buoyancy. It underlies the operation of hydrometers and contributes to the design and analysis of ships, submarines, floats, balloons and underwater equipment. Its conceptual importance extends beyond its simple formula because it demonstrates how a distributed pressure field can be replaced, for force calculations, by an equivalent resultant associated with displaced fluid. Correct application requires identifying the immersed volume, surrounding fluid density, gravitational acceleration and equilibrium conditions rather than assuming that buoyancy is determined by the object's total volume in every circumstance.
