Objects float when the upward buoyant force acting on them is sufficient to balance their weight before they become completely submerged. For a freely floating object at equilibrium, the buoyant force equals the object's weight, so the net vertical force is zero. The buoyant force arises because pressure in a fluid generally increases with depth. The lower portions of an immersed object therefore experience greater fluid pressure than the upper portions, producing a resultant upward force.
Archimedes' principle quantifies this force as equal to the weight of the fluid displaced by the immersed portion of the object. An object floats when it can displace enough fluid for the weight of that displaced fluid to equal the object's weight. For a homogeneous object floating in a homogeneous fluid, the fraction of its volume that is submerged is related to the ratio of the object's average density to the fluid density. Thus an object with an average density of 0.6 times the fluid density will float with approximately 60 percent of its volume submerged, under ideal conditions.
Density provides a particularly useful way of understanding floating. If an object's average density is less than the density of the surrounding fluid, it can displace a volume of fluid whose weight equals the object's own weight before the object becomes completely submerged. It therefore settles at a partially submerged equilibrium position. If the object's average density equals the fluid density, it can remain fully submerged in neutral equilibrium under ideal conditions, provided there is no other net force.
If its average density is greater than the fluid density, the maximum buoyant force available when it is fully submerged is less than its weight, so it accelerates downward and sinks. The phrase average density is crucial because an object may contain air spaces or hollow regions. A steel ship floats even though steel itself is much denser than water because the ship's overall mass divided by its enclosed external volume can be less than the density of water.
Floating is not determined solely by the material from which an object is made. Geometry and enclosed volume can radically change average density and therefore buoyant behaviour. A solid steel sphere generally sinks in water because its density exceeds that of water. A hollow steel vessel can float because its internal volume increases the total volume associated with its mass without adding proportional mass. Boats, ships, pontoons, and floating platforms exploit this principle.
The volume that contributes to buoyancy is the volume of the object that displaces fluid, which for a sealed floating vessel is effectively the submerged external volume. Water does not need to enter the hollow interior for the vessel to displace water. If water enters the vessel, however, the average mass increases without a corresponding increase in external displacement, reducing buoyancy relative to weight and potentially causing the vessel to sink.
A floating object is in mechanical equilibrium when the upward buoyant force equals its downward weight and there is no unbalanced torque causing it to rotate. Translational equilibrium alone is not enough to guarantee stable floating. The distribution of mass and displaced fluid volume determines the object's rotational stability.
A floating body can heel or tilt when a force acts on it, and the relative positions of the centre of mass and centre of buoyancy influence whether the resulting buoyant force creates a restoring or overturning torque. Ships are designed with stability characteristics that help them return toward an upright configuration after small disturbances. The shape of the hull, distribution of cargo, location of the centre of gravity, and geometry of the submerged volume all influence stability. Thus the simple density condition explains whether floating is possible, while hydrostatics and rotational equilibrium determine whether the floating state is stable.
Surface effects can also allow very small objects to float even when their density exceeds that of the liquid under some circumstances. Surface tension creates forces along a liquid surface and can support small objects if their geometry and wetting properties allow the surface to deform without breaking. Certain insects exploit surface tension to remain at the water surface. This is not the same mechanism as ordinary bulk buoyancy, although buoyant forces can still be present.
Similarly, capillary effects can support or move small quantities of liquid in narrow structures. For large everyday floating objects, however, the dominant explanation is usually hydrostatic buoyancy. Distinguishing surface tension from buoyancy prevents the misconception that every object at a liquid surface is supported exclusively by Archimedes' principle.
Floating also depends on the surrounding fluid. An object that floats in water may sink in a denser fluid or rise higher in a less dense fluid. Saltwater is denser than freshwater, so an object of fixed mass and volume generally floats with a smaller fraction of its volume submerged in saltwater than in freshwater. Temperature can alter fluid density and therefore slightly alter the submerged fraction. Pressure can also affect densities, particularly in gases and under extreme conditions.
In air, many objects that are denser than air fall under gravity, while balloons filled with sufficiently low density gas or heated air can float because their average density is lower than the surrounding atmosphere. The same physical principles therefore apply to floating in liquids and gases, although the density contrasts and magnitudes of buoyant forces differ substantially.
Floating can be described quantitatively through force balance. If an object of mass m floats in a fluid of density rho fluid, the buoyant force is F buoyant = rho fluid g V displaced, while its weight is mg. At equilibrium, rho fluid g V displaced = mg. Cancelling g gives V displaced = m divided by rho fluid.
Dividing by the object's total volume V object gives the submerged fraction equal to rho object divided by rho fluid when the object's average density is defined as m divided by V object. This equation shows why the submerged fraction does not depend directly on gravitational acceleration under the idealised conditions because g appears on both sides of the equilibrium equation. The actual geometry, fluid motion, density variations, and surface effects can introduce additional complications, but the basic relation provides a powerful first approximation for floating bodies.
The common misconception that an object floats because its weight disappears is incorrect. The object's weight continues to act downward due to gravity. Floating occurs because the surrounding fluid produces an upward force that balances that weight. Another misconception is that floating requires the object itself to be less dense than the fluid in every local region. What matters for ordinary hydrostatic floating is the object's overall average density and the volume of fluid it displaces.
An object can therefore contain dense materials and still float if sufficient low density volume is included in its overall geometry. Floating is consequently a force balance resulting from fluid pressure, and density is a convenient way of predicting the outcome. The principles are fundamental to ships, submarines, life jackets, buoys, hydrometers, atmospheric balloons, and many natural systems involving organisms and fluids.
