Laws of Floatation Explained Simply with Easy Examples

Archimedes' principle handles all immersed bodies, but floating bodies deserve their own spotlight: a floating object is in a delicate balance, with part above the surface and part below. The laws of floatation describe exactly how that balance works.

They matter for everything that floats — cargo ships loaded to their safe limit, icebergs drifting in the ocean, and the humble hydrometer. Two short laws capture the whole story.

Key Concepts

• First law: a floating body displaces a weight of liquid exactly equal to its own weight.
• Second law: the body's centre of gravity and the displaced liquid's centre of buoyancy lie on the same vertical line, keeping the body upright.
• Fraction submerged: the submerged fraction of a floating object equals its density divided by the liquid's density.
• Equilibrium: floating is a true balance — weight pulls down, buoyancy pushes up, and they are exactly equal.
• Stability: a floating body stays upright only if tipping it raises its centre of gravity, creating a righting push; top-heavy loads capsize.

Formulas

For a floating body, ρ_body × V_total × g = ρ_liquid × V_submerged × g, so the submerged fraction is V_submerged ÷ V_total = ρ_body ÷ ρ_liquid. Densities are in kg/m³ and volumes in m³; g cancels out. This assumes the body floats freely in a calm, uniform liquid. A direct consequence: a body denser than the liquid cannot float (fraction > 1 is impossible), and one of negligible density barely dips below the surface.

Worked Example

How much of an iceberg hides underwater? Ice has density 917 kg/m³ and seawater 1025 kg/m³. The submerged fraction is 917 ÷ 1025 = 0.8946, about 89.5% — nearly nine-tenths of the iceberg lurks invisibly below the surface, the origin of the phrase "tip of the iceberg." For a 1000 m³ iceberg, 895 m³ sits underwater and only about 105 m³ shows. The same law explains the Plimsoll line painted on ships: as cargo is loaded, the ship sinks deeper until the extra displaced water's weight equals the added cargo — and the line marks the deepest legal sinking.

Common Misconceptions

• "A floating object has no forces acting on it." Two large forces act — its full weight downward and an equal buoyant force upward. Floating means balanced, not force-free.
• "Adding weight sinks a boat proportionally." It sinks deeper only until the newly displaced water weighs as much as the added load; a boat rated for it simply floats lower, which is why load lines exist.
• "Floatation contradicts Archimedes' principle." It is Archimedes' principle applied to equilibrium: the "coincidence" that displaced weight equals body weight is exactly what floating means.

Real-World Applications

• Cargo ships: the Plimsoll line ensures loading never pushes the submerged fraction past the safe mark.
• Submarines: hovering mid-water means tuning average density until displaced water weight exactly equals the vessel's weight.
• Icebergs: their hidden bulk, predicted by the density ratio, is what threatens ships — the Titanic lesson.
• Hydrometers and lactometers: they float higher in denser liquids, giving a direct density reading for battery acid or milk.
• Pontoons and rafts: flat floating platforms are designed so the deck stays above water at full load.

The laws of floatation are Archimedes' principle at rest: a floating body displaces its own weight of liquid, balanced upright on a shared vertical line. From icebergs to oil tankers, the submerged fraction is just a density ratio — simple, exact, and sometimes a matter of survival.