Archimedes' Principle: Why Things Float, Sink, or Hang in Between

The principle, precisely stated

Archimedes' principle says that a body wholly or partly submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. As a formula, the buoyant force is

F_b = ρ_fluid × V_displaced × g
where ρ_fluid = density of the fluid, V_displaced = submerged volume, g = gravitational acceleration

That is the entire law. It says nothing about the shape of the object, its own density, or the depth it sits at — only the volume of fluid it physically pushes aside. A cube, a sphere and a ship hull of equal submerged volume in the same fluid feel exactly the same upward push.

Why it works: pressure increases with depth

The principle follows directly from hydrostatic pressure. Pressure in a fluid at rest grows linearly with depth, P(h) = P_0 + ρ g h, because each layer of fluid has to support the weight of everything above it. A submerged object therefore has fluid pushing on it harder from below than from above — the bottom face sits deeper, so it feels a larger pressure than the top face. Integrate that pressure difference over the object's entire surface and, remarkably, the sideways components all cancel by symmetry while the vertical components sum to exactly the weight of the displaced fluid. Buoyancy is not a separate force bolted onto the physics; it is what net hydrostatic pressure looks like once you add it all up.

Floating, sinking, and the density ratio

Compare the buoyant force to the object's own weight, W = ρ_object × V_object × g. If the object is fully submerged, V_displaced equals its own volume, so the ratio of forces is exactly the density ratio ρ_object / ρ_fluid. Three cases follow directly. If ρ_object < ρ_fluid, the fully submerged buoyant force already exceeds the weight, so the object rises and settles floating with only a fraction submerged — that fraction is precisely ρ_object / ρ_fluid, which is why an ice cube (ρ ≈ 0.92 g/cm³) floats in water with about 92% of its volume underwater and only 8% showing. If ρ_object = ρ_fluid, the two forces balance at any depth and the object is neutrally buoyant, drifting wherever it is placed. If ρ_object > ρ_fluid, buoyancy can never catch up and the object sinks to the bottom.

Why steel ships float

Steel is roughly eight times denser than water, yet steel ships float, because Archimedes' principle cares about the average density of the whole hull, not the density of the material it is made from. A hull shaped as a hollow shell displaces a volume of water far larger than the volume of steel used to build it; as long as the ship's total weight (steel plus cargo plus the air inside) divided by its total submerged volume stays below the water's density, it floats, with the hull sinking exactly deep enough that the displaced water's weight matches the ship's weight. Load more cargo and the ship simply sits lower in the water, displacing more, until balance is restored — up to the point where the hull is fully submerged and can sink no lower without water breaching the deck.

Changing the fluid changes the answer

Because the law depends on the fluid's density as much as the object's, the same object floats differently in different fluids. Swap water for vegetable oil (ρ ≈ 0.92 g/cm³) and objects that floated high in water now sit far lower, or sink outright if their own density exceeds the oil's. Swap in mercury (ρ ≈ 13.5 g/cm³) and a solid iron block, which sinks instantly in water, floats on mercury with most of its volume above the surface, because iron at ρ ≈ 7.9 g/cm³ is still less than half as dense as mercury. This simulation lets you swap the fluid and watch exactly that: the same object, the same principle, a different equilibrium depth.

Frequently asked questions

Try it live

Everything above runs in your browser — open Archimedes' Principle and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.