Archimedes' principle: the upward buoyant force on a submerged or floating body equals the weight of the fluid it displaces — F_b = ρVg. This free calculator solves for the buoyant force, the fluid density or the displaced volume, in any unit, with presets for water, seawater, oil and air, and shows every step of the working.
Buoyancy is the upward push a fluid exerts on anything placed in it. Archimedes' principle pins it down exactly: the buoyant force equals the weight of the fluid the object displaces. Physically it arises because fluid pressure grows with depth, so the push on the bottom of a submerged object exceeds the push on its top, leaving a net upward force. Multiply three things to get it: the fluid density ρ, the displaced volume V and the local gravity g — F_b = ρ·V·g. The answer is a force in newtons.
There are three steps. First, decide what you want — the buoyant force, or instead the fluid density or the displaced volume — and pick it in the calculator's Solve for menu. Second, enter the values you know: the density in kg/m³ (or choose fresh water, seawater, oil or air from the preset list), the volume in cubic metres, litres or cubic centimetres, and the gravity for Earth, the Moon, Mars or Jupiter. Third, read the answer with the worked steps, which show the formula, your numbers substituted in, and the result in newtons and kilonewtons.
The key comparison is between the buoyant force and the object's own weight. If the object's average density is less than the fluid's, the buoyant force on a fully submerged volume exceeds its weight, so it rises and floats with part of itself above the surface; if its density is greater, it sinks. A floating object settles at the depth where it displaces exactly its own weight of fluid — which is why a hollow steel ship floats while a solid steel bar of the same metal drops straight to the bottom.
Buoyancy rarely acts alone. A body that actually moves through the fluid also meets a drag force resisting its motion, and at terminal velocity drag, weight and buoyancy all balance. To work out the displaced mass behind the force, or to convert between mass and volume, see the density calculator, or look up a term in the physics glossary.
A solid object of volume V = 0.01 m³ is fully submerged in fresh water (ρ = 1000 kg/m³) on Earth (g = 9.81 m/s²). The buoyant force is F_b = ρ·V·g = 1000 × 0.01 × 9.81 = 98.1 N upward. Move the same object into seawater (ρ = 1025 kg/m³) and the force rises to about 100.5 N; take it to the Moon (g = 1.62 m/s²) and it falls to roughly 16.2 N — a direct illustration of how buoyancy scales with both fluid density and gravity.
Buoyancy governs ship and submarine design, hot-air and helium balloons, hydrometers, life-jacket sizing, dredging and floating-platform engineering, and the way fish and divers control their depth. Anywhere an object has to float, sink or hover in a fluid, Archimedes' principle is the starting point.
Archimedes' principle states that the upward buoyant force on a body immersed in a fluid equals the weight of the fluid the body displaces. In formula form that is F_b = ρVg, where ρ is the fluid density, V is the displaced volume and g is gravity. The force always points upward because it is the net result of fluid pressure pushing harder on the deeper, lower surface of the object than on its upper surface.
Compare the object’s average density with the fluid’s. If the object is less dense than the fluid, the buoyant force from displacing a volume equal to the object exceeds the object’s weight, so it floats and rises until only part of it is submerged. If it is denser, its weight wins and it sinks. A floating object displaces exactly its own weight of fluid, which is why a steel ship — mostly hollow, so low in average density — stays afloat while a solid steel block does not.
Fluid density ρ is in kg/m³, displaced volume V in cubic metres (or litres / cubic centimetres), and gravity g in m/s². The buoyant force is returned in newtons, with a kilonewton value alongside. Presets cover fresh water (1000 kg/m³), seawater (1025), oil (900) and air (1.225), plus Earth, Moon, Mars and Jupiter gravity.
For a fully submerged, incompressible object in a liquid of constant density, no — the buoyant force is the same at 1 m or 100 m, because it depends only on the displaced volume, the fluid density and gravity, not on the absolute pressure. Depth matters only when the fluid’s density changes with depth (as in the atmosphere) or when the object itself compresses, as a submarine’s hull or a diver’s wetsuit can.
Yes. Seawater is about 2.5% denser than fresh water (≈1025 vs 1000 kg/m³), so it pushes up about 2.5% harder for the same displaced volume. That is why you float more easily in the sea than in a freshwater lake, and why ships sit slightly higher in salt water — the same hull displaces less volume to support its weight.