Buoyancy force calculator (Archimedes' principle)

Archimedes' principle (c. 250 BC): the buoyancy force acting on a body immersed in fluid equals the weight of the fluid displaced by that body. F = rho_fluid * V_submerged * g.

The mass of displaced fluid is m = rho * V. Its weight (gravitational force) is F = m * g = rho * V * g. The fluid exerts this force upward on the submerged body as a reaction to displacement.

An object floats when its average density is less than the fluid density (F_buoy > F_weight). It sinks when denser. It is neutrally buoyant when equal. For a human (rho ≈ 985 kg/m^3) the margin is narrow near fresh water.

Solid iron has density ~7800 kg/m^3 > water. A ship's total volume (including enclosed air) gives it an average density below 1000 kg/m^3. The hull displaces enough water to provide the required buoyancy.

V in the formula refers to the submerged volume only, not total volume. For a floating object V_submerged = mass / rho_fluid – the amount of water displaced to achieve equilibrium.

Yes – denser fluids produce greater buoyancy for the same volume. In the Dead Sea (rho ≈ 1240 kg/m^3) people float effortlessly. In mercury (rho = 13 600 kg/m^3) even a lead ball would float.

Ship design, submarine ballast tanks, hot-air balloons and blimps (air buoyancy), diving buoyancy compensators, hydrometers for measuring liquid density.

Yes – buoyancy is a general fluid principle. A helium balloon rises because rho_He < rho_air. The formula F = rho_gas * V * g applies equally to gases.

Archimedes was asked to verify whether King Hiero II's crown was pure gold without melting it. By immersing it in water he measured its volume (displaced water) and therefore its density. Gold (19 300 kg/m^3) and silver (10 500 kg/m^3) give different volumes for the same mass.

g varies slightly with latitude and altitude. At the equator g ≈ 9.78 m/s^2, at the poles ≈ 9.83 m/s^2. The difference is less than 0.5%, so g = 9.81 is adequate for engineering calculations.