Buoyant Force Calculator (Archimedes)

Archimedes' principle

An object immersed in a fluid is pushed upward by a force equal to the weight of the fluid it displaces. This is the buoyant force:

F = ρ × g × V

ρ is the density of the fluid, g the acceleration of gravity and V the volume of the object that is in the fluid (the submerged volume). The force does not depend on what the object is made of, only on the submerged volume and the density of the fluid.

Will it float or sink?

An object floats if its average density is lower than that of the fluid, sinks if it is higher and stays suspended if the two are equal. A floating object settles until the buoyant force equals its weight. The fraction of its volume that is submerged equals the ratio of the densities:

submerged volume / total volume = density of the object / density of the fluid

Example

A 2 litre block of wood with a density of 600 kg/m³ floats in water with 600 / 1000 = 60 percent of its volume submerged. Taking the density of ice as 917 kg/m³ and of sea water as 1025 kg/m³, 917 / 1025 = 89.5 percent of an iceberg lies below the surface.

One litre of steel (7800 kg/m³) sinks in water. Its weight is 76.5 N and the buoyant force is 9.8 N, so its apparent weight in water is 66.7 N.

Finding density by weighing

Weigh an object in air and then fully immersed in water, and the difference between the two readings is the buoyant force. That gives the volume and the density of the object: density of the object = density of the liquid × W / (W − W'), where W is the reading in air and W' the reading in the liquid. A coin that reads 8.630 g in air and 7.800 g in water has a density of 8.630 / 0.830 = 10.4 g/cm³. This is the method in the story of Archimedes and the crown.

Limits

Fluid densities are approximate and vary with temperature and, for sea water, with salinity. The tool does not examine the stability of a floating object (whether it will capsize). Boat and pontoon design is outside its scope.