Buoyancy Calculator

Buoyancy is the upward force exerted by a fluid on any object that is fully or partially submerged in it. This force results from the pressure difference between the bottom and top of the submerged object: fluid pressure increases with depth, so the upward pressure on the object's bottom face exceeds the downward pressure on the top face. The net upward pressure difference produces the buoyant force. Buoyancy explains why objects feel lighter in water and why some objects float while others sink.

Archimedes' Principle states that the buoyant force on an object equals the weight of fluid displaced by that object: Fb = rho_fluid * V_submerged * g. Here rho_fluid is the fluid density (kg/m³), V_submerged is the submerged volume (m³), and g is gravitational acceleration (9.80665 m/s²). The principle is attributed to the ancient Greek mathematician Archimedes of Syracuse (circa 287 to 212 BCE), who reportedly discovered it while stepping into a bath.

A ship floats because its overall average density (hull plus enclosed air spaces) is less than that of water. Although steel has a density of about 7,800 kg/m³ (much denser than seawater at about 1,025 kg/m³), the ship's hollow hull encloses a large volume of air. The total mass of the ship divided by the total volume it occupies gives an average density below that of water. The ship sinks only deep enough to displace water equal in weight to the ship's total weight, then it floats. This is Archimedes' Principle in action.

Approximate densities at standard conditions: fresh water 1,000 kg/m³, sea water 1,025 kg/m³, air 1.225 kg/m³ (at 15°C, 101,325 Pa), mercury 13,534 kg/m³, ethanol 789 kg/m³, diesel 820 to 845 kg/m³, honey 1,400 to 1,450 kg/m³. These values vary with temperature and pressure. This calculator includes preset buttons for fresh water, sea water, air, and mercury; you can also enter any value manually.

Apparent weight is the effective weight of an object as measured when it is submerged in a fluid. It equals the true weight (m * g) minus the buoyant force (rho_fluid * V * g). If apparent weight is positive, the object sinks because gravity exceeds buoyancy. If apparent weight is zero or negative, the object floats because buoyancy equals or exceeds gravity. An object with a density exactly equal to the fluid has zero apparent weight and will be neutrally buoyant, hovering at any depth.