Buoyancy Calculator

Understanding Buoyancy and Archimedes' Principle

Buoyancy is the upward force exerted on an object immersed in a fluid. It was first explained by the Greek mathematician Archimedes around 250 BC, who discovered that the buoyant force equals the weight of the fluid displaced by the object: F_b = ρ_fluid × V_object × g. This principle applies to all fluids, including liquids and gases, and is the fundamental reason why ships float, submarines dive and surface, and helium balloons rise in air.

This calculator determines the buoyant force acting on an object given its mass, volume, and the fluid it is immersed in. It also computes the object's weight, net force, apparent weight when submerged, and the fraction of the object that would be submerged if floating. Choose from common fluids or enter a custom density for any fluid.

Float, Sink, or Neutral Buoyancy

Whether an object floats or sinks depends on the comparison between its density and the fluid's density. If the object's density is less than the fluid's, the buoyant force exceeds the weight and the object floats, with only a fraction of its volume submerged. If denser, the object sinks because its weight exceeds the buoyant force. If densities are exactly equal, the object is neutrally buoyant, hovering at whatever depth it is placed. Submarines achieve controlled buoyancy by filling or emptying ballast tanks to change their effective density.

Apparent Weight and Underwater Measurement

The apparent weight of a submerged object is its actual weight minus the buoyant force. This explains why objects feel lighter underwater. Jewelers use this principle to determine the density of gems and metals: by weighing an object in air and then in water, the difference reveals the buoyant force, from which the volume and density can be calculated. Hydrostatic weighing is also used in body composition analysis to estimate body fat percentage.

Real-World Applications

Ship design relies heavily on buoyancy calculations to ensure vessels float at the correct waterline with their intended cargo. Hydrometers use buoyancy to measure fluid density in brewing, winemaking, and battery testing. Life jackets and flotation devices work by increasing the wearer's volume without significantly increasing mass, lowering average density below that of water. In geology, isostasy describes how the Earth's crust floats on the denser mantle, with mountains having deep roots, much like an iceberg with most of its mass below the waterline.

Frequently Asked Questions

What is Archimedes' principle?

Archimedes' principle states that the buoyant force on a submerged object equals the weight of the displaced fluid: F_b = ρVg.

How do you know if an object floats or sinks?

Compare densities: if the object is less dense than the fluid, it floats; if denser, it sinks. Equivalently, it floats when buoyant force exceeds weight.

What is apparent weight?

Apparent weight = actual weight - buoyant force. It is the effective weight felt when an object is submerged, which is why things feel lighter in water.

What fraction of a floating object is submerged?

The fraction submerged equals ρ_object / ρ_fluid. Ice in water is about 92% submerged because ice density is about 917 kg/m³.

Does shape affect buoyancy?

Shape does not change the buoyancy formula, but it determines displaced volume. A hollow steel hull displaces more water than a solid steel ball of the same mass, allowing ships to float.