Buoyancy calculator

How do you calculate buoyant force?

By Archimedes’ principle, the buoyant force equals the weight of the fluid the object displaces: F = ρ × V × g, where ρ is the fluid’s density, V the volume under the surface and g gravity (OpenStax University Physics).

Example

A fully submerged 1-cubic-foot object in fresh water displaces 0.02832 m³: 1,000 × 0.02832 × 9.807 = 277.7 N, about 62.4 pounds-force.

Will my object float?

An object floats if it weighs less than the fluid it would displace when fully under — that is, if it is less dense than the fluid. A floating object settles until the fluid it displaces weighs as much as it does.

Why is it easier to float in the sea?

Seawater is denser than fresh water — 1,025 to 1,030 kg/m³ in OpenStax tables against 1,000 kg/m³ — so the same volume under water pushes up about 2.5% to 3% harder.

Which volume should I enter?

Only the part that is under the surface. For an object held fully under water, that is its whole volume.

How much weight can a raft or float carry?

The maximum load is the buoyant force with the float fully under water, minus the float's own weight. A raft of 0.5 m³ of displacement in fresh water has a maximum buoyant force of 4,903 N, which supports 500 kg. If the raft itself has a mass of 30 kg, the most it can carry before it sinks is about 470 kg, and in practice you would load it much less.

Does the shape of an object change the buoyant force?

Only through the volume of fluid it displaces. A block of steel sinks, but the same steel shaped into a hollow hull displaces much more water and can float. The force depends on the displaced volume, not on the shape or the material.

What units should the density be in?

Use kilograms per cubic meter with the volume in cubic meters to get newtons. Water is 1,000 kg/m³, which is the same as 1 g/cm³ or about 62.4 lb/ft³. A mix of units, such as g/cm³ with m³, gives a result that is wrong by a factor of 1,000.

How the calculation works

The buoyant force is the weight of the fluid pushed aside, F = ρ V g. The density ρ is that of the fluid, V is the volume of the object below the surface, and g is 9.80665 m/s². The result is in newtons; dividing by 4.4482 gives pounds-force. To decide whether an object floats, compare its density with that of the fluid. If it is less dense, it floats and sinks only until the displaced fluid weighs as much as the object. If it is denser, the object sinks, and the buoyant force at full submersion is still the same formula but is smaller than its weight.

Worked example

A block has a mass of 2 kg and a volume of 0.004 m³, so its density is 500 kg/m³. Fully under fresh water it would feel an upward force of 1000 × 0.004 × 9.80665 = 39.2 N, while its weight is 2 × 9.80665 = 19.6 N. Since the buoyant force is larger, the block floats. It settles until the displaced water weighs as much as the block: the displaced volume is 2 ÷ 1000 = 0.002 m³, so 50% of it is under water. In seawater at 1025 kg/m³ the same block displaces only 0.00195 m³, so it floats slightly higher.

Common mistakes

• Using the whole volume for a floating object. Only the part under the surface displaces fluid. A floating block displaces only its own weight in fluid.
• Confusing mass and force. Kilograms are mass and newtons are force. The buoyant force is ρ V g, not ρ V.
• Mixing pounds and pounds-force. In US units, density is in pounds per cubic foot, and the answer is in pounds-force.

Sources and related calculators

Archimedes' principle and buoyancy: OpenStax University Physics Volume 1, chapter 14 (Fluid Mechanics); standard gravity 9.80665 m/s² is the exact conventional value (NIST SP 330 and SP 811). Related: density calculator, pressure calculator and Bernoulli equation calculator.