Every object in a fluid feels an upward push. A rubber duck floats, a steel ship floats, a brick sinks but feels lighter in the bath, and a hot-air balloon rises: all are explained by the same principle, attributed to Archimedes more than two thousand years ago. This calculator finds the buoyant force from the fluid density and the submerged volume, or works backward to either one. Add the object’s mass and it tells you whether the object sinks or floats, its apparent weight underwater and how deeply a floating object sits.
How to use the buoyancy calculator
- Under Solve for, choose buoyant force, fluid density or submerged volume.
- Pick a Fluid: fresh water at 20 °C or 4 °C, seawater, Dead Sea brine, air, gasoline, ethanol, vegetable oil, glycerin or mercury, or enter a custom density.
- Choose the Gravity: Earth’s standard value or another world from the list.
- Enter the Submerged volume: the whole object if it is fully under, or just the part below the surface. Units include L, mL, m³, cm³, ft³, in³ and US gallons.
- Optionally enter the Object mass to see its weight, whether it sinks or floats, its apparent weight and, for floaters, the fraction submerged and the extra load needed to sink it.
Buoyant force formula
ρ is the fluid’s density in kg/m³, g the gravitational acceleration and Vsub the submerged volume in m³. The force comes from pressure increasing with depth: the bottom of an object is pushed up harder than its top is pushed down. For a floating object, the weight equals the buoyant force, so the fraction under the surface is ρobject ÷ ρfluid.
Worked example
A stone in a bucket
A 5 kg stone with a volume of 2 L (0.002 m³) is fully submerged in fresh water at 20 °C (998.2 kg/m³).
Fb = 998.2 × 9.80665 × 0.002 = 19.58 N
Its weight is 5 × 9.80665 = 49.03 N, so it sinks. Its density is 2,500 kg/m³, and its apparent weight is 49.03 − 19.58 = 29.46 N: a scale would read about 3.0 kg.
Floating in the sea. An 80 kg swimmer with a body volume of 80 L displaces 80 L of seawater when fully under. Fb = 1,025 × 9.80665 × 0.08 = 804.1 N, more than the 784.5 N weight, so the swimmer floats with 97.6% of the body submerged. In fresh water the same body gets only 783.1 N of lift and slowly sinks.
Densities of common fluids
| Fluid | Density (kg/m³) |
|---|---|
| Air (20 °C, sea level) | 1.204 |
| Gasoline | about 745 |
| Ethanol | 789 |
| Vegetable oil | about 920 |
| Fresh water (20 °C) | 998.2 |
| Seawater | about 1,025 |
| Dead Sea brine | about 1,240 |
| Glycerin | 1,261 |
| Mercury | 13,546 |
Ships, submarines and balloons
A steel ship floats because its hull encloses so much air that its average density is far below that of water. Load it and it settles deeper until it displaces water equal to its new weight; the Plimsoll line painted on cargo ships marks the safe limit for different water densities. Submarines take on or pump out ballast water to switch between sinking, hovering at neutral buoyancy and rising. Hot-air balloons heat the air inside so that it becomes less dense than the surrounding air.
To find an object’s density from its mass and volume, use the density calculator; to compare weights on other worlds, the weight calculator; and for the pressure that produces buoyancy, the pressure calculator.
Frequently asked questions
What is Archimedes' principle?
An object in a fluid is pushed upward by a force equal to the weight of the fluid it displaces. A 2-liter stone fully under fresh water pushes aside 2 L of water weighing about 19.6 N, so the water pushes back up with 19.6 N.
How do I know if something will float?
Compare densities. If the object's average density is less than the fluid's, it floats; if greater, it sinks. Enter the object's mass and its full volume and the calculator reports which happens and, for a floater, what fraction rides below the surface.
Why do people float more easily in the sea?
Seawater is denser than fresh water, about 1,025 kg/m³ versus 998 kg/m³, so the same body displaces heavier fluid. An 80 kg person with a volume of 80 liters just sinks in a pool but floats in the ocean with about 2.4% of the body above the surface.
What is apparent weight?
The weight minus the buoyant force: what a scale reads when the object hangs in the fluid. A 5 kg stone of 2 L volume in fresh water reads about 3.0 kg, which is why heavy rocks feel lighter underwater.
Does buoyancy work in air?
Yes. Air is about 1.2 kg/m³, so every cubic meter displaced gives about 11.8 N of lift. A helium balloon rises because the helium plus the balloon weighs less than the air it pushes aside.