Buoyancy Calculator
This buoyancy calculator finds the upward force a fluid exerts on a submerged object using Archimedes’ principle, F = ρ · V · g. Enter the density of the fluid (kg/m³) and the submerged volume of the object (m³) and it returns the buoyant force in newtons plus the mass of fluid displaced in kilograms. Use it to check whether something will float or sink, to size flotation for boats and pontoons, or to solve physics homework. Water is preset at 1000 kg/m³, but you can model seawater, oil, or any other fluid in seconds.
How to calculate buoyant force
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1
Enter the fluid density
Type the density of the surrounding fluid in kilograms per cubic metre. Fresh water is about 1000 kg/m³ and seawater about 1025 kg/m³.
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2
Enter the submerged volume
Give the volume of the object that is actually underwater, in cubic metres. For a fully submerged object this equals its total volume.
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3
Read the buoyant force
The tool multiplies density × volume × 9.81 and shows the upward force in newtons, along with the mass of fluid displaced in kilograms.
The formula
Archimedes’ principle says the buoyant force equals the weight of the fluid displaced by a submerged object:
- F = ρ · V · g
where F is the buoyant force in newtons (N), ρ (rho) is the fluid density in kg/m³, V is the submerged volume in m³, and g is gravitational acceleration, taken as 9.81 m/s². The mass of fluid displaced is simply m = ρ · V, and its weight (ρ · V · g) is exactly the upward push the object feels.
Worked example
A sealed container with a submerged volume of 0.05 m³ sits in fresh water (ρ = 1000 kg/m³):
F = 1000 × 0.05 × 9.81 = 490.5 N
The mass of water displaced is 1000 × 0.05 = 50 kg. If the container itself weighs less than 50 kg, the upward 490.5 N exceeds its weight and it floats; if it weighs more, it sinks.
Buoyant force in common fluids (V = 0.05 m³)
| Fluid | Density (kg/m³) | Mass displaced (kg) | Buoyant force (N) |
|---|---|---|---|
| Air | 1.2 | 0.06 | 0.59 |
| Vegetable oil | 920 | 46.0 | 451.3 |
| Fresh water | 1000 | 50.0 | 490.5 |
| Seawater | 1025 | 51.25 | 502.8 |
| Glycerine | 1260 | 63.0 | 618.0 |
Denser fluids push harder, which is why you float more easily in the salty Dead Sea than in a freshwater lake.
Pitfalls to avoid
- Volume vs. submerged volume. For a partly floating object, use only the part below the surface, not the whole object.
- Mixed units. Keep density in kg/m³ and volume in m³. A litre is 0.001 m³, so a 50 L object has a volume of 0.05 m³.
- Float vs. sink. Buoyancy alone does not decide it — compare the buoyant force to the object’s weight (its own mass × g).
- Gravity choice. This tool uses g = 9.81 m/s²; on the Moon (≈1.62 m/s²) both weight and buoyant force shrink together.
Frequently Asked Questions
Buoyant force equals fluid density times submerged volume times gravity: F = ρ · V · g, with g = 9.81 m/s². Enter density in kg/m³ and volume in m³ and the result is in newtons.
Compare the buoyant force to the object’s weight (its mass × 9.81). If the buoyant force is greater, it floats; if the weight is greater, it sinks; if they are equal, it stays neutrally buoyant.
Use 1000 kg/m³ for fresh water and about 1025 kg/m³ for seawater. The calculator presets fresh water at 1000 kg/m³, which you can change to model any fluid.
Divide litres by 1000. For example, 50 litres = 0.05 m³ and 1 litre = 0.001 m³. Keep volume in cubic metres so it matches the kg/m³ density unit.
No. The calculation runs entirely in your browser. Your density and volume values never leave your device and nothing is logged or transmitted.
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