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Buoyancy Calculator
Work out the upward buoyant force on any object with Archimedes’ principle, F = ρ × V × g. Choose a fluid and gravity, enter the volume, and add the object’s mass to see whether it floats, how much of it sits below the surface, or how heavy it feels underwater.
Last updated:
Fluid
kg/m³
Object
Enter your values to see the result.
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How to use the Buoyancy Calculator
- Pick the fluid or choose Custom and type its density.
- Choose the gravity (Earth by default).
- Enter the displaced volume and its unit. For a fully submerged object this is the object's volume.
- Tick the float/sink check and enter the object's mass to compare densities.
- Read the buoyant force, the verdict and the working, then compare fluids in the table.
Archimedes’ principle
A body immersed in a fluid is pushed up by a force equal to the weight of the fluid it displaces:
Fb = ρfluid × Vdisplaced × g
The force comes from the pressure difference between the bottom and top of the object: pressure grows with depth (P = ρgh), so the upward push on the lower faces is larger than the downward push on the upper faces. For a floating object, the displaced volume is only the part below the surface, and at equilibrium the buoyant force exactly equals the object's weight.
Typical fluid densities
| Fluid | Density (kg/m³) | Force per liter on Earth |
|---|---|---|
| Air (sea level, 15 °C) | 1.225 | 0.012 N |
| Gasoline | ~740 | 7.26 N |
| Ethanol | 789 | 7.74 N |
| Olive oil | ~911 | 8.93 N |
| Fresh water (4 °C) | 1000 | 9.81 N |
| Seawater | ~1025 | 10.05 N |
| Glycerin | 1260 | 12.36 N |
| Mercury | 13,534 | 132.7 N |
Common solids: float or sink in water?
| Material | Approx. density (kg/m³) | In fresh water |
|---|---|---|
| Cork | ~240 | Floats, ~24% submerged |
| Pine wood | ~500 | Floats, ~50% submerged |
| Oak wood | ~700 | Floats, ~70% submerged |
| Ice | 917 | Floats, ~92% submerged |
| Aluminium | 2700 | Sinks |
| Steel | ~7850 | Sinks (floats on mercury) |
| Gold | 19,300 | Sinks (even in mercury) |
Ships made of steel float because their hull encloses a large volume of air, so the average density of the whole ship is below that of water.
Frequently asked questions
What is the buoyancy formula?
Archimedes’ principle: the buoyant force equals the weight of the displaced fluid, F_b = ρ_fluid × V_displaced × g. In fresh water on Earth, 1 liter displaced gives about 9.81 N (1 kgf) of lift.
How do I know if an object will float?
Compare densities. If the object's average density (mass ÷ volume) is less than the fluid's, it floats; if greater, it sinks; if equal, it is neutrally buoyant and hovers.
How much of a floating object is underwater?
The submerged fraction equals ρ_object ÷ ρ_fluid. Ice (about 917 kg/m³) in seawater (1025 kg/m³) floats with roughly 89% below the surface.
Why is it easier to float in the sea?
Seawater is about 2.5% denser than fresh water, and very salty water like the Dead Sea is over 20% denser, so the same displaced volume produces more upward force.
Does gravity change whether something floats?
No. Gravity scales both the weight and the buoyant force equally, so float or sink depends only on density. The size of the forces does change: on the Moon they are about one sixth of Earth's.
What is apparent weight?
It is the weight minus the buoyant force: what a scale reads when the object hangs fully submerged. A 7.85 kg steel block (1 L) weighs about 6.85 kgf in fresh water.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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