Buoyant Force Calculator
Inputs
| Fluid density | 1,000 kg/m³ |
|---|---|
| Displaced volume | 1 L |
| Gravity | 9.8067 m/s² |
Buoyant Force Calculator
Calculate the buoyant (upthrust) force on a submerged object with Archimedes' principle — the buoyant force equals ρ·V·g. Enter the fluid density, the displaced volume and gravity to get the upward force and the mass of fluid displaced.
Inputs
Constants
Results
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Details
Buoyant Force
When an object is placed in a fluid, the fluid pushes up on it with a force called buoyancy, or upthrust. Archimedes' principle gives its size: the buoyant force equals the weight of the fluid the object displaces, , where is the fluid's density, is the displaced volume and is gravity. This single idea explains why ships float, why you feel lighter in a swimming pool, and how a hot-air balloon rises. Archimedes is said to have discovered it in his bath, over two thousand years ago.
This calculator returns the upward buoyant force and the mass of fluid displaced, from the fluid density, the displaced volume and gravity.
Why displaced fluid is the key
A submerged object pushes aside a volume of fluid equal to its own submerged volume. That displaced fluid would have had weight, and the surrounding fluid pushes back up with exactly that weight of force. Nothing about the object's own material enters the buoyancy formula — only how much fluid it shoves out of the way. A beach ball and a cannonball of the same size feel the same buoyant force underwater; they behave so differently only because their weights differ so much.
Formula
| Quantity | Symbol | Meaning |
|---|---|---|
| Buoyant force | Upward force, | |
| Fluid density | Density of the surrounding fluid | |
| Displaced volume | Volume of fluid pushed aside (submerged volume) | |
| Gravity | Gravitational acceleration |
The product is the mass of the displaced fluid, so the buoyant force is just that mass times — the weight of the displaced fluid, exactly as Archimedes stated.
Worked example
A sealed container with a volume of 1 litre (0.001 m³) is held fully under fresh water (density 1000 kg/m³). The buoyant force is:
Fb=ρVg=1000×0.001×9.80665=9.81 NThe container displaces kg of water, whose weight is 9.81 N — the same as the buoyant force. If the container plus its contents weigh less than 9.81 N it will bob to the surface; if more, it will sink.
Float or sink
Whether an object floats comes down to a comparison of densities. If the object's average density is less than the fluid's, the buoyant force when fully submerged is greater than its weight, so it rises until it floats partly out of the water, displacing just enough fluid to match its own weight. If its average density is greater, it sinks. A steel ship floats because its hull shape encloses a large volume of air, dropping the average density of the whole vessel below that of water — even though steel itself is nearly eight times denser than water.
Limitations
This calculator assumes a single uniform fluid at rest and a known displaced volume. For a partly floating object you must enter only the submerged volume, not the whole object. The model ignores surface tension, which matters for very small objects, and assumes the fluid density is constant — a fair assumption for liquids but only an approximation deep in the atmosphere or ocean, where density rises with depth.
Frequently Asked Questions (FAQ)
What is the formula for buoyant force?
The buoyant force is the weight of the fluid displaced: ρ·V·g, where ρ is the density of the fluid, V is the volume of fluid displaced (the submerged volume of the object) and g is gravitational acceleration. The product ρ·V is the mass of the displaced fluid, so the buoyant force is simply the weight of the fluid the object pushes out of the way.
What is Archimedes' principle?
Archimedes' principle states that the upward buoyant force on a body immersed in a fluid equals the weight of the fluid the body displaces. It applies whether the object is fully or partly submerged. A floating object displaces exactly its own weight of fluid; a fully submerged object displaces its own volume, and whether it then rises or sinks depends on how that displaced weight compares with its own.
Will an object float or sink?
Compare the object's average density with the fluid's. If the object is less dense than the fluid, the buoyant force at full submersion exceeds its weight and it floats, settling so that it displaces just its own weight. If it is denser, its weight wins and it sinks. This is why a steel ship floats — its hull encloses enough air that the average density of the whole vessel is below that of water.
What density should I use for common fluids?
Fresh water is 1000 kg/m³ (1 g/cm³) by definition at 4 °C. Seawater is denser at about 1025 kg/m³, which is why you float a little higher in the sea. Other common values: air ≈ 1.2 kg/m³, vegetable oil ≈ 920, ethanol ≈ 789, mercury ≈ 13 600, and glycerine ≈ 1260. Use the density of whatever fluid surrounds the object.