Buoyancy Calculator
Buoyant force from Archimedes’ principle, with apparent weight and a float-or-sink check.
Object density 750 kg/m³ against fluid 1000 kg/m³
Archimedes’ principle says the upward force on a submerged object equals the weight of the fluid it displaces: F_b = ρVg. A 2-litre object fully under fresh water displaces 2 kg of water and feels an upward push of about 19.6 N, whatever the object is made of.
Why displaced fluid is the whole answer
Pressure in a fluid grows with depth, so the bottom of a submerged object is pushed up harder than its top is pushed down. The net upward force that leaves is exactly the weight of the fluid that would have occupied that space — which is Archimedes’ principle, and why the object’s own material never enters the formula. A steel cube and a wooden cube of the same size feel the same buoyant force; they behave differently because their weights differ, not their buoyancy.
That is also why the apparent weight of a submerged object is its true weight minus the buoyant force. A 15 N object displacing 5 N of water reads 10 N on a scale underwater, and the missing 5 N is the fluid holding it up.
Floating is a density comparison
An object floats when it is less dense on average than the fluid, and that average is what matters — a steel ship floats because most of its volume is air. At equilibrium a floating object displaces exactly its own weight in fluid, so it sits with the fraction of itself submerged equal to the ratio of the two densities. Ice at about 920 kg/m³ in seawater at 1025 kg/m³ floats with roughly 90% of its volume below the surface.
ρ the fluid’s density in kg/m³, V the displaced volume in m³, g = 9.807 m/s²
- 1 Find the displaced volume. A fully submerged object displaces its own volume: 2 litres is 0.002 m³.
- 2 Take the density of the fluid, not the object. Fresh water is 1000 kg/m³; the object’s material plays no part in this step.
- 3 Multiply by g. 1000 × 0.002 × 9.807 = 19.61 N upward.
- 4 Compare with the object’s weight. A 1.5 kg object weighs 14.71 N, which is less than the buoyant force, so it floats.
- 5 Subtract for the apparent weight if it sinks. A denser object reads its true weight minus the buoyant force on an underwater scale.
Densities worth knowing
In kg/m³, at roughly room temperature. An object floats in any fluid denser than itself.
| Substance | Density | Floats in water? |
|---|---|---|
| Air (sea level) | 1.225 | — |
| Ethanol | 789 | Mixes rather than floats |
| Ice | ≈ 917 | Yes — about 92% submerged in fresh water |
| Vegetable oil | ≈ 920 | Yes, it sits on top |
| Fresh water | 1000 | — |
| Seawater | ≈ 1025 | — |
| Aluminium | 2700 | No |
| Mercury | 13534 | — |
The details that change the answer
Only the submerged volume counts. A partly floating object displaces just the part below the surface, so using its whole volume overstates the buoyant force — the tool asks for displaced volume rather than object volume for exactly this reason. Units matter too: densities are per cubic metre, and a litre is 0.001 m³, so a volume left in litres is out by a factor of a thousand.
Buoyancy also acts in gases, which is how a helium balloon rises — air is the fluid, and the balloon displaces its own volume of it. The force is small because air is about 800 times less dense than water, but it is the same physics. One further subtlety: the fluid must be able to get underneath. An object sealed flat against the bottom of a tank with no fluid below it feels no upward pressure at all, and does not float even if it would otherwise.