Archimedes’ principle
Any object immersed in a fluid is pushed upward by a force equal to the weight of the fluid it displaces. That is Archimedes’ principle, and it explains why ships float, why balloons rise and why you feel lighter in a pool. The calculator gives this buoyant force, the apparent weight of the object under the surface, and whether it floats or sinks.
The formulas
- Buoyant force = fluid density × volume × g
- Apparent weight = mass of the object − mass of the fluid displaced
- Share underwater for a floating object = object density ÷ fluid density
If the apparent weight is negative, the fluid pushes up harder than gravity pulls down: the object rises and floats with only part of its volume submerged.
Worked example
A sealed box of 1 cubic foot weighing 50 lb is placed in fresh water.
- Water displaced when fully submerged: 1 ft³ × 62.4 lb/ft³ = 62.4 lb.
- Buoyant force: 62.4 lbf, or 278 N.
- Apparent weight: 50 − 62.4 = −12.4 lb: the box floats.
- It floats with 50 ÷ 62.4 = 80% of its volume underwater, since its density is 801 kg/m³ against 1,000 kg/m³ for water.
Fluid densities
| Fluid | Density |
|---|---|
| Air at sea level | 1.204 kg/m³ |
| Vegetable oil | about 920 kg/m³ |
| Fresh water | 1,000 kg/m³ (62.4 lb/ft³) |
| Seawater | about 1,025 kg/m³ (64 lb/ft³) |
| Dead Sea water | about 1,240 kg/m³ |
| Mercury | 13,534 kg/m³ |
Floating and sinking
Compare densities: an object less dense than the fluid floats, a denser one sinks. Steel is eight times denser than water, yet steel ships float because their hull encloses a large volume of air, so the average density of the ship is lower than water’s. A submarine controls its depth by filling or emptying ballast tanks, and a diver uses a buoyancy compensator and weights to reach neutral buoyancy, where the apparent weight is zero.
Fresh water versus seawater
A boat sits slightly higher in the sea than in a river, because seawater is about 2.5% denser. Cargo ships carry load lines that show how deep they may sit in fresh, tropical and winter seawater. For the same reason, an iceberg, at 917 kg/m³, floats with about 89% of its volume hidden below the surface.
Buoyancy in air
Air is about 800 times lighter than water, but buoyancy still applies. A helium balloon rises because the air it displaces weighs more than the balloon and its gas. Precision scales correct for air buoyancy when weighing low-density materials.
Limits
The calculator assumes the object is rigid and that the fluid has a uniform density. It does not account for surface tension, which lets insects and small needles rest on water, or for objects that absorb fluid, like wood soaking up water over time.