How Buoyant Force Works
When an object is submerged (fully or partially) in a fluid, the fluid exerts an upward force on the object. This upward force is called the buoyant force or upthrust. It arises because fluid pressure increases with depth: the pressure on the bottom face of a submerged object is greater than the pressure on the top face, producing a net upward push.
Archimedes' principle states that the buoyant force on an object equals the weight of the fluid displaced by that object. This gives the formula:
Fb = ρfluid × Vdisplaced × g
where ρfluid is the density of the fluid in kg/m³, Vdisplaced is the volume of fluid displaced in m³, and g is the gravitational acceleration in m/s². The result, Fb, is in newtons (N).
Floating, Sinking, and Neutral Buoyancy
The relationship between an object's weight and the maximum available buoyant force determines what happens:
- Floats: Object weight < maximum buoyant force (the object only needs to displace part of its volume to achieve equilibrium).
- Sinks: Object weight > maximum buoyant force at full submersion (the object is denser than the fluid).
- Neutrally buoyant: Object weight = buoyant force at full submersion (the object neither rises nor falls and can be suspended at any depth).
A steel ship floats not because steel is less dense than water, but because the ship's hull traps air. The average density of the hull-plus-air system is less than water, so it displaces enough water to support its weight before fully submerging.
Common Fluid Densities
| Fluid | Density (kg/m³) | Notes |
|---|
| Fresh water (20°C) | 998 | Varies slightly with temperature; often rounded to 1,000 |
| Sea water | 1,025 | Varies with salinity (1,020 to 1,030 typical) |
| Air (sea level, 15°C) | 1.225 | Buoyancy in air is small but relevant for balloons |
| Ethanol | 789 | Objects float more easily in less dense fluids |
| Diesel fuel | 870 | Typical automotive diesel at 15°C |
| Mercury | 13,534 | Very dense; even dense metals float in mercury |
| Honey | ~1,400 | Varies with water content and type |
| Whole milk | ~1,030 | Similar to sea water |
Worked Example
A wooden crate with a submerged volume of 0.5 m³ is placed in fresh water (ρ = 1,000 kg/m³) on Earth (g = 9.81 m/s²).
- Displaced fluid mass: 1,000 × 0.5 = 500 kg
- Buoyant force: 500 × 9.81 = 4,905 N (4.905 kN, 500 kgf)
If the crate weighs 3,000 N, the net upward force is 4,905 − 3,000 = 1,905 N, so it floats. If it weighed 6,000 N, the net force would be downward (6,000 − 4,905 = 1,095 N downward) and the crate sinks.
Applications of Archimedes' Principle
- Ship and vessel design: Hull shape and internal air volume are engineered so the vessel displaces enough water to carry its full load.
- Submarines: Use ballast tanks to adjust average density, enabling them to dive, ascend, or hover neutrally buoyant.
- Balloons and airships: Lighter-than-air gases (helium, hot air) give the balloon a lower average density than surrounding air, generating lift.
- Hydrometry: A hydrometer floats at a depth that reveals the fluid's density directly, using buoyancy principles.
- Density measurement: Weighing an object in air and in water allows calculation of its density via the buoyant force difference.
- Diving and submersibles: Divers use weight belts and buoyancy compensator devices (BCDs) to achieve neutral buoyancy underwater.
Related Calculators
Method: Archimedes' principle: buoyant force equals the weight of fluid displaced (Fb = ρVg). SI units throughout. Standard gravity 9.81 m/s² per ISO 80000-3. Kilogram-force conversion: 1 kgf = 9.81 N. Pound-force conversion: 1 lbf = 4.44822 N.
This calculator uses standard Archimedes' principle for incompressible fluids at rest. It does not account for dynamic (moving fluid) effects, surface tension, compressibility, or variable gravity. For engineering design work, consult a qualified engineer.
