Archimedes' Principle
An object submerged (fully or partially) in a fluid experiences an upward buoyant force equal to the weight of fluid displaced.
Buoyant Force Formula
F_b = ρ_fluid × g × V_displaced
ρ = fluid density (kg/m³)
g = 9.81 m/s²
V = volume of fluid displaced (m³)
Object weight: W = ρ_object × g × V_object
Float condition: F_b ≥ W → ρ_object ≤ ρ_fluidWorked Examples
Steel ball (V=0.001 m³) in water:
F_b = 1000 × 9.81 × 0.001 = 9.81 N
W_steel = 7850 × 9.81 × 0.001 = 77.0 N
Net = 77-9.81 = 67.2 N downward → sinks
Wood block (ρ=600 kg/m³, V=0.01 m³) in water:
W = 600×9.81×0.01 = 58.9 N
Full submersion F_b = 1000×9.81×0.01 = 98.1 N
→ Floats (62.5% submerged at equilibrium)Common Fluid Densities (kg/m³)
- Fresh water: 1000
- Sea water: 1025
- Mercury: 13,600
- Air (sea level): 1.225
- Petrol/gasoline: 680-740
Calculate buoyancy: Free Buoyancy Calculator
Buoyancy Quick-Reference Table
| Object | Volume (m³) | Fluid | Buoyant Force (N) |
|---|---|---|---|
| 1 L water bottle | 0.001 | Water | 9.81 |
| 50 kg person (70 L ≈ body volume) | 0.070 | Water | 686 |
| Steel cube (0.1 m³) | 0.1 | Water | 981 |
| 1 m³ object | 1 | Seawater (1,025 kg/m³) | 10,055 |
| Helium balloon (1 L) | 0.001 | Air (1.225 kg/m³) | 0.012 |
How Buoyancy Works
Archimedes' Principle: the buoyant force on a submerged (or floating) object equals the weight of the fluid it displaces. F_b = ρ_fluid × V_submerged × g. An object floats if its average density is less than the fluid; it sinks if denser. A ship floats despite being steel because its hollow hull displaces a large volume of water relative to its mass, keeping average density below 1,025 kg/m³ (seawater).
Buoyancy is critical in naval architecture (hull design), submarine ballast systems, scuba diving (buoyancy compensator devices), hot air ballooning, oil/water separation (density differences), and geological processes (isostasy — continental crust "floats" on the mantle). The neutral buoyancy point — where buoyant force exactly equals weight — is the target for divers and submarine operators.
Common Mistakes
- Using object density instead of fluid density: Buoyant force depends on the fluid's density, not the object's. Steel has ρ ≈ 7,850 kg/m³; water is 1,000 kg/m³ — the buoyant force uses 1,000.
- Forgetting partially submerged objects: A floating object only displaces fluid equal to its submerged volume. A 10 kg, 12-litre foam block floating in water displaces only 10 litres (mass 10 kg), not its full 12 litres.
- Ignoring fluid temperature effects: Water density decreases from 1,000 kg/m³ at 4°C to 958 kg/m³ at 100°C. This reduces buoyant force in hot water by ~4%.
Frequently Asked Questions
A ship's hull encloses a large air volume, making the overall average density of the vessel (steel + air + cargo) less than seawater (~1,025 kg/m³). Plimsoll lines on ships mark how deeply the hull sinks with various cargo loads in fresh water vs. seawater — denser seawater provides more buoyancy for the same displacement.
Submarines use ballast tanks that can be flooded with seawater or blown clear with compressed air. Filling tanks increases the submarine's average density above seawater (it sinks); expelling water decreases density (it rises). Fine depth control uses dive planes (horizontal fins) and slight positive or negative buoyancy maintained by adjusting ballast water volume precisely.
The Dead Sea has salinity around 34% (vs. 3.5% for typical ocean water), giving it a density of ~1,240 kg/m³. Since the human body averages about 985 kg/m³ in density, we normally just barely float in seawater. In the Dead Sea, the much higher fluid density means a large fraction of your body sits above the waterline — making it almost impossible to sink.