Buoyancy Force Calculator
Calculate the buoyancy (upward) force on any object submerged in a fluid.
Uses Archimedes Principle.
Supports water, seawater, oil, and custom fluids.
Buoyancy is the upward force exerted by a fluid on any object submerged in it. This force was first described by the ancient Greek mathematician Archimedes around 250 BC.
Archimedes’ Principle: An object submerged in a fluid experiences an upward force equal to the weight of the fluid it displaces.
The formula:
Buoyancy Force (F_b) = ρ_fluid × V_displaced × g
Where:
- ρ_fluid = density of the fluid (kg/m³)
- V_displaced = volume of fluid displaced by the object (m³)
- g = gravitational acceleration = 9.81 m/s² (32.2 ft/s²)
Common fluid densities:
| Fluid | Density (kg/m³) | Density (lb/ft³) |
|---|---|---|
| Fresh water (20°C / 68°F) | 998 | 62.3 |
| Seawater (average) | 1,025 | 64.0 |
| Seawater (Dead Sea) | ~1,240 | ~77.5 |
| Mercury | 13,546 | 846 |
| Olive oil | 910 | 56.8 |
| Engine oil | 870 | 54.3 |
| Air (sea level, 20°C) | 1.204 | 0.075 |
| Honey | 1,400 | 87.4 |
Will the object float or sink?
An object floats if its average density is less than the fluid density.
- If F_b > Weight → object floats
- If F_b = Weight → object is neutrally buoyant (hovers in place)
- If F_b < Weight → object sinks
Real-world applications:
- Ship hull design — engineers calculate displacement to ensure the vessel floats
- Submarine ballast tanks — adding/removing water changes buoyancy to dive or surface
- Hot air balloons — heated air is less dense than surrounding air, creating lift
- Hydrometry — measuring the sugar content of liquids (e.g., wine, beer) using density
- Life jacket design — enough buoyancy to keep an unconscious person face-up in water
Example: A solid cube of wood: 0.1 m × 0.1 m × 0.1 m = 0.001 m³ volume, fully submerged in fresh water. F_b = 998 × 0.001 × 9.81 = 9.79 N (approximately 1 kg of upward force)