Buoyancy Formula (Archimedes Principle)
The buoyancy formula calculates the upward force on a submerged object using fluid density and displaced volume.
The Formula
The buoyant force is the upward force exerted on any object submerged in a fluid. It equals the weight of the fluid displaced by the object. This principle was discovered by Archimedes of Syracuse around 250 BC in ancient Greece.
Variables
| Symbol | Meaning |
|---|---|
| Fb | Buoyant force (measured in newtons, N) |
| ρ | Density of the fluid (measured in kg/m³). Water = 1,000 kg/m³. Seawater = 1,025 kg/m³ |
| V | Volume of fluid displaced by the object (measured in m³) |
| g | Acceleration due to gravity (9.81 m/s² on Earth) |
Example 1
A ball with a volume of 0.002 m³ is fully submerged in fresh water. What is the buoyant force?
Identify values: ρ = 1,000 kg/m³, V = 0.002 m³, g = 9.81 m/s²
Apply the formula: Fb = 1,000 × 0.002 × 9.81
Fb = 19.62 N
Example 2
A boat displaces 5 m³ of seawater (ρ = 1,025 kg/m³). What is its buoyant force, and how much can it carry?
Fb = 1,025 × 5 × 9.81
Fb = 50,276 N
Convert to mass: m = F / g = 50,276 / 9.81
The boat can support approximately 5,125 kg (11,299 lbs)
When to Use It
Use the buoyancy formula to understand floating, sinking, and fluid displacement.
- Determining if an object will float or sink (compare buoyant force to weight)
- Calculating the load capacity of boats and ships
- Designing submarines and underwater vehicles
- Understanding why hot air balloons rise (air density difference)
- Measuring the density of irregular objects by displacement
Floating vs Sinking
An object floats when the buoyant force equals its weight. An object sinks when its weight exceeds the maximum buoyant force (when fully submerged). This is why steel ships float — the hull shape displaces enough water to create a buoyant force greater than the ship's weight, even though steel is denser than water.