Buoyant Force (Archimedes)
Upward force equals the weight of displaced water.
Formula
Variables
Example
V=2 m³ seawater (1025): F_b ≈ 20.1 kN
How it works
This formula gives the upward buoyant force acting on an object in a fluid, and it is equal to the weight of the fluid that the object displaces. It comes from the pressure in a fluid increasing with depth, so the bottom of an immersed object is pushed up more strongly than the top is pushed down. If the buoyant force matches the object’s weight, it floats; if it is smaller, the object sinks.
When to use it
Use this when you need to find the lift on a ship, submarine, dock float, or any object partly or fully submerged in water. It is also useful for checking whether something will float, sink, or stay neutrally buoyant.
Worked example, step by step
A submerged equipment pod displaces 0.75 m³ of freshwater. Take ρ = 1000 kg/m³ and g = 9.81 m/s². F_b = ρgV F_b = 1000 × 9.81 × 0.75 F_b = 7357.5 N F_b ≈ 7.36 kN
Common mistakes to avoid
- Using the object’s own volume instead of the volume of fluid displaced
- Forgetting to convert density or volume into SI units before calculating
- Mixing up buoyant force with the object’s weight or treating the result as a mass
Did You Know?
Archimedes reportedly leapt from his bath shouting 'Eureka!' on discovering this principle.
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