Archimedes' Principle
Buoyant force equals weight of displaced fluid.
Formula
Variables
How it works
When an object is partly or fully submerged in a fluid, the pressure on its lower surfaces is greater than the pressure on its upper surfaces, creating a net upward force. That upward force depends on how much fluid is displaced, so a larger displaced volume or a denser fluid produces a larger buoyant force. In equilibrium, this buoyant force is what helps floating objects support their own weight.
When to use it
Use this formula for objects in water, oil, air, or any fluid when you need the upward buoyant force. It is especially useful for finding whether something will float, how much of a boat is submerged, or the apparent weight of an object in a fluid.
Worked example, step by step
A solid block displaces 0.015 m^3 of freshwater. Given: rho = 1000 kg/m^3, g = 9.8 m/s^2, V = 0.015 m^3 Use F_b = rho g V F_b = (1000)(9.8)(0.015) F_b = 147 N Final answer: The buoyant force on the block is 147 N upward.
Common mistakes to avoid
- Using the object's total volume instead of the volume actually submerged/displaced
- Forgetting to convert units so density is in kg/m^3 and volume is in m^3
- Confusing buoyant force with the object's weight instead of the fluid's displaced weight
Did You Know?
A steel ship floats because its hull displaces enough water to weigh more than the ship itself.
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