Definition · Plain-language
Archimedes’ principle
Archimedes’ principle states that the upward buoyant force on a body immersed in a fluid equals the weight of the fluid that the body displaces.
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Buoyancy equals displaced weight
Archimedes’ principle, credited to the ancient Greek thinker Archimedes, gives the size of the buoyant (upward) force on anything placed in a fluid. That force equals the weight of the fluid pushed aside — displaced — by the object. The principle arises because pressure in a fluid increases with depth, so the upward push on the bottom of a submerged object is greater than the downward push on its top, leaving a net upward force. The deeper or larger the displacement, the heavier the displaced fluid and the greater the buoyant force.
Floating, sinking and density
Whether an object floats or sinks comes down to a contest between its weight and the buoyant force. If the object weighs less than the fluid it would displace, the buoyant force wins and it floats, settling so that it displaces just enough fluid to balance its weight. If it weighs more, it sinks. This is equivalent to comparing densities: an object less dense than the fluid floats, and one denser sinks. It explains why a steel ship floats while a steel ball sinks — the ship’s hull encloses enough air to displace a large weight of water for its own weight.
Everyday and historical examples
Archimedes’ principle is everywhere. It is why you feel lighter in a swimming pool — the water’s buoyant force supports much of your weight — and why a beach ball is so hard to push under. It explains how submarines dive and surface by taking in or expelling water to change their effective density, and how hot-air balloons and helium balloons rise by displacing a weight of air greater than their own. The famous legend has Archimedes realising the principle in his bath and using it to test whether a king’s crown was pure gold by comparing displaced water.
Key facts
At a glance
- Definition: the buoyant force equals the weight of fluid an object displaces
- Buoyant force: acts upward, caused by pressure rising with depth
- Floats if: the object weighs less than the fluid it would displace
- Sinks if: the object weighs more than the displaced fluid
- Density rule: less dense than the fluid floats; denser sinks
- Examples: ships, submarines, hot-air balloons, feeling lighter in water
Common misconceptions
What people often get wrong
Often heard: Heavy objects always sink and light objects always float.
Actually: It depends on density, not raw weight. A heavy steel ship floats because its shape displaces a large weight of water, while a small dense pebble sinks.
Often heard: The buoyant force depends on how deep the object is in the fluid.
Actually: For a fully submerged object the buoyant force depends on the volume of fluid displaced, not the depth. Deeper does not mean more buoyancy once it is fully under.
Often heard: Buoyancy comes from the fluid actively pushing objects up on purpose.
Actually: It arises simply because fluid pressure increases with depth, so the upward push on the object’s underside exceeds the downward push on its top.
Going deeper
