An easy introduction to Archimedes' principle

Archimedes' principle is the simple idea that water or air pushes up on things placed inside it. The rule says that this upward push, called the buoyant force, is equal to the weight of the fluid the object pushes aside, or displaces [2]/10%3A_Fluids/10.3%3A_Archimedes_Principle).

That sounds technical at first, but the everyday meaning is simple. Put a rock into water and it feels easier to lift. Sit in a pool and your body feels supported. A ship stays up not because metal is magically light, but because it pushes aside enough water for the water's upward push to balance its weight. The whole page turns on three ideas: why things feel lighter in water, what displaced fluid means, and how that explains floating and sinking.

Why things feel lighter in water

Pick up a heavy rock in air. Then lower it into a bucket or pool and try again. The rock's mass has not changed. Earth is still pulling it downward. But now the water is also pushing upward on it. That upward push reduces how heavy the rock feels.

This is the first thing to get straight: water does not remove the rock's weight. It changes the rock's apparent weight. In other words, the rock is still the same rock, but you do not need to support all of its weight by yourself because the water is supporting part of it.

The same thing happens with your body. In a swimming pool, you can stand, float, or move with much less effort than on land because the water is helping hold you up. That upward support has a name: buoyant force.

The trap here is to think buoyancy is some special property only for floating objects. It is not. Even a stone at the bottom of a lake feels buoyant. It still gets pushed up by the water. It sinks only because its weight is greater than that upward push .

What displaced fluid means

Displaced fluid just means fluid that had to move out of the way when an object entered.

Drop a stone into a full cup of water. Some water spills out. That spilled water is the most obvious picture of displacement. Even if no water spills, the object still takes up space, so water must shift aside to make room.

A few concrete examples make this easier:

Put an empty cup upside down into water. It pushes water aside because it occupies space.
Drop a small stone into a bowl. It displaces a small amount of water because it has a small volume.
Press a floating toy down deeper. It displaces more water than before, so the upward push becomes larger.

The key link is this: the more fluid an object displaces, the more fluid is involved in pushing up on it. That is why a tiny pebble gets only a tiny upward push, while a large floating raft can get a very large one .

The core rule: buoyant force equals the weight of displaced fluid

Now the full statement.

Archimedes' principle: the buoyant force on an object is equal to the weight of the fluid displaced by that object .

That is the sentence worth remembering.

It works in water, but not only in water. It works in any fluid, and in physics a fluid means a substance that can flow. So liquids are fluids, and gases are fluids too. Air counts. That is why the same idea helps explain hot-air balloons as well as boats [2]/10%3A_Fluids/10.3%3A_Archimedes_Principle).

It also works whether the object is:

fully submerged, like a rock underwater
partially submerged, like a boat floating at the surface

If only part of the object is underwater, then only that underwater part counts for water displacement. That is why floating objects sink deeper when you load them with more weight: they must displace more water to get a bigger upward push.

Why some things float and others sink

Floating and sinking become easy once the forces are compared.

An object floats when the upward buoyant force can balance its downward weight. An object sinks when its weight is greater than the buoyant force. If the buoyant force is greater than the weight, the object rises upward until balance is reached.

Think in three cases:

Buoyant force = weight. The object can float or remain suspended.
Buoyant force < weight. The object sinks.
Buoyant force > weight. The object rises.

This explains a lot of everyday puzzles.

Wood usually floats because, for its size, its average density is low enough that water can support it before it is fully submerged.
A solid iron nail sinks because it is heavy for the small volume of water it displaces.
A ship made of steel can float because its hollow shape gives it a large overall volume, so it can displace enough water to balance its total weight.
Human bodies can float more easily when the lungs are full of air, because that increases volume without adding much weight.

The trap here is to think "heavy things sink, light things float." That is not quite right. A huge ship is far heavier than a coin, yet the ship floats and the coin sinks. What matters is not weight alone, but weight compared with how much fluid gets displaced. In practice, that is why shape and average density matter so much .

A simple worked example with a block in water

Imagine a small block being lowered into water.

Case 1: just touching the water

At first, almost none of the block is underwater, so it displaces very little water. That means the buoyant force is very small.

Case 2: pushed deeper

As more of the block goes underwater, it pushes more water out of the way. More displaced water means a larger buoyant force.

In compact form, the idea is:

where is the buoyant force, is the fluid density, is the displaced volume, and is gravity .

Do not let the symbols hide the meaning. The important part for a beginner is just this: bigger displaced volume bigger buoyant force.

Case 3: what happens next?

From here, there are two possibilities:

If the block's weight is still greater than the buoyant force, it keeps sinking.
If the buoyant force grows until it matches the block's weight, the block can float.

That ties the whole story together. Displacement tells you how much water is pushed aside. That determines buoyant force. Then buoyant force compared with weight tells you whether the object floats or sinks.

Everyday examples of Archimedes' principle

Once you see the principle, it shows up everywhere.

Swimming: your body displaces water, and the water pushes upward on you.
Life jackets: they increase your overall volume and help you displace more water for your weight, so floating becomes easier.
Ships: their shape lets them displace a large weight of water even though they are made of metal.
Submarines: they control whether they sink or rise by changing how dense they are overall.
Hot-air balloons: air is also a fluid, so the balloon rises when the upward buoyant force from the surrounding air is enough to support it .

The big payoff is that one rule explains all of these. Water and air both push upward. The amount of that push depends on how much fluid is displaced. Once that clicks, floating stops looking mysterious and starts looking inevitable.