Buoyancy Explained: Why Things Float in Water

Things float in water when the upward push of the water, called the buoyant force, equals their weight. That push is equal to the weight of the water the object displaces, so anything whose average density is lower than water's (about 1,000 kg/m³, or 1 g/cm³) floats, and anything denser sinks. Shape matters because it changes how much water an object moves aside, which is how a steel ship floats while a steel ball does not. Here is how buoyancy works, how to calculate it, and what changes it.

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Float or sink: the quick rules

The test is a density comparison. Fresh water at room temperature has a density of about 998 kg/m³. Work out the object's average density (its total mass divided by its total volume, including any air trapped inside) and compare:

Values are rounded and typical. Wood density varies with species and moisture, and submerged percentages are estimates worked out from the density ratio.

Two details are worth noticing. First, a floating object does not sit on top of the water. It sinks until the water it displaces weighs exactly as much as it does, so a pine plank rides about half under. Second, an object with the same density as water, such as a human body with a moderate breath of air in the lungs, hovers just at the surface and moves up or down with small changes in breathing.

What buoyancy actually is

Buoyancy comes from pressure. Water pressure rises with depth, at about 0.43 psi for every foot of fresh water. Lower an object into a tank and the water pushes on every surface, but not equally. The bottom sits deeper than the top, so it feels a higher pressure, and the water pushes up on it harder than it pushes down on the top. The sideways pushes cancel each other out.

The leftover upward push is the buoyant force. Work through the geometry and it turns out to equal the weight of the water that would fill the space the object occupies. That is not a coincidence: if you swapped the object for a same-shaped bag of water, the bag would hang motionless, so the surrounding water must already be supporting exactly that much weight.

Gravity pulls the object down with its own weight, and the water pushes up with the buoyant force. Whichever is larger wins. If they are equal, the object floats or hovers.

Archimedes' principle in plain terms

The rule that captures all of this is named for the ancient Greek scholar Archimedes: the upward buoyant force on an object in a fluid equals the weight of the fluid the object displaces. It works in two cases.

• Fully submerged. The displaced volume equals the whole object's volume. If the buoyant force is bigger than the object's weight, it rises; if smaller, it sinks.
• Floating. Only the submerged part displaces water, and the object settles at the depth where the displaced water's weight equals its own. A floating boat displaces its own weight in water, no more and no less.

That second case is a handy shortcut. To find out how much of a floating object is underwater, you never need to measure the hull: you only need the ratio of its density to the fluid's.

Why a steel ship floats but a steel ball sinks

Steel is nearly eight times denser than water, so a solid ball sinks. A ship floats because it is not solid. The hull encloses a huge volume of air, and what counts is the average density of the whole vessel, steel plus air, compared with water. Spread the same steel around a large, hollow shape and the average density drops well below that of water.

Naval architects call the spare lift a ship has before it would sink its reserve buoyancy. Every ton of cargo pushes the hull lower, displaces more water, and uses some of that reserve. Flooding does the opposite: as water replaces the air inside the hull, the average density climbs, the reserve disappears, and the ship sinks. This is also why ships carry load-line marks on the hull. The safe loading depth differs between fresh water and denser salt water, so the marks show a different limit for each.

How to calculate buoyant force

The math is a direct translation of Archimedes' principle: the weight of the displaced water is its density times its volume times gravity.

Take a fully submerged object with a volume of 0.05 m³ (50 liters). In fresh water:

For the floating case, you can also skip the force entirely. The fraction of an object that sits below the surface is its density divided by the fluid's density:

If you'd rather think in pounds and gallons, each volume of displaced water gives you its weight as lift. The table below shows the maximum lift for common volumes in fresh water and in seawater.

Because the calculation depends only on the displaced volume and the fluid, it works the same way for a life jacket, a fishing float or a barge. Our buoyancy calculator runs these numbers for you, including the fraction submerged.

What changes buoyancy

Salt. Dissolved salt makes seawater roughly 3% denser than fresh water, so the same displaced volume gives about that much more lift. A boat floats a little higher in the ocean than in a lake, and people float more easily in the sea. Very salty water is more dramatic: the Dead Sea's density is well over 1,200 kg/m³, which is why swimmers there bob up like corks.

Temperature. Warm water is less dense, so it gives less lift for the same displaced volume. Compared with water at 4 °C, water near boiling is about 4% less dense. Across the temperatures of a lake or a pool the change is small enough to ignore for most purposes.

Depth. For a rigid object, buoyancy does not change as it goes deeper, because water is nearly incompressible and the displaced volume stays the same. The exceptions are objects that squash. A foam wetsuit or an air-filled bag shrinks under pressure, displaces less water, and loses lift as it goes down. This is why scuba divers add air to a buoyancy vest as they descend.

The fluid itself. Everything above is about water, but the principle applies to any liquid or gas. In a fluid denser than steel, such as mercury, a steel ball floats. In air, buoyancy still exists, but the density is so low (about 1.2 kg/m³) that the lift is negligible for everyday objects, though it is enough to hold up a helium balloon.

Real-world examples

A few worked cases show how the numbers play out:

The bottom line

Buoyancy is the net upward push that water pressure puts on any object placed in it, and it always equals the weight of the water the object displaces. An object floats when its average density is lower than the water's and sinks when it is higher, which is why shape, trapped air and the water itself all count as much as the material. To work it out, multiply the displaced volume by the fluid's density and gravity. For a floating object, the fraction below the surface is simply the density ratio.