Why Do Things Float? Density and Archimedes' Principle

Why do things float? An object floats when its average density is less than the density of the liquid it is in. The liquid pushes up on any object placed in it with a force called upthrust, and a floating object sinks only as far as it must to make that upthrust equal to its own weight. Wood floats on water because it is less dense than water; a steel nail sinks because it is about eight times denser.

What is density, and how does it decide floating and sinking?

Density is mass per unit volume: density = mass ÷ volume, measured in kg/m³ or g/cm³. Pure water has a density of 1000 kg/m³ (1.00 g/cm³). Anything with a lower average density floats in it, and anything with a higher average density sinks.

Material	Density (kg/m³)	In water
Cooking oil	about 920	Floats
Ice	about 917	Floats
Oak wood	about 700	Floats
Aluminium	about 2700	Sinks
Iron	about 7870	Sinks
Gold	about 19,300	Sinks

The word average matters in density and buoyancy. A ship is made of steel, which is denser than water, but its hull encloses a huge volume of air. Divide the ship's total mass by its total volume and the result is far below 1000 kg/m³.

What is Archimedes' principle?

Archimedes' principle says that the upthrust on an object in a fluid equals the weight of the fluid it displaces. The Greek scientist Archimedes of Syracuse worked this out in the 3rd century BC.

The upthrust formula is:

F = ρ × g × V

where ρ is the density of the liquid (kg/m³), g is the gravitational field strength (9.8 N/kg) and V is the volume of liquid displaced (m³).

Where does upthrust come from?

Pressure in a liquid increases with depth. The bottom of a submerged object is deeper than its top, so the liquid pushes up on the bottom harder than it pushes down on the top. The difference is the upthrust.

Worked examples

Will a 0.5 kg block of volume 0.0004 m³ float in water?

Its density is 0.5 ÷ 0.0004 = 1250 kg/m³, which is above 1000, so it sinks. Check with forces: the weight is 0.5 × 9.8 = 4.9 N. Fully under water, the upthrust is 1000 × 9.8 × 0.0004 = 3.92 N. The weight is bigger, so the block sinks.

How much of a floating block is underwater?

A block of density 600 kg/m³ floats in water. For a floating object, upthrust equals weight, so the fraction submerged equals the density ratio: 600 ÷ 1000 = 0.6. Sixty per cent of the block is below the surface. Ice, at 917 kg/m³, floats with about 92% of its volume underwater, which is why icebergs are mostly hidden.

Why do ships float?

Ships float because a steel hull displaces a very large volume of water. A ship sinks until the weight of water it displaces equals its own weight, and the hull is shaped so that happens before the deck reaches the water. Load more cargo and the ship sits lower. The Plimsoll line painted on a hull marks the safe loading limit for different water densities.

Why is it easier to float in the Dead Sea?

The Dead Sea has a density of about 1240 kg/m³ because it is extremely salty. Water that dense gives a larger upthrust for the same volume displaced, so a person floats with much more of their body above the surface. Ordinary sea water is about 1025 kg/m³, so you float a little better in the sea than in a swimming pool.

Common mistakes

• Thinking heavy objects sink and light ones float. A huge ship floats, a tiny pebble sinks. Density, not weight, decides.
• Mixing up units. Convert g/cm³ to kg/m³ by multiplying by 1000 before using the upthrust formula.
• Using the object's volume when it is only part submerged. Use the volume of liquid displaced, which is just the submerged part.
• Forgetting that the liquid matters. The same iron nail sinks in water but floats in mercury, which has a density of about 13,500 kg/m³.

Frequently asked questions

Why do some things float and others sink?

An object floats when its average density is lower than the liquid's, so the upthrust can balance its weight before it is fully submerged. If its average density is higher, even full submersion gives an upthrust smaller than its weight, so it sinks. Shape can change average density: a steel bowl floats, while the same steel squashed into a ball sinks.

What is the formula for upthrust?

Upthrust = ρ × g × V, where ρ is the liquid's density in kg/m³, g is 9.8 N/kg and V is the volume of liquid displaced in m³. It is equal to the weight of the displaced liquid. For 0.001 m³ of water displaced, the upthrust is 1000 × 9.8 × 0.001 = 9.8 N.

Does a heavier object always sink?

No. A ship weighing thousands of tonnes floats, while a small coin sinks. Floating depends on density, which compares mass to volume. A heavy object that spreads its mass over a large volume has a low average density and can float easily.

Why does ice float on water?

When water freezes, its molecules form an open hexagonal lattice that takes up about 9% more volume. Ice therefore has a density of about 917 kg/m³, lower than liquid water at 1000 kg/m³, so it floats with roughly 92% of its volume under the surface.

Try it yourself

Open the Density & Buoyancy simulator, choose Water, and press "Drop them all in" to see which objects float and which sink. Then switch the liquid to the Dead Sea, oil, honey and mercury and drop them again: objects that sank in water start to float as the liquid gets denser. Turn on "Show the forces" to watch the upthrust arrow grow as an object goes deeper, and see when it balances the weight. For more on density, read states of matter and Newton's laws of motion.