Buoyancy describes the tendency an object has to float or rise when it sits in a fluid, which can be liquid or gas. An object floats when its average density sits below that of the fluid surrounding it. A boat counts as one object together with the air inside it. Averaged over the whole boat, that density sits below that of water, and the water pressing up on the underside of the hull holds the boat afloat. A solid chunk of iron or clay sinks in water, yet clay shaped like a boat floats. Heavy material can float when it is made into a hollow shape filled with air instead of staying a solid lump. Buoyant force always acts against gravity, even though gravity is what produces it. The weight of the fluid above makes pressure grow with depth, and the growing pressure pushes up on anything under the surface.

Archimedes announced his principle before ideas about force were well established. Britannica says gravity had not yet been conceptualized in his time, and today buoyancy is explained with the idea of forces. Written as F_B = w_fl, Archimedes' principle states that the buoyant force matches the weight of fluid displaced, for any object in any fluid, whether partly or wholly submerged. Something that floats settles to the depth where the displaced water weighs exactly as much as the thing itself, and a ship slid into the sea sinks just that far. Compare the buoyant force with the weight of an object: a larger force lifts it to float, a smaller force lets it sink, and equal forces leave it hanging in place. Depth makes no difference, so a thing that stays afloat at a depth of 2 feet will also stay afloat at 2000 feet.

Three balls, one each of cork, aluminum and lead and each 10 cubic centimeters in size, come to 2, 27 and 113 grams in mass. Each pushes aside 10 grams of water, so each feels an equal buoyant force, and the cork rises while the other two sink. Water also pushes up on something that sinks, which makes it seem lighter when it is submerged. Density ties together mass and volume, because it tells how much mass fills a certain amount of space. An object lowered under water shoves aside its own volume of water, which makes water a handy tool for working out a lumpy object's volume. Specific gravity sets an object's density beside the density of water: below 1, the object floats, and above 1, it sinks.

As of November 2026, fresh water has a density near 1 gram per cubic centimeter (equal to 1 gram per milliliter), and sea water runs slightly higher at from 1.02 up to 1.03 grams for every cubic centimeter. Water in general gets denser as it gets colder, so its density changes with temperature. Ice has a density about 9 percent below that of liquid water, so most of an ice cube sits below the water line. A hydrometer reads a liquid's density by how it floats: it rides lower in a liquid with less density and higher in a denser liquid. Dividing the volume of the hull under the water by the volume per unit weight of the water a ship will sail in gives the weight of water displaced. That weight must match the ship's total weight, and the value differs for fresh, brackish and salt water.

A ship carrying no cargo rides higher than it does fully loaded. Fresh water has less density than salt water, so the same ship rides higher in salt water than in fresh. To dive, a submarine lets water flow into its ballast tanks, and to surface, it uses compressed air to push the water back out. Emptying the tanks drops its average density under that of the surrounding water. A body whose density matches the fluid hangs there without sinking or rising, and scuba divers aim for this balance to hover. Most fish carry a gas-filled swim bladder, which lets them stay suspended in the water. As the bladder expands, the fish's volume grows but its mass does not change, so the fish's specific gravity drops and it rises, and when the bladder shrinks, the fish sinks. Among fishes, a gas-filled swim bladder is the most usual way to gain buoyancy.

Sharks use large oil-filled livers in place of a swim bladder. Having none, a shark gets help from its big, oily liver, which slows its sinking, while a lighter skeleton of cartilage and a body and fins shaped like a glider also help keep it up. In water that is as salty as the Dead Sea's, a swimmer is held up so firmly that floating is easy, and very few organisms can live there. As of November 2026, the University of Hawaii puts the salinity at around eight times that of average seawater. Its deep water became saturated with sodium chloride, which settled to the bottom, and because that water was so salty and dense, it stayed down there for a long time. After the 1960s, the flow of fresh water from the Jordan River was sharply reduced, and by the late 1970s the upper water had grown saltier and denser than the lower layers (Britannica, as of 2026).

Book two of Archimedes' On Floating Bodies works out the stable positions that a floating paraboloid, a bowl-like curved solid, can take, and Britannica describes it as a mathematical tour de force unmatched in antiquity. For the crown, a balance makes a better test: hang the crown from one side and an equal mass of gold from the other, then dip both in water. A wreath of 1000 grams with 30 percent silver would tip the scale by about 13 grams, which is easy for ancient scales to show, according to NYU's Archimedes page. Whether the water is salty or fresh, deep or shallow, ask first before any swim or any play in the water, and make sure that a grown-up is watching.

Words to know

• buoyancy: upward push
• paraboloid: bowl-like solid
• hydrometer: density meter
• brackish: slightly salty