Density relates mass to the amount of space (volume) that mass occupies, and as of November 2026 a cubic centimeter of fresh water holds about 1 gram (a milliliter does as well), so a liter, which is 1,000 milliliters, holds about 1,000 grams. Neither size nor heaviness settles whether something floats; an object floats when its average density falls below that of the fluid around it. Iron and clay, as solid lumps, go to the bottom, yet clay pressed into the shape of a boat floats; what lets heavy material float is a hollow form full of air, and big ships float for that reason, since they have lots of air inside. Counted over the whole hull, with its air, a floating boat is less dense than the water, and a ship with no cargo floats higher than the same ship when loaded.

Water pushes up on whatever sits in it, and the push on a boat's underside is what holds the boat afloat. That push exists because pressure grows with depth, so water presses harder on the underside of an object than on its top, and the difference is the buoyant force. Archimedes' principle sets that force equal to the weight of the displaced fluid; set against the object's own weight, a larger force makes it rise and float, a smaller one makes it sink, and equal forces make it hang. Many kinds of wood float on water, as does ice. Cooking oil rests on top of the water, and a helium balloon floats in air because helium is lighter than air. Water that is very salty, as in the Dead Sea, supports swimmers so strongly that they float easily. Air is a fluid as well. For some accurate weighings, a correction for the buoyancy of the surrounding air must be applied, so even the reading of a precise balance is shaped by Archimedes' principle.

Cork, aluminum and lead balls of equal volume, 10 cubic centimeters each, have masses of 2, 27 and 113 grams, yet all three push aside 10 grams of water and meet equal buoyant forces; the cork floats up, and the others go down. Specific gravity sets an object's density against that of water: under 1, it floats; over 1, it sinks. A sinking object still feels an upward push, so it appears lighter once submerged, and depth changes nothing, because a thing that floats in 2 feet of water floats equally in water 2000 feet deep. A coin can be weighed twice, once in air and once under water. The weight it seems to lose equals the weight of the water displaced, which gives its volume, and so its density follows. That can show whether a coin is genuine: an ancient Greek coin of 8.630 g in air had an apparent mass of 7.800 g in water, giving a density close to pure silver, while most modern counterfeits are not pure silver. The 0.830 g difference is the displaced water, so the volume is 0.830 cubic centimeters and the density about 10.4 grams per cubic centimeter.

Archimedes lived in Syracuse, on Sicily, between about 287 and 212 BCE. He wrote On Floating Bodies, the first known work in the field of hydrostatics, and he is recognized as that field's founder. Britannica notes that he stated his principle before the idea of gravity had been conceptualized, and that forces are now used to explain buoyancy. It also singles out the second book of On Floating Bodies, which finds the stable positions of a floating paraboloid, as a mathematical "tour de force" with no match in antiquity. About 2,000 years ago the Roman architect Vitruvius gave an account in which a goldsmith had cheated King Hiero II of Syracuse and Archimedes caught him; the king had suspected silver was mixed into a golden crown. In the popular telling, Archimedes found buoyancy in a bath and ran shouting "Eureka!" through the streets, and that account was recorded in the first century BC, long after his lifetime.

Some doubt that Archimedes used Vitruvius's overflow method: it needs much less imagination than his writings show, ignores his law of buoyancy and the lever, and would be hard to measure accurately with ancient tools. Take a wreath of 1000 grams. If 30 percent of it were silver, the water level in a container whose width is 20 centimeters would sit about 0.41 millimeters above where pure gold would put it. Galileo reasoned that Archimedes probably used a hydrostatic balance, drawing on his own proofs in On Floating Bodies, and wrote that he thought it probable his method was the one Archimedes followed. Galileo's own treatise, La Bilancetta ("The Little Balance"), was written in 1586 when he was 22, and in it he doubted Vitruvius's account and proposed a method using water. Another test uses a balance. Gold of equal mass hangs on one side and the crown on the other, and both are dipped in water. According to NYU's Archimedes page, a wreath that is 30 percent silver and weighs 1000 grams would pull the scale about 13 grams out of balance, which ancient scales could easily show.

Deep-sea sharks have large oil-filled livers and were believed to be neutrally buoyant, but this had never been confirmed in the wild. A study with swim-effort loggers on two species, the bluntnose sixgill and the prickly shark, found them positively buoyant. The authors of the shark study say positive buoyancy could be widespread among fish that make daily vertical migrations in the deep sea; few such animals have been tested, so how common it is remains an open question. For nearly a century the density maximum of water was explained only qualitatively, as a mix of ordered and disordered structures; the authors of a 2026 preprint (not yet peer reviewed, as of November 2026) say their results point to a more delicate mechanism than the usual picture. The same preprint used a machine-learned model of water, trained on quantum calculations, to study the density maximum; its authors say the maximum comes from structure that is tetrahedral up close but collapses at medium range. Only play or swim in water with a grown-up watching, and always ask first.

Words to know

• preprint: study before review
• counterfeits: fake copies
• hydrostatic: fluid-resting
• migrations: regular trips