Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D (or d) can also be used:
ρ = m V , {\displaystyle \rho ={\frac {m}{V}},}
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance, the density is equal to its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium is the densest known element at standard conditions for temperature and pressure. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one relative to water means that the substance floats in water. The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance while maintaining a constant pressure decreases its density by increasing its volume (with a few exceptions). In most fluids, heating the bottom of the fluid results in convection due to the decrease in the density of the heated fluid, which causes it to rise relative to denser unheated material. The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass. Other conceptually comparable quantities or ratios include specific density, relative density (specific gravity), and specific weight. The concept of mass density is generalized in the International System of Quantities to volumic quantities, the quotient of any physical quantity and volume, such as charge density or volumic electric charge.
History
Density, floating, and sinking The understanding that different materials have different densities, and of a relationship between density, floating, and sinking must date to prehistoric times. Much later it was put in writing. Aristotle, for example, wrote:
There is so great a difference in density between salt and fresh water that vessels laden with cargoes of the same weight almost sink in rivers, but ride quite easily at sea and are quite seaworthy. And an ignorance of this has sometimes cost people dear who load their ships in rivers. The following is a proof that the density of a fluid is greater when a substance is mixed with it. If you make water very salt by mixing salt in with it, eggs will float on it. ... If there were any truth in the stories they tell about the lake in Palestine it would further bear out what I say. For they say if you bind a man or beast and throw him into it he floats and does not sink beneath the surface.
Volume vs. density; volume of an irregular shape
In a well-known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" (Ancient Greek: Εύρηκα!, lit. 'I have found it'). As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment. The story first appeared in written form in Vitruvius' books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. Nevertheless, in 1586, Galileo Galilei, in one of his first experiments, made a possible reconstruction of how the experiment could have been performed with ancient Greek resources.
Units From the equation for density (ρ = m/V), mass density has any unit that is mass divided by volume. As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per cubic metre (kg/m3) and the cgs unit of gram per cubic centimetre (g/cm3) are probably the most commonly used units for density. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density. Densities using the following metric units all have exactly the same numerical value, one-thousandth of the value in kg/m3. Liquid water has a density of about 1 g/cm3 or 1000 kg/m3, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 g/cm3.
gram per cubic centimetre (g/cm3) kilogram per cubic decimetre (kg/dm3) megagram per cubic metre (Mg/m3) Units employing the metric units litre and tonne (metric ton), which are not part of the SI, include:
gram per millilitre (g/mL) kilogram per litre (kg/L) tonne per cubic metre (t/m3) In US customary units density can be stated in:
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