Density ( volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ρ (the lower case Greek language letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:
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 has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements 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 (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, 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, and specific weight.
The story first appeared in written form in Vitruvius' De architectura, two centuries after it supposedly took place. target="_blank" rel="nofollow"> Vitruvius on Architecture, Book IX, paragraphs 9–12, translated into English and in the original Latin. 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.
m = \int_V \rho(\vec{r})\,dV.
Voids are regions which contain something other than the considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or gaseous mixture.
The bulk volume of a material—inclusive of the void fraction—is often obtained by a simple measurement (e.g. with a calibrated measuring cup) or geometrically from known dimensions.
Mass divided by bulk volume determines bulk density. This is not the same thing as volumetric mass density.
To determine volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the closepacking of equal spheres the nonvoid fraction can be at most about 74%. It can also be determined empirically. Some bulk materials, however, such as sand, have a variable void fraction which depends on how the material is agitated or poured. It might be loose or compact, with more or less air space depending on handling.
In practice, the void fraction is not necessarily air, or even gaseous. In the case of sand, it could be water, which can be advantageous for measurement as the void fraction for sand saturated in water—once any air bubbles are thoroughly driven out—is potentially more consistent than dry sand measured with an air void.
In the case of noncompact materials, one must also take care in determining the mass of the material sample. If the material is under pressure (commonly ambient air pressure at the earth's surface) the determination of mass from a measured sample weight might need to account for buoyancy effects due to the density of the void constituent, depending on how the measurement was conducted. In the case of dry sand, sand is so much denser than air that the buoyancy effect is commonly neglected (less than one part in one thousand).
Mass change upon displacing one void material with another while maintaining constant volume can be used to estimate the void fraction, if the difference in density of the two voids materials is reliably known.
The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10^{−6} bar^{−1} (1 bar = 0.1 MPa) and a typical thermal expansivity is 10^{−5} Kelvin^{−1}. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.
In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is
where is the molar mass, is the pressure, is the Gas constant, and is the absolute temperature. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.
In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is
where $\backslash rho\_\{T\_0\}$ is the density at a reference temperature, $\backslash alpha$ is the thermal expansion coefficient of the material at temperatures close to $T\_0$.
Mass (massic) concentration of each given component ρ_{i} in a solution sums to density of the solution,
Expressed as a function of the densities of pure components of the mixture and their volume participation, it allows the determination of excess molar volumes:
Knowing the relation between excess volumes and activity coefficients of the components, one can determine the activity coefficients:
+Densities of various materials covering a range of values 
Air contained in material excluded when calculating density New carbon nanotube struructure aerographite is lightest material champ . Phys.org (July 13, 2012). Retrieved on July 14, 2012. Aerographit: Leichtestes Material der Welt entwickelt – SPIEGEL ONLINE . Spiegel.de (July 11, 2012). Retrieved on July 14, 2012. 
At sea level 
One of the heaviest known gases at standard conditions 
At approx. −255 °C 
Approx. 
Approx. 
Least dense metal 
Seasoned, typical 
(1970). 9781315214092, CRC Press. ISBN 9781315214092 
At temperature < 0 °C 
At 4 °C, the temperature of its maximum density 
3% 
At approx. −219 °C 
Approx.; for polypropylene and PETE/PVC 
glycerol composition at . Physics.nist.gov. Retrieved on July 14, 2012. 
Between 1,600 and 2000 
(2023). 9780321696861, AddisonWesley. ISBN 9780321696861 
Compact 
Liquid at room temperature 
Approx. 
Densest natural element on Earth 
Assuming 90% H, 10% He; variable T 
Mean density. 
Approx., as listed in Earth. 
Approx. 
Approx. 
Does not depend strongly on size of nucleus 
+ Density of liquid water at 1 atm pressure  
983.854  
993.547  
998.117  
999.8395  
999.9720  
999.7026  
999.1026  
998.2071  
997.7735  
997.0479  
995.6502  
992.2  
983.2  
971.8  
958.4  
Notes: 
+Density of air at 1 atm pressure 
1.423 
1.395 
1.368 
1.342 
1.316 
1.293 
1.269 
1.247 
1.225 
1.204 
1.184 
1.164 
1.146 
The litre and tonne are not part of the SI, but are acceptable for use with it, leading to the following units:
Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m^{3}). Liquid water has a density of about 1 kg/dm^{3}, making any of these SI units numerically convenient to use as most and have densities between 0.1 and 20 kg/dm^{3}.
In US customary units density can be stated in:
Imperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. The Imperial gallon was based on the concept that an Imperial fluid ounce of water would have a mass of one Avoirdupois ounce, and indeed 1 g/cm^{3} ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. The density of could conceivably be based on Troy weight ounces and pounds, a possible cause of confusion.
Knowing the volume of the unit cell of a crystalline material and its formula weight (in daltons), the density can be calculated. One dalton per cubic ångström is equal to a density of 1.660 539 066 60 g/cm^{3}.

