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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 letter
rho Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the sa ...
), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac 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 Packaging is the science, art and technology of enclosing or protecting products for distribution, storage, sale, and use. Packaging also refers to the process of designing, evaluating, and producing packages. Packaging can be described as a co ...
.
Osmium Osmium (from Greek grc, ὀσμή, osme, smell, label=none) is a chemical element with the symbol Os and atomic number 76. It is a hard, brittle, bluish-white transition metal in the platinum group that is found as a trace element in alloys, mos ...
and iridium are the densest known elements at
standard conditions for temperature and pressure Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union o ...
. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "
relative density Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ...
" 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 Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is on ...
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.


History

In a well-known but probably
apocryphal Apocrypha are works, usually written, of unknown authorship or of doubtful origin. The word ''apocryphal'' (ἀπόκρυφος) was first applied to writings which were kept secret because they were the vehicles of esoteric knowledge considered ...
tale,
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...
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 Displacement may refer to: Physical sciences Mathematics and Physics *Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "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.


Measurement of density

A number of techniques as well as standards exist for the measurement of density of materials. Such techniques include the use of a hydrometer (a buoyancy method for liquids), Hydrostatic balance (a buoyancy method for liquids and solids), immersed body method (a buoyancy method for liquids), pycnometer (liquids and solids), air comparison pycnometer (solids), oscillating densitometer (liquids), as well as pour and tap (solids). However, each individual method or technique measures different types of density (e.g. bulk density, skeletal density, etc.), and therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question.


Unit

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 The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
per
cubic metre The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is m ...
(kg/m3) and the cgs unit of gram per cubic centimetre (g/cm3) are probably the most commonly used units for density. One g/cm3 is equal to 1000 kg/m3. One cubic centimetre (abbreviation cc) is equal to one millilitre. 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.


Homogeneous materials

The density at all points of a
homogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
object equals its total mass divided by its total volume. The mass is normally measured with a scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. To determine the density of a liquid or a gas, a
hydrometer A hydrometer or lactometer is an instrument used for measuring density or relative density of liquids based on the concept of buoyancy. They are typically calibrated and graduated with one or more scales such as specific gravity. A hydrometer ...
, a dasymeter or a
Coriolis flow meter A mass flow meter, also known as an inertial flow meter, is a device that measures mass flow rate of a fluid traveling through a tube. The mass flow rate is the mass of the fluid traveling past a fixed point per unit time. The mass flow meter do ...
may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object.


Heterogeneous materials

If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: \rho(\vec) = dm/dV, where dV is an elementary volume at position r. The mass of the body then can be expressed as : m = \int_V \rho(\vec)\,dV.


Non-compact materials

In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules. 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 close-packing of equal spheres the non-void 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 non-compact 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.


Changes of density

In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures. 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 Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar * Chocolate bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a layer of cloud * Bar (u ...
−1 (1 bar = 0.1 MPa) and a typical thermal expansivity is 10−5  K−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 The degree Celsius is the unit of temperature on the Celsius scale (originally known as the centigrade scale outside Sweden), one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The ...
. In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is :\rho = \frac , where is the molar mass, is the pressure, is the universal 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 :\rho = \frac, where \rho_ is the density at a reference temperature, \alpha is the thermal expansion coefficient of the material at temperatures close to T_0.


Density of solutions

The density of a
solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...
is the sum of mass (massic) concentrations of the components of that solution. Mass (massic) concentration of each given component ρi in a solution sums to density of the solution, :\rho = \sum_i \varrho_i . 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: :\rho = \sum_i \rho_i \frac\, = \sum_i \rho_i \varphi_i = \sum_i \rho_i \frac, provided that there is no interaction between the components. Knowing the relation between excess volumes and activity coefficients of the components, one can determine the activity coefficients: :\overline_i = RT \frac.


Densities


Various materials

:''Selected chemical elements are listed here. For the densities of all chemical elements, see
List of chemical elements This is a list of the 118 chemical elements which have been identified as of 2022. A chemical element, often simply called an element, is a type of atom which has the same number of protons in its atomic nucleus (i.e., the same atomic number, or ' ...
''


Others


Water


Air


Molar volumes of liquid and solid phase of elements


Common units

The SI unit for density is: *
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
per
cubic metre The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is m ...
(kg/m3) The litre and tonne are not part of the SI, but are acceptable for use with it, leading to the following units: *
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
per litre (kg/L) * gram per millilitre (g/mL) * tonne per cubic metre (t/m3) 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 kg/dm3, making any of these SI units numerically convenient to use as most solids and
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
s have densities between 0.1 and 20 kg/dm3. * kilogram per cubic decimetre (kg/dm3) * gram per cubic centimetre (g/cm3) ** 1 g/cm3 = 1000 kg/m3 * megagram (metric ton) per cubic metre (Mg/m3) In US customary units density can be stated in: * Avoirdupois ounce per cubic inch (1 g/cm3 ≈ 0.578036672 oz/cu in) * Avoirdupois ounce per fluid ounce (1 g/cm3 ≈ 1.04317556 oz/US fl oz = 1.04317556 lb/US fl pint) * Avoirdupois pound per cubic inch (1 g/cm3 ≈ 0.036127292 lb/cu in) * pound per
cubic foot Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system ...
(1 g/cm3 ≈ 62.427961 lb/cu ft) * pound per cubic yard (1 g/cm3 ≈ 1685.5549 lb/cu yd) * pound per
US liquid gallon The gallon is a unit of volume in imperial units and United States customary units. Three different versions are in current use: *the imperial gallon (imp gal), defined as , which is or was used in the United Kingdom, Ireland, Canada, Austral ...
(1 g/cm3 ≈ 8.34540445 lb/US gal) * pound per US bushel (1 g/cm3 ≈ 77.6888513 lb/bu) *
slug Slug, or land slug, is a common name for any apparently shell-less terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced shell, or only a smal ...
per cubic foot 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/cm3 ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. The density of
precious metal Precious metals are rare, naturally occurring metallic chemical elements of high economic value. Chemically, the precious metals tend to be less reactive than most elements (see noble metal). They are usually ductile and have a high lustre. ...
s could conceivably be based on Troy 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/cm3.


See also

* Densities of the elements (data page) * List of elements by density *
Air density The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature a ...
*
Area density The area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is ...
* Bulk density * Buoyancy * Charge density * Density prediction by the Girolami method * Dord *
Energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or extract ...
* Lighter than air * Linear density *
Number density The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...
*
Orthobaric density The orthobaric density of a compound is the density of coexisting phases (liquid, gas, or solid) at a given temperature. Liquid - Gas Equilibrium For any temperature below the critical point, the density of the gas will be less than that of th ...
*
Paper density Paper density is a paper product's mass per unit volume. The density can be calculated by dividing the grammage of paper (in grams per square metre or "gsm") by its caliper (usually in micrometres, occasionally in mils). The "ISO 534:2011, Pap ...
* Specific weight *
Spice (oceanography) In oceanography, the term spice refers to spatial variations in the temperature and salinity of seawater whose effects on density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most ...
*
Standard temperature and pressure Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union o ...


References


External links

* *
Video: Density Experiment with Oil and Alcohol

Video: Density Experiment with Whiskey and Water

Glass Density Calculation – Calculation of the density of glass at room temperature and of glass melts at 1000 – 1400°C

List of Elements of the Periodic Table – Sorted by Density

Calculation of saturated liquid densities for some components






* ttp://www.adamequipment.com/education/Documents/EdExp1.pdf A delicious density experiment
Water density calculator
Water density for a given salinity and temperature.
Liquid density calculator
Select a liquid from the list and calculate density as a function of temperature.
Gas density calculator
Calculate density of a gas for as a function of temperature and pressure.


Determination of Density of Solid
instructions for performing classroom experiment. * * {{Authority control Physical quantities