Density (volumetric mass density or specific mass) is the substance's
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
per unit of
volume. The symbol most often used for density is ''ρ'' (the lower case
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
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
The specific weight, also known as the unit weight, is the weight per unit volume of a material.
A commonly used value is the specific weight of water on Earth at , which is .National Council of Examiners for Engineering and Surveying (2005). ''Fu ...
.
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
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
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
In thermodynamics, the specific volume of a substance (symbol: , nu) is an intrinsic property of the substance, defined as the ratio of the substance's volume () to its mass (). It is the reciprocal of density (rho) and it is related to the m ...
, 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
Specific density is the ratio of the mass versus the volume of a material.
Density vs. gravity
Specific density is based upon units of mass and volume, while specific gravity
Relative density, or specific gravity, is the ratio of the ...
,
relative density (specific gravity), and
specific weight
The specific weight, also known as the unit weight, is the weight per unit volume of a material.
A commonly used value is the specific weight of water on Earth at , which is .National Council of Examiners for Engineering and Surveying (2005). ''Fu ...
.
History
In a well-known but probably
apocryphal tale,
Archimedes was given the task of determining whether
King Hiero's
goldsmith
A goldsmith is a metalworker who specializes in working with gold and other precious metals. Nowadays they mainly specialize in jewelry-making but historically, goldsmiths have also made silverware, platters, goblets, decorative and servicea ...
was embezzling
gold during the manufacture of a golden
wreath
A wreath () is an assortment of flowers, leaves, fruits, twigs, or various materials that is constructed to form a circle .
In English-speaking countries, wreaths are used typically as household ornaments, most commonly as an Advent and Chri ...
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!" (Εύρηκα! Greek "I have found it"). As a result, the term "
eureka
Eureka (often abbreviated as E!, or Σ!) is an intergovernmental organisation for research and development funding and coordination. Eureka is an open platform for international cooperation in innovation. Organisations and companies applying th ...
" 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 per
cubic metre (kg/m
3) and the
cgs unit of
gram
The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram.
Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to th ...
per
cubic centimetre
A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cub ...
(g/cm
3) are probably the most commonly used units for density. One g/cm
3 is equal to 1000 kg/m
3. 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
United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being standardized and adopted in 1832. The United States customary system (USCS or USC) developed from English uni ...
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 object equals its total
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
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
dasymeter
A dasymeter was meant initially as a device to demonstrate the buoyant effect of gases like air (as shown in the adjacent pictures). A dasymeter which allows weighing acts as a densimeter used to measure the density of gases.
Principle
The ...
or a
Coriolis flow meter may be used, respectively. Similarly,
hydrostatic weighing
Hydrostatic weighing, also referred to as underwater weighing, hydrostatic body composition analysis and hydrodensitometry, is a technique for measuring the density of a living person's body. It is a direct application of Archimedes' principle, t ...
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:
, where
is an elementary volume at position
. The mass of the body then can be expressed as
:
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 Bulk density, also called apparent density or volumetric density, is a property of powders, granules, and other "divided" solids, especially used in reference to mineral components (soil, gravel), chemical substances, (pharmaceutical) ingredient ...
. 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
In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occu ...
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
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
or the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer.
Thermometers are calibrated in various Conversion of units of temperature, temp ...
. 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
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
increases between its melting point at 0 °C and 4 °C; similar behavior is observed in
silicon
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
at low temperatures.
The effect of pressure and temperature on the densities of liquids and solids is small. The
compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...
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
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions.
Temperature is a monotonic function of the average molecular kinetic ...
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.
In contrast, the density of gases is strongly affected by pressure. The density of an
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
is
:
where is the
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
, is the pressure, is the
universal gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
, and is the
absolute temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wor ...
. 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
is the density at a reference temperature,
is the thermal expansion coefficient of the material at temperatures close to
.
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 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:
:
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:
:
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 per
cubic metre (kg/m
3)
The litre and tonne are not part of the SI, but are acceptable for use with it, leading to the following units:
*
kilogram per
litre
The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3 ...
(kg/L)
*
gram
The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram.
Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to th ...
per
millilitre
The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3) ...
(g/mL)
*
tonne
The tonne ( or ; symbol: t) is a unit of mass equal to 1000 kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton to distinguish it from the non-metric units of the short ton ( United State ...
per cubic metre (t/m
3)
Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m
3). Liquid
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
has a density of about 1 kg/dm
3, making any of these SI units numerically convenient to use as most
solid
Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural ...
s 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/dm
3.
* kilogram per cubic decimetre (kg/dm
3)
* gram per cubic centimetre (g/cm
3)
** 1 g/cm
3 = 1000 kg/m
3
* megagram (metric ton) per cubic metre (Mg/m
3)
In
US customary units
United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being standardized and adopted in 1832. The United States customary system (USCS or USC) developed from English uni ...
density can be stated in:
*
Avoirdupois ounce
The ounce () is any of several different units of mass, weight or volume and is derived almost unchanged from the , an Ancient Roman unit of measurement.
The avoirdupois ounce (exactly ) is avoirdupois pound; this is the United States custom ...
per
cubic inch
The cubic inch (symbol in3) is a unit of volume in the Imperial units and United States customary units systems. It is the volume of a cube with each of its three dimensions (length, width, and height) being one inch long which is equivalent ...
(1 g/cm
3 ≈ 0.578036672 oz/cu in)
*
Avoirdupois ounce
The ounce () is any of several different units of mass, weight or volume and is derived almost unchanged from the , an Ancient Roman unit of measurement.
The avoirdupois ounce (exactly ) is avoirdupois pound; this is the United States custom ...
per
fluid ounce
A fluid ounce (abbreviated fl oz, fl. oz. or oz. fl., old forms ℥, fl ℥, f℥, ƒ ℥) is a unit of volume (also called ''capacity'') typically used for measuring liquids. The British Imperial, the United States customary, and the United ...
(1 g/cm
3 ≈ 1.04317556 oz/US fl oz = 1.04317556 lb/US fl pint)
*
Avoirdupois pound
The pound or pound-mass is a unit of mass used in British imperial and United States customary systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is legally defin ...
per cubic inch (1 g/cm
3 ≈ 0.036127292 lb/cu in)
* pound per
cubic foot (1 g/cm
3 ≈ 62.427961 lb/cu ft)
* pound per
cubic yard
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 w ...
(1 g/cm
3 ≈ 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, Austr ...
(1 g/cm
3 ≈ 8.34540445 lb/US gal)
* pound per US
bushel
A bushel (abbreviation: bsh. or bu.) is an imperial and US customary unit of volume based upon an earlier measure of dry capacity. The old bushel is equal to 2 kennings (obsolete), 4 pecks, or 8 dry gallons, and was used mostly for agric ...
(1 g/cm
3 ≈ 77.6888513 lb/bu)
*
slug per cubic foot
Imperial units
The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed th ...
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
A fluid ounce (abbreviated fl oz, fl. oz. or oz. fl., old forms ℥, fl ℥, f℥, ƒ ℥) is a unit of volume (also called ''capacity'') typically used for measuring liquids. The British Imperial, the United States customary, and the United ...
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
precious metals could conceivably be based on
Troy
Troy ( el, Τροία and Latin: Troia, Hittite language, Hittite: 𒋫𒊒𒄿𒊭 ''Truwiša'') or Ilion ( el, Ίλιον and Latin: Ilium, Hittite language, Hittite: 𒃾𒇻𒊭 ''Wiluša'') was an ancient city located at Hisarlik in prese ...
ounces and pounds, a possible cause of confusion.
Knowing the volume of the
unit cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
of a crystalline material and its formula weight (in
daltons), the density can be calculated. One dalton per cubic
ångström
The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...
is equal to a density of 1.660 539 066 60 g/cm
3.
See also
*
Densities of the elements (data page) Density, solid phase
In the following table, the use row is the value recommended for use in other Wikipedia pages in order to maintain consistency across content.
Density, liquid phase
Density, gas phase
Notes
* The suggested values ...
*
List of elements by density
This is a list of the 118 chemical elements which have been Timeline of chemical element discoveries, 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 n ...
*
Air density
*
Area density
*
Bulk density Bulk density, also called apparent density or volumetric density, is a property of powders, granules, and other "divided" solids, especially used in reference to mineral components (soil, gravel), chemical substances, (pharmaceutical) ingredient ...
*
Buoyancy
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the ...
*
Charge density
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in ...
*
Density prediction by the Girolami method
*
Dord
The word ''dord'' is a dictionary error in lexicography. It was accidentally created, as a ghost word, by the staff of G. and C. Merriam Company (now part of Merriam-Webster) in the '' New International Dictionary'', second edition (1934). That ...
*
Energy density
*
Lighter than air
A lifting gas or lighter-than-air gas is a gas that has a density lower than normal atmospheric gases and rises above them as a result. It is required for aerostats to create buoyancy, particularly in lighter-than-air aircraft, which include free ...
*
Linear density
Linear density is the measure of a quantity of any characteristic value per unit of length. Linear mass density (titer in textile engineering, the amount of mass per unit length) and linear charge density (the amount of electric charge per unit ...
*
Number density
*
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 t ...
*
Paper density
*
Specific weight
The specific weight, also known as the unit weight, is the weight per unit volume of a material.
A commonly used value is the specific weight of water on Earth at , which is .National Council of Examiners for Engineering and Surveying (2005). ''Fu ...
*
Spice (oceanography)
*
Standard temperature and pressure
References
External links
*
*
Video: Density Experiment with Oil and AlcoholVideo: Density Experiment with Whiskey and WaterGlass Density Calculation – Calculation of the density of glass at room temperature and of glass melts at 1000 – 1400°CList of Elements of the Periodic Table – Sorted by DensityCalculation of saturated liquid densities for some components*
ttp://www.adamequipment.com/education/Documents/EdExp1.pdf A delicious density experimentWater density calculator Water density for a given salinity and temperature.
Liquid density calculatorSelect a liquid from the list and calculate density as a function of temperature.
Gas density calculatorCalculate 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