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# DENSITY

The density of a material is defined as its mass per unit volume. The symbol of density is ρ

### 1. Formula

Mathematically: where: (rho) is the density, is the mass, is the volume.

Different materials usually have different densities, so density is an important concept regarding buoyancy, metal purity and packaging.

In some cases density is expressed as the dimensionless quantities specific gravity (SG) or relative density (RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas.

### 2. History

In a well-known story, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a 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 weight; but the king did not approve of this.

Baffled, Archimedes took a relaxing immersion bath and observed from the rise of the warm water upon entering that he could calculate the volume of the gold crown through the displacement of the water. Allegedly, upon this discovery, he went running naked through the streets shouting, "Eureka! Eureka!" (Greek "I found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

This 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.  

### 3. Measurement of density

For a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. Hydrostatic weighing is a method that combines these two.

If the body is not homogeneous or heterogeneous, the density is a function of the coordinates , where is elementary volume with coordinates . The mass of the body then can be expressed as ,

where the integration is over the volume of the body V.

A very common instrument for the direct measurement of the density of a liquid is the hydrometer, which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a pycnometer; a related device for measuring the absolute density of a solid is a gas pycnometer. Another instrument used to determine the density of a liquid or a gas is the digital density meter - based on the oscillating U-tube principle.

The density of a solid material can be ambiguous, depending on exactly how its volume is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be low; when the same sand is compacted into the same container, it will occupy less volume and consequently exhibit a greater density. This is because sand, like all powders and granular solids contains a lot of air space in between individual grains; this overall density is called the bulk density, which differs significantly from the density of an individual grain of sand.

### 4. Common units

The SI unit for density is:

• kilograms per cubic metre (kg/m³)

The following non-SI metric units all have exactly the same numerical value, 1000 times the SI value in (kg/m³). Liquid water has a density of about 1kg/L (exactly 1.000 kg/L by definition at 4 °C), making any of these units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/L.; density is usually given in these units rather than the SI unit.

• kilograms per litre (kg/L).
• kilograms per cubic decimeter (kg/dm³),
• grams per millilitre (g/mL),
• grams per cubic centimeter (g/cc or g/cm³).

In U.S. customary units density can be stated in:

• Avoirdupois ounces per cubic inch (oz/cu in)
• Avoirdupois pounds per cubic inch (lb/cu in)
• pounds per cubic foot (lb/cu ft)
• pounds per cubic yard (lb/cu yd)
• pounds per U.S. liquid gallon or per U.S. dry gallon (lb/gal)
• pounds per U.S. bushel (lb/bu)
• slugs per cubic foot.

In principle there are Imperial units different from the above as the Imperial gallon and bushel differ from the U.S. units, but in practice they are no longer used, though found in older documents. The density of precious metals could conceivably be based on Troy ounces and pounds, a possible cause of confusion.

### 5. Changes of density

In general density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalisation. For example, the density of water increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility for a liquid or solid is 10-6bar-1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10-5K-1.

In contrast, the density of gases is strongly affected by pressure. Boyle's law says that the density of an ideal gas is given by where is the universal gas constant, is the pressure, the molar mass, and the absolute temperature.

This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.

Osmium is the densest known substance at standard conditions for temperature and pressure.

### 6. Density of water

Temp (°C)Density (kg/m3)
100958.4
80971.8
60983.2
40992.2
30995.6502
25997.0479
22997.7735
20998.2071
15999.1026
10999.7026
4999.9720
0999.8395
−10998.117
−20993.547
−30983.854
The density of water in kilograms per cubic meter (SI unit)
at various temperatures in degrees Celsius.
The values below 0 °C refer to
supercooled water.

### 7. Density of air

T in °C ρ in kg/m 3 (at 1 atm) -25 1.423 -20 1.395 -15 1.368 -10 1.342 -5 1.316 0 1.293 5 1.269 10 1.247 15 1.225 20 1.204 25 1.184 30 1.164 35 1.146

### 8. Density of solutions

The density of a solution is the sum of the mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component ρi in a solution can be called partial density of that component.

### 9. Density of composite material

ASTM specification D792-00  describes the steps to measure the density of a composite material. where: is the density of the composite material, in g/cm3

and is the weight of the specimen when hung in the air is the weight of the partly immersed wire holding the specimen is the weight of the specimen when immersed fully in distilled water, along with the partly immersed wire holding the specimen is the density in g/cm3 of the distilled water at 23°C

# DENSITY

The density of a material is defined as its mass per unit volume: $\rho = \frac{m}{V}$

Different materials usually have different densities, so density is an important concept regarding buoyancy, metal purity and packaging.

In some cases density is expressed as the dimensionless quantities specific gravity or relative density, in which case it is expressed in multiples of the density of some other standard material, usually water or air.

## History

In a well known issue, Archimedes were given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a wreath dedicated to the gods and replacing it with another, cheaper alloy.

Archimedes knew that the irregular shaped wreath could be smashed into a cube, where the volume could be calculated more easily when compared with the weight; the king did not approve of this.

Baffled, Archimedes took a bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the displacement of the water. Allegedly, upon this discovery, Archimedes went running though the streets in the nude shouting, "Eureka! Eureka!" (Greek "I found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

This 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

For a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid.

If the body is inhomogeneous, the density is a function of the coordinates $\rho(\vec{r})=dm/dv$, where dv is elementary volume with coordinates $\vec{r}$. The mass of the body then can be expressed as $m = \int_V \rho(\vec{r})dv$,

where the integration is over the volume of the body V.

A very common instrument for the direct measurement of the density of a liquid is the hydrometer, which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a pycnometer; a related device for measuring the absolute density of a solid is a gas pycnometer. Another instrument used to determine the density of a liquid or a gas is the digital density meter - based on the oscillating U-tube principle.

The density of a solid material can be ambiguous, depending on exactly how its volume is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be low; when the same sand is compacted into the same container, it will occupy less volume and consequently exhibit a greater density. This is because sand, like all powders and granular solids contains a lot of air space in between individual grains; this overall density is called the bulk density, which differs significantly from the density of an individual grain of sand.

## Common units

SI units for density are:

• kilograms per cubic metre (kg/m³)
• grams per cubic centimetre (g/cm³)

Units outside the SI

• kilograms per litre (kg/L). Water generally has a density around 1 kg/L, making this a convenient unit.
• grams per millilitre (g/mL), which is equivalent to (g/cm³).
• grams per cubic centimeter (g/cc)

They also happen to be numerically equivalent to kg/L (1 kg/L = 1 g/cm³ = 1 g/mL).

In U.S. customary units or Imperial units, the units of density include:

• ounces per cubic inch (oz/cu in)
• pounds per cubic inch (lb/cu in)
• pounds per cubic foot (lb/cu ft)
• pounds per cubic yard (lb/cu yd)
• pounds per gallon (for U.S. or imperial gallons) (lb/gal)
• pounds per U.S. bushel (lb/bu)
• slugs per cubic foot.

## Changes of density

In general density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalisation. For example, the density of water increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility for a liquid or solid is 10–6 bar–1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10–5 K–1.

In contrast, the density of gases is strongly affected by pressure. Boyle's law says that the density of an ideal gas is given by $\rho = \frac {MP}{RT}$

where R is the universal gas constant, P is the pressure, M the molar mass, and T the absolute temperature.

This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.

Iridium is the densest known substance at standard conditions for temperature and pressure.

## Density of water

Temp (°C)Density (g/cm3)
1000.9584
800.9718
600.9832
400.9922
300.9956502
250.9970479
220.9977735
200.9982071
150.9991026
100.9997026
40.9999720
00.9998395
−100.998117
−200.993547
−300.983854
The density of water in grams per cubic centimeter
at various temperatures in degrees Celsius 
The values below 0 °C refer to
supercooled water.

Water - Density and Specific Weight

See Water Density

## Density of air

T in °Cρ in kg/m³ (at 1 atm)
–101.342
–51.316
01.293
51.269
101.247
151.225
201.204
251.184
301.165

## Density of solutions

The density of a solution is the sum of the mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component ρi in a solution can be called partial density of that component.

## Density of composite material

ASTM specification D792-00 describes the steps to measure the density of a composite material. $\rho = \frac{W_a}{W_a + W_w - W_b} \left (0.9975 \right ) \$

where:

ρ is the density of the composite material, in g/cm3

and

Wa is the weight of the specimen when hung in the air
Ww is the weight of the specimen when immersed fully in distilled water, along with the partly immersed wire holding the specimen
Wb is the weight of the partly immersed wire holding the specimen
0.9975 is the density in g/cm3 of the distilled water at 23°C

## Densities of various materials

Materialρ in kg/m³Notes
Interstellar medium10-25 − 10-15Assuming 90% H, 10% He; variable T
Earth's atmosphere1.2At sealevel
Aerogel1 − 2
Styrofoam30 − 120From
Cork220 − 260From
Water1000At STP
Plastics850 − 1400For polypropylene and PETE/PVC
The Earth5515.3Mean density
Copper8920 − 8960Near room temperature
The Inner Core~13000As listed in Earth
Uranium19100Near room temperature
Iridium22500Near room temperature
The core of the Sun~150000
Atomic nuclei~3 × 1017As listed in neutron star
Neutron star8.4 × 1016 − 1 × 1018
Black hole2 × 1030Mean density inside the Schwarzschild radius of an earth-mass black hole (theoretical)

# DENSITY

The density of a material is defined as its mass per unit volume: $\rho = \frac{m}{V}$

Different materials usually have different densities, so density is an important concept regarding buoyancy, metal purity and packaging.

In some cases density is expressed as the dimensionless quantities specific gravity or relative density, in which case it is expressed in multiples of the density of some other standard material, usually water or air.

## History

In a well-known story, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a 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 weight; but the king did not approve of this.

Baffled, Archimedes took a bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the displacement of the water. Allegedly, upon this discovery, he went running naked though the streets shouting, "Eureka! Eureka!" (Greek "I found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

This 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

For a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid.

If the body is inhomogeneous, the density is a function of the coordinates $\rho(\vec{r})=dm/dv$, where dv is elementary volume with coordinates $\vec{r}$. The mass of the body then can be expressed as $m = \int_V \rho(\vec{r})dv$,

where the integration is over the volume of the body V.

A very common instrument for the direct measurement of the density of a liquid is the hydrometer, which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a pycnometer; a related device for measuring the absolute density of a solid is a gas pycnometer. Another instrument used to determine the density of a liquid or a gas is the digital density meter - based on the oscillating U-tube principle.

The density of a solid material can be ambiguous, depending on exactly how its volume is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be low; when the same sand is compacted into the same container, it will occupy less volume and consequently exhibit a greater density. This is because sand, like all powders and granular solids contains a lot of air space in between individual grains; this overall density is called the bulk density, which differs significantly from the density of an individual grain of sand.

## Common units

The SI unit for density is:

• kilograms per cubic metre (kg/m³)

Metric units outside the SI

• kilograms per litre (kg/L). Water generally has a density around 1 kg/L, making this a convenient unit.
• kilograms per cubic decimeter (kg/dm³)
• grams per millilitre (g/mL),
• grams per cubic centimeter (g/cc or g/cm³).

These are numerically equivalent to kg/L (1 kg/L = 1 kg/dm³ = 1 g/cm³ = 1 g/mL).

In U.S. customary units or Imperial units, the units of density include:

• ounces per cubic inch (oz/cu in)
• pounds per cubic inch (lb/cu in)
• pounds per cubic foot (lb/cu ft)
• pounds per cubic yard (lb/cu yd)
• pounds per gallon (for U.S. or imperial gallons) (lb/gal)
• pounds per U.S. bushel (lb/bu)
• slugs per cubic foot.

## Changes of density

In general density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalisation. For example, the density of water increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility for a liquid or solid is 10–6 bar–1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10–5 K–1.

In contrast, the density of gases is strongly affected by pressure. Boyle's law says that the density of an ideal gas is given by $\rho = \frac {MP}{RT}$

where R is the universal gas constant, P is the pressure, M the molar mass, and T the absolute temperature.

This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.

Iridium is the densest known substance at standard conditions for temperature and pressure.

## Density of water

Temp (°C)Density (g/cm3)
1000.9584
800.9718
600.9832
400.9922
300.9956502
250.9970479
220.9977735
200.9982071
150.9991026
100.9997026
40.9999720
00.9998395
−100.998117
−200.993547
−300.983854
The density of water in grams per cubic centimeter
at various temperatures in degrees Celsius
The values below 0 °C refer to
supercooled water.

Water - Density and Specific Weight

## Density of air

T in °Cρ in kg/m3 (at 1 atm)
–101.342
–51.316
01.293
51.269
101.247
151.225
201.204
251.184
301.165

## Density of solutions

The density of a solution is the sum of the mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component ρi in a solution can be called partial density of that component.

## Density of composite material

ASTM specification D792-00 describes the steps to measure the density of a composite material. $\rho = \frac{W_a}{W_a + W_w - W_b} \left (0.9975 \right ) \$

where:

ρ is the density of the composite material, in g/cm3

and

Wa is the weight of the specimen when hung in the air
Ww is the weight of the specimen when immersed fully in distilled water, along with the partly immersed wire holding the specimen
Wb is the weight of the partly immersed wire holding the specimen
0.9975 is the density in g/cm3 of the distilled water at 23°C

## Densities of various materials

Materialρ in kg/m3Notes
Interstellar medium10-25 − 10-15Assuming 90% H, 10% He; variable T
Earth's atmosphere1.2At sealevel
Aerogel1 − 2
Styrofoam30 − 120From
Cork220 − 260From
Water1000At STP
Plastics850 − 1400For polypropylene and PETE/PVC
The Earth5515.3Mean density
Copper8920 − 8960Near room temperature
The Inner Core~13000As listed in Earth
Uranium19100Near room temperature
Iridium22500Near room temperature
The core of the Sun~150000
Atomic nuclei~3 × 1017As listed in neutron star
Neutron star8.4 × 1016 − 1 × 1018
Black hole2 × 1030Mean density inside the Schwarzschild radius of an earth-mass black hole (theoretical)

# DENSITY

The density of a material is defined as its mass per unit volume: $\rho = \frac{m}{V}$

Different materials usually have different densities, so density is an important concept regarding buoyancy, metal purity and packaging.

In some cases density is expressed as the dimensionless quantities specific gravity or relative density, in which case it is expressed in multiples of the density of some other standard material, usually water or air.

## History

In a well known issue, Archimedes were given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a wreath dedicated to the gods and replacing it with another, cheaper alloy.

Archimedes knew that the irregular shaped wreath could be smashed into a cube, where the volume could be calculated more easily when compared with the weight; the king did not approve of this.

Baffled, Archimedes took a bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the displacement of the water. Allegedly, upon this discovery, Archimedes went running though the streets in the nude shouting, "Eureka! Eureka!" (Greek "I found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

This 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

For a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid.

If the body is inhomogeneous, the density is a function of the coordinates $\rho(\vec{r})=dm/dv$, where dv is elementary volume with coordinates $\vec{r}$. The mass of the body then can be expressed as $m = \int_V \rho(\vec{r})dv$,

where the integration is over the volume of the body V.

A very common instrument for the direct measurement of the density of a liquid is the hydrometer, which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a pycnometer; a related device for measuring the absolute density of a solid is a gas pycnometer. Another instrument used to determine the density of a liquid or a gas is the digital density meter - based on the oscillating U-tube principle.

The density of a solid material can be ambiguous, depending on exactly how its volume is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be low; when the same sand is compacted into the same container, it will occupy less volume and consequently exhibit a greater density. This is because sand, like all powders and granular solids contains a lot of air space in between individual grains; this overall density is called the bulk density, which differs significantly from the density of an individual grain of sand.

## Common units

SI units for density are:

• kilograms per cubic metre (kg/m³)
• grams per cubic centimetre (g/cm³)

Units outside the SI

• kilograms per litre (kg/L). Water generally has a density around 1 kg/L, making this a convenient unit.
• grams per millilitre (g/mL), which is equivalent to (g/cm³).
• grams per cubic centimeter (g/cc)

They also happen to be numerically equivalent to kg/L (1 kg/L = 1 g/cm³ = 1 g/mL).

In U.S. customary units or Imperial units, the units of density include:

• ounces per cubic inch (oz/cu in)
• pounds per cubic inch (lb/cu in)
• pounds per cubic foot (lb/cu ft)
• pounds per cubic yard (lb/cu yd)
• pounds per gallon (for U.S. or imperial gallons) (lb/gal)
• pounds per U.S. bushel (lb/bu)
• slugs per cubic foot.

## Changes of density

In general density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalisation. For example, the density of water increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility for a liquid or solid is 10–6 bar–1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10–5 K–1.

In contrast, the density of gases is strongly affected by pressure. Boyle's law says that the density of an ideal gas is given by $\rho = \frac {MP}{RT}$

where R is the universal gas constant, P is the pressure, M the molar mass, and T the absolute temperature.

This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.

Iridium is the densest known substance at standard conditions for temperature and pressure.

## Density of water

Temp (°C)Density (g/cm3)
1000.9584
800.9718
600.9832
400.9922
300.9956502
250.9970479
220.9977735
200.9982071
150.9991026
100.9997026
40.9999720
00.9998395
−100.998117
−200.993547
−300.983854
The density of water in grams per cubic centimeter
at various temperatures in degrees Celsius 
The values below 0 °C refer to
supercooled water.

Water - Density and Specific Weight

See Water Density

## Density of air

T in °Cρ in kg/m³ (at 1 atm)
–101.342
–51.316
01.293
51.269
101.247
151.225
201.204
251.184
301.165

## Density of solutions

The density of a solution is the sum of the mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component ρi in a solution can be called partial density of that component.

## Density of composite material

ASTM specification D792-00 describes the steps to measure the density of a composite material. $\rho = \frac{W_a}{W_a + W_w - W_b} \left (0.9975 \right ) \$

where:

ρ is the density of the composite material, in g/cm3

and

Wa is the weight of the specimen when hung in the air
Ww is the weight of the specimen when immersed fully in distilled water, along with the partly immersed wire holding the specimen
Wb is the weight of the partly immersed wire holding the specimen
0.9975 is the density in g/cm3 of the distilled water at 23°C

## Densities of various materials

Materialρ in kg/m³Notes
Interstellar medium10-25 − 10-15Assuming 90% H, 10% He; variable T
Earth's atmosphere1.2At sealevel
Aerogel1 − 2
Styrofoam30 − 120From
Cork220 − 260From
Water1000At STP
Plastics850 − 1400For polypropylene and PETE/PVC
The Earth5515.3Mean density
Copper8920 − 8960Near room temperature
The Inner Core~13000As listed in Earth
Uranium19100Near room temperature
Iridium22500Near room temperature
The core of the Sun~150000
Atomic nuclei~3 × 1017As listed in neutron star
Neutron star8.4 × 1016 − 1 × 1018
Black hole2 × 1030Mean density inside the Schwarzschild radius of an earth-mass black hole (theoretical)

# DENSITY

In physics, density is mass (m) per unit volume (V) — the ratio of the amount of matter in an object compared to its volume. A small, heavy object, such as a rock or a lump of lead, is denser than a larger object of the same mass, such as a piece of cork or foam.

In the common case of a homogeneous substance, density is expressed as: $\rho = \frac {m}{V}$

where, in SI Units:

ρ (rho) is the density of the substance, measured in kg·m–3
m is the mass of the substance, measured in kg
V is the volume of the substance, measured in m3

In some cases the density is expressed as a specific gravity or relative density, in which case it is expressed in multiples of the density of some other standard material, usually water or air.

#### History

In a well known problem, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a wreath dedicated to the gods and replacing it with another, cheaper alloy.

Archimedes knew that the irregular shaped wreath could be smashed into a cube or sphere, where the volume could be calculated more easily when compared with the weight; the king did not approve of this.

Baffled, Archimedes went to take a bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the displacement of the water. Allegedly, upon this discovery, Archimedes went running though the streets in the nude shouting, "Eureka! Eureka!" (Greek "I have found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

This 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.

The true genius of Archimedes' solution lay not in the recognition that different materials displace different volumes, but in the manner in which he determined the displacement. It is an easy experiment to weigh an object twice, once when it rests on the bottom of a container of water, and a second when it is suspended by a thin thread so that it is entirely under water without touching the sides or bottom of the container. The density is the ratio of these two weights, because the second weight is simply the volume of water displaced.

## Measurement of density

For a homogeneous object, the formula mass/volume may be used. The mass is normally measured with an appropriate scale; the volume may be measured directly (from the geometry of the object) or by the displacement of a liquid. A very common instrument for the direct measurement of the density of a liquid is the hydrometer. A less common device for measuring fluid density is a pycnometer, a similar device for measuring the absolute density of a solid is a gas pycnometer.

Another possibility for determining the density of a liquid or a gas is the measurement with a digital density meter - based on the oscillating U-tube principle.

The density of a solid material can be ambiguous, depending on exactly how it is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be small; when the same sand is compacted into the same container, it will occupy less volume and consequently carry a greater density. This is because "sand" contains a lot of air space in between individual grains; this overall density is called the bulk density, which differs significantly from the density of an individual grain of sand.

## Common units

SI units for density are:

• kilograms per cubic meter (kg/m3)
• grams per cubic centimeter (g/cm3) (1 g/cm3 = 1000 kg/m3)
• grams per milliliter (g/ml) (1 ml = 1 cm3)

In U.S. customary units or Imperial units, the units of density include:

• ounces per cubic inch (oz/in3)
• pounds per cubic inch (lb/in3)
• pounds per cubic foot (lb/ft3)
• pounds per cubic yard (lb/yd3)
• pounds per gallon (for U.S. or imperial gallons) (lb/gal)
• pounds per U.S. bushel (lb/bu)
• slugs per cubic foot.

## Changes of density

In general density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalisation. For example, the density of water increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility for a liquid or solid is 10–6 bar–1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10–5 K–1.

In contrast, the density of gases is strongly affected by pressure. Boyle's law says that the density of an ideal gas is given by $\rho = \frac {MP}{RT}$

where R is the universal gas constant, P is the pressure, M the molar mass, and T the absolute temperature.

This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.

## Density of water

TemperatureDensity (at 1 atm)
°C°Fkg/m³
0.032.0999.8425
4.039.2999.9750
15.059.0999.1026
20.068.0998.2071
25.077.0997.0479
37.098.6993.3316
50.0122.0988.04
100.0212.0958.3665

## Density of air

T in °Cρ in kg/m³ (at 1 atm)
–101.342
–51.316
01.293
51.269
101.247
151.225
201.204
251.184
301.164

## Density of solutions

The density of a solution is the sum of the mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component ρi in a solution can be called partial density of that component. 