# Density of Matter

by Ron Kurtus (updated 8 February 2022)

The * density* of a quantity

*is its mass divided by its volume. It is usually measured at 0 °C and at 1 atmosphere of pressure.*

**of matter**Density is important in determining the bouyancy of materials in fliuds, as well as in comparing materials and in other measurements.

The standard unit of density is **kg/m ^{3}**. However, they can also be in

**g/cm**, as well as

^{3}**kg/L**and

**lb/ft**. Gases are usually stated in

^{3}**kg/m**, while liquids and solids are stated in

^{3}**g/cm**.

^{3}The densities of various materials range from **19.3 g/cm ^{3}** for Gold to

**0.09 kg/m**

^{3}^{}for Hydrogen.

Questions you may have include:

- What is the density equation?
- What are the units of density?
- What is the density of various materials?

This lesson will answer those questions. Useful tool: Units Conversion

## Density equation

The density of a material is its mass divided by its volume. The equation for density is

ρ = m/V

where:

**ρ**is the density (**ρ**is the Greek letter**rho**)**m**is the mass**V**is the volume**m/V**is**m**divided by**V**

The volume of a material is affected by its temperature and pressure on the material. Thus, the density can change with different temperatures and pressures.

Also note that mass is not weight, which is mass affected by gravity. Under the same conditions of pressure and temperature, the density of a material is the same on the Earth, Moon and Mars, even though the weight would be different due to different forces of gravity.

## Density units

The units used for density depend on which measurement system you are using.

### Metric units

The International (SI) units for density are kilograms per cubic meter (**kg/m ^{3}**).

When the density is large—such as the case with solids—metric units for density can be stated in grams per cubic centimeter (**g/cm ^{3}**).

Notethat sometimescmis designated as^{3}ccfor cubic centimeters.

Conversion **kg/m ^{3}** to

**g/cm**is as follows:

^{3}1000

g =1kg100

cm =1m1,000,000

cm1^{3}=m^{3}

Thus:

1

kg/m= 1000^{3}g/1,000,000cm^{3}1

kg/m= (1/1000)^{3}g/cm^{3}

Or

1

g/cm1000^{3}=kg/m^{3}

For example, if the density of Gold is 19,300** kg/m ^{3}**, a better way to state that density would be as 19.3

**g/cm**. Just divide the

^{3}**kg/m**value by 1000 to get the

^{3}**g/cm**value.

^{3}### Density of water

The definitions of the sizes of a cubic centimeter and a gram were made such that the density of water in the metric system is equal to 1. It was defined that 1 cubic centimeter of water weighs 1 gram. Thus, the density of pure water is:

ρ = m/V =1gram/1cc =1.0g/cm^{3}

Since a quantity of water changes with temperature, 4°**C, **the point where water is the most contracted, was selected as the temperature of water for this measurement.

### Liquids

Liquids are often and kilograms per liter (**kg/L**) or grams per milliliter (**g/mL**). A milliliter is the volume a liquid and is equal to 1 **cm ^{3}**.

A liter is 1000** mL** and this 1** L = **1000** cm ^{3}**. The reason liters and milliliters are used in finding the density of liquids is that it is easy to measure the volume by pouring the liquid into a standard container.

### English units

The English, Imperial or American units are either pounds per cubic feet (lb/ft^{3}) or pounds per cubic inch (**lb/in ^{3}**). But note that pounds are weight and not mass and some confusion can occur with this designation.

The conversion from English to metric units is:

1

lb/ft16.02^{3}=kg/m^{3}

The different units can be confusing, but you should make certain you are consistent in which one you use.

## Density chart

The following chart allows you to compare the density of various materials under the same conditions of atmospheric pressure and temperature (unless stated otherwise).

The density of solids and liquids are usually stated in **g/cm ^{3}**, while gases are usually in

**kg/m**.

^{3}State | Material | Density (g/cm ^{3}) |
---|---|---|

Solids | ||

Gold | 19.3 | |

Iron | 7.8 | |

Aluminum | 2.7 | |

Ice (0°C) | 0.92 | |

Liquids | ||

Mercury | 13.6 | |

Seawater | 1.03 | |

Water (5°C) | 1.00 | |

Ethyl alcohol | 0.81 | |

Gases | (at normal pressure and a given temperature) |
Density (kg/m ^{3}) |

Air (0°C) | 1.29 | |

Air (10°C) | 1.25 | |

Hydrogen (0°C) | 0.090 | |

Helium (0°C) | 0.178 |

You can see that seawater is slightly denser than pure water. That is why things float better in seawater than regular water.

Also, you can see that warmer air is less dense than cold air. That is why warm air rises. Helium is less dense than air, causing Helium balloons to rise.

## Summary

The density of a quantity of matter is its mass divided by its volume. The equation is **ρ = m/V**. The units of density are typically **kg/m ^{3}**, but they can also have other designations that may be more convenient. The densities of various materials range from large values for heavy metals to very small values for gases.

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## Density of Matter