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Density of Matter
by Ron Kurtus (revised 15 November 2011)
The density of a quantity of matter is its mass divided by its volume. Density is important in determining the bouyance of materials in fliuds, as well as in comparing materials and in other measurements.
The standard unit of density is kg/m3. However, they can also be in g/cm3, as well as kg/L and lb/ft3. Gases are usually stated in kg/m3, while liquids and solids are stated in g/cm3.
The densities of various materials range from 19.3 g/cm3 for Gold to 0.09 kg/m3 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. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
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. Don't ask me why they use that letter. Someone just decided it was a good idea)
- 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/m3).
When the density is large—such as the case with solids—metric units for density can be stated in grams per cubic centimeter (g/cm3).
Note that sometimes cm3 is designated as cc for cubic centimeters.
Conversion kg/m3 to g/cm3 is as follows:
1000 g = 1 kg
100 cm = 1 m
1,000,000 cm3 = 1 m3
Thus:
1 kg/m3 = 1000 g/1,000,000 cm3
1 kg/m3 = (1/1000) g/cm3
Or
1 g/cm3 =1000 kg/m3
For example, if the density of Gold is 19,300 kg/m3, a better way to state that density would be as 19.3 g/cm3. Just divide the kg/m3 value by 1000 to get the g/cm3 value.
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 = 1 gram/1 cc = 1.0 g/cm3
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 cm3.
A liter is 1000 mL and this 1 L = 1000 cm3. 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/ft3) or pounds per cubic inch (lb/in3). 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/ft3 = 16.02 kg/m3
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/cm3, while gases are usually in kg/m3.
| State | Material | Density (g/cm3) |
|---|---|---|
| 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/m3) |
| 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/m3, 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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Resources and references
The following resources provide information on this subject:
Websites
Books
Top-rated
books on Physical Science
College-level
books on Density Science
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Physics. If you had problems, you had better look over the material again.
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Density of Matter