The Quick Answer
Density is a physical property that measures how much mass is contained in a given volume of a substance, calculated as mass divided by volume (d = m/V).
To calculate density, divide the mass of an object by its volume:
Density = Mass / Volume
A block of aluminum weighing 270 grams with a volume of 100 cm3 has a density of 270 / 100 = 2.7 g/cm3. That single number tells you the material is aluminum, whether it will float, and how heavy any size piece of it will be.
The Density Formula
The core formula and its two rearrangements cover every density problem:
Density = Mass / Volume d = m / V
Mass = Density x Volume m = d x V
Volume = Mass / Density V = m / d
These three forms let you find whichever quantity is unknown when you know the other two.
SI and Common Units
The SI unit for density is kg/m3 (kilograms per cubic meter). In chemistry and everyday use, g/cm3 (grams per cubic centimeter) is more common because the numbers are easier to work with.
The conversion factor is straightforward:
1 g/cm3 = 1,000 kg/m3
Other useful equivalences:
- 1 g/cm3 = 1 g/mL = 1 kg/L
- 1 kg/m3 = 0.001 g/cm3
For example, water's density of 1.00 g/cm3 equals 1,000 kg/m3.
Worked Examples
Example 1: Density of a Solid Block
Problem: A rectangular block of aluminum weighs 270 grams and measures 10 cm x 5 cm x 2 cm. What is its density?
Step 1 -- Find the volume: Volume = length x width x height = 10 x 5 x 2 = 100 cm3
Step 2 -- Apply the formula: d = m / V = 270 g / 100 cm3 = 2.70 g/cm3
Check: The known density of aluminum is 2.70 g/cm3. The measurement matches, confirming the material identity.
Example 2: Density of an Unknown Liquid
Problem: A liquid fills a 500 mL container and has a mass of 650 grams. What is its density, and will it sink in water?
Step 1 -- Note the volume equivalence: 500 mL = 500 cm3
Step 2 -- Apply the formula: d = m / V = 650 g / 500 cm3 = 1.30 g/cm3
Conclusion: Since 1.30 g/cm3 is greater than water's density (1.00 g/cm3), this liquid is denser than water. If the two liquids do not mix, the unknown liquid will sink below the water layer.
Example 3: Finding Mass from Density
Problem: How much does 2 liters of honey weigh?
Step 1 -- Look up the density: Honey has a density of approximately 1.42 g/cm3.
Step 2 -- Convert volume: 2 liters = 2,000 mL = 2,000 cm3
Step 3 -- Rearrange the formula to find mass: m = d x V = 1.42 g/cm3 x 2,000 cm3 = 2,840 grams = 2.84 kg
A 2-liter jar of honey weighs about 2.84 kg (6.26 pounds), noticeably heavier than the same volume of water (2.00 kg).
Material Density Reference Table
The following densities are measured at standard conditions (approximately 20 degrees Celsius, 1 atmosphere) unless otherwise noted. Values come from the CRC Handbook of Chemistry and Physics and NIST Standard Reference Data.
| Material | Density (g/cm3) | Notes |
|---|---|---|
| Air (sea level) | 0.0012 | Gas; varies with altitude and temperature |
| Cork | 0.12 -- 0.24 | Range depends on species and processing |
| Wood (pine) | 0.35 -- 0.55 | Varies by species; most wood floats |
| Ice | 0.917 | At 0 degrees Celsius |
| Water | 1.00 | At 4 degrees Celsius (maximum density) |
| Seawater | 1.025 | Average; varies with salinity |
| Honey | 1.42 | Approximate; depends on water content |
| Glass | 2.4 -- 2.8 | Varies by type (soda-lime, borosilicate) |
| Aluminum | 2.70 | Pure; alloys range 2.63 -- 2.82 |
| Steel | 7.75 -- 8.05 | Varies by alloy; 7.85 is typical for mild steel |
| Copper | 8.96 | Pure copper |
| Lead | 11.34 | Pure lead |
| Gold | 19.32 | Pure gold |
| Osmium | 22.59 | Densest naturally occurring element |
Why Density Matters
Buoyancy and Floating
An object floats in a fluid when its density is lower than the fluid's density. This principle, formalized as Archimedes' principle, explains why ships made of steel (7.85 g/cm3) float: the overall density of the hull including the air-filled interior is less than water (1.00 g/cm3).
The fraction submerged equals the ratio of densities. Ice (0.917 g/cm3) in water (1.00 g/cm3) floats with about 91.7% of its volume below the surface -- which is why roughly nine-tenths of an iceberg is underwater.
Material Identification
Density is a characteristic property of each substance. If you measure an unknown metal sample and find a density of 8.96 g/cm3, you can identify it as copper by comparing against reference tables. Jewelers use this method to verify gold (19.32 g/cm3) versus gold-plated counterfeits.
Quality Control
Manufacturing processes rely on density measurements to check material purity and consistency. A batch of aluminum alloy with an unexpected density may contain impurities or voids. Density testing of concrete, polymers, and ceramics is standard practice in industrial quality assurance.
Special Properties of Water
Water behaves unusually compared to most substances. While nearly all materials contract as they cool and expand as they warm, water reaches its maximum density at 4 degrees Celsius (1.00 g/cm3), not at its freezing point.
Below 4 degrees Celsius, water expands as hydrogen bonds lock molecules into an open crystalline lattice. This is why ice (0.917 g/cm3) is less dense than liquid water and floats. This property is critical for aquatic life: ice forming on the surface insulates the liquid water beneath, preventing lakes and rivers from freezing solid.
How Temperature Affects Density
Density changes with temperature because volume changes while mass stays constant. For most materials, heating causes expansion (volume increases), which decreases density.
Example: Water at 20 degrees Celsius has a density of 0.9982 g/cm3, while water at 80 degrees Celsius has a density of 0.9718 g/cm3 -- a decrease of about 2.6%.
Gases are far more affected by temperature than solids or liquids. Air at 0 degrees Celsius has a density of about 1.293 kg/m3, while at 30 degrees Celsius it drops to approximately 1.164 kg/m3 -- a decrease of about 10%. This density difference drives convection currents, weather patterns, and the design of heating and cooling systems.
Measuring Volume for Irregular Objects
For regular shapes (cubes, spheres, cylinders), calculate volume with geometry formulas. For irregular objects, use water displacement:
- Fill a graduated cylinder partway with water and record the level (V1).
- Carefully submerge the object completely.
- Record the new water level (V2).
- Object volume = V2 - V1.
Example: Water level rises from 50.0 mL to 73.5 mL when a rock is submerged. The rock's volume is 73.5 - 50.0 = 23.5 cm3. If the rock weighs 63.5 grams, its density is 63.5 / 23.5 = 2.70 g/cm3.
This method only works for objects that do not dissolve in or absorb water. For water-soluble or porous materials, use alternative displacement fluids or gas pycnometry.
Common Mistakes
Mixing up mass and weight. Mass (grams, kilograms) measures the amount of matter. Weight (newtons, pounds-force) measures gravitational force. Density uses mass, not weight. On Earth's surface, this distinction rarely causes errors in practice because weight is proportional to mass, but it matters for precise scientific work.
Forgetting unit consistency. If mass is in grams and volume is in liters, the result is g/L, not g/cm3. Always check that your units match before dividing. 1 liter = 1,000 cm3, so g/L = g/cm3 x 1,000... or just keep both in compatible units from the start.
Ignoring temperature. Reporting a density without specifying temperature is incomplete. Reference tables list densities at stated conditions, and your measurements should note the temperature too.
FAQ
What is the formula for density?
Density equals mass divided by volume: d = m / V. Rearranged, mass = density x volume (m = d x V), and volume = mass / density (V = m / d).
What is the density of water?
Pure water at 4 degrees Celsius has a density of exactly 1.00 g/cm3 (1,000 kg/m3). This value decreases slightly as temperature rises -- at 25 degrees Celsius, water's density is about 0.997 g/cm3.
What element has the highest density?
Osmium is the densest naturally occurring element at approximately 22.59 g/cm3, followed closely by iridium at 22.56 g/cm3. Both are platinum-group metals.
Why does ice float on water?
Ice has a density of about 0.917 g/cm3, which is lower than liquid water at 1.00 g/cm3. The hydrogen bonds in ice form an open crystalline lattice that takes up more volume than liquid water, making it less dense.
Is density the same as weight?
No. Weight is the gravitational force on an object (measured in newtons or pounds-force), while density is mass per unit volume (measured in kg/m3 or g/cm3). Two objects can have the same weight but very different densities -- a kilogram of feathers takes up far more space than a kilogram of lead.
How do I measure the volume of an irregular object?
Use water displacement. Partially fill a graduated cylinder, record the water level, submerge the object, and record the new level. The difference equals the object's volume. This technique dates back to Archimedes.
How do I convert g/cm3 to kg/m3?
Multiply by 1,000. For example, aluminum's density of 2.70 g/cm3 equals 2,700 kg/m3. The factor arises because there are 1,000 grams in a kilogram and 1,000,000 cm3 in a m3.
Does density change with temperature?
Yes. Most substances expand when heated, increasing volume while mass stays constant, so density decreases. Water is unusual because it reaches maximum density at 4 degrees Celsius, not at its freezing point.
How can I tell if an object will float?
An object floats in a fluid if its average density is lower than the fluid's density. Wood (0.35--0.55 g/cm3) floats on water (1.00 g/cm3); steel (7.85 g/cm3) sinks. A steel ship floats because its overall density -- including the air inside -- is less than water.
What is the density of air?
Dry air at sea level and 20 degrees Celsius has a density of approximately 0.0012 g/cm3 (1.2 kg/m3). Air density decreases with altitude (about 12% lower per 1,000 meters of elevation) and increases with decreasing temperature.
Related Tools
- Density Calculator -- Calculate density, mass, or volume from any two known values
- Volume Calculator -- Find the volume of common geometric shapes
- Weight Unit Converter -- Convert between grams, kilograms, pounds, and ounces
- Volume Unit Converter -- Convert between liters, gallons, cubic centimeters, and more