How Do You Calculate the Density of a Cube: Formula and Worked Examples
To calculate the density of a cube, divide its mass by its volume. A cube’s volume is its side length multiplied by itself three times, so the formula is:
Density = mass ÷ side length³
ρ = m ÷ s³
For example, a cube with a mass of 432 g and a side length of 4 cm has a volume of 4³ = 64 cm³. Its density is 432 ÷ 64 = 6.75 g/cm³.
Use compatible units: grams and centimeters give density in g/cm³, while kilograms and meters give density in kg/m³.
Calculate the density step by step
- Measure the cube’s mass.
- Measure the length of one edge. All edges of a true cube are equal.
- Calculate the volume: V = s³.
- Divide the mass by the volume: ρ = m ÷ V.
Here, ρ (rho) represents density, m is mass, V is volume, and s is the cube’s side length.
Cube the side length; don’t square it. For a 5 cm edge, the volume is 5³ = 125 cm³, not 5² = 25 cm³. Measure an edge, not a diagonal.
Worked example
A solid cube has a mass of 432 g and an edge length of 4 cm.
Find the volume:
V = s³
V = 4 cm × 4 cm × 4 cm = 64 cm³
Divide the mass by the volume:
ρ = m ÷ V
ρ = 432 g ÷ 64 cm³ = 6.75 g/cm³
Grams divided by cubic centimeters gives grams per cubic centimeter.
The same density can be expressed in kg/m³. Convert the mass to 0.432 kg and the edge length to 0.04 m. The volume is 0.04³ = 0.000064 m³, so the density is 0.432 ÷ 0.000064 = 6,750 kg/m³. To convert from g/cm³ to kg/m³, multiply by 1,000.
Check units and precision
Keep units consistent. If the edge length is in centimeters and the mass is in kilograms, convert one measurement before calculating. In the metric system, grams and centimeters give g/cm³; kilograms and meters give kg/m³. NIST’s Mass and Density Measurements page provides information on measuring mass and density.
Round the result according to the precision of your measurements. For instance, if an edge is recorded as 4.0 cm, account for that precision in the final density rather than reporting unsupported decimal places.
When the cube is hollow or not a true cube
The formula V = s³ gives the volume of a solid cube. For a hollow cube, the outer dimensions give the volume enclosed by the exterior, not the volume of the material. To find the material’s density, subtract the interior volume from the exterior volume, then divide the mass by the remaining material volume.
For an object that is only roughly cube-shaped, one edge may not give a reliable volume. Use another suitable method to measure its volume, then divide its mass by that volume.
Key Takeaways
- A cube’s density is mass ÷ side length³.
- Measure one edge, cube it to find the volume, then divide the mass by that volume.
- Use compatible units: grams and centimeters give g/cm³; kilograms and meters give kg/m³.
- A cube with a mass of 432 g and a 4 cm edge has a density of 6.75 g/cm³, or 6,750 kg/m³.
- For a hollow cube, use the volume of the material, not the volume enclosed by its outer dimensions.
