One relationship, three ways to solve it
Density is mass per unit of volume. The three forms are the same equation rearranged: give the solver any two of density, mass and volume and it returns the third. The only rule is that all three must be in consistent units before you divide or multiply.
Density of common materials
| Material | g/cm³ | kg/m³ |
|---|---|---|
| Gold | 19.3 | 19,300 |
| Lead | 11.3 | 11,300 |
| Copper | 8.96 | 8,960 |
| Iron / steel | 7.85–7.87 | 7,850–7,870 |
| Aluminum | 2.70 | 2,700 |
| Concrete | 2.40 | 2,400 |
| Water (4°C) | 1.000 | 1,000 |
| Ice | 0.917 | 917 |
| Oak wood | 0.75 | 750 |
| Gasoline | 0.74 | 740 |
| Air (STP) | 0.0012 | 1.2 |
A handy anchor: 1 cm³ of water weighs 1 g. Most metals are roughly 8 times denser than water, wood is about 0.7 times, and gases at ordinary pressure are around 1000 times thinner.
Two units, and what floats
- kg/m³ vs g/cm³ — they differ by a factor of 1000, so 1000 kg/m³ is 1.0 g/cm³. Slipping between them is the classic error.
- Floats or sinks — anything less dense than the liquid floats. Ice (917) and oak (750) float on water (1000); gold and iron sink.
- Temperature shifts it — most materials expand and get less dense when heated. Water is the oddity: it peaks at 4°C, which is why ice is lighter than the liquid and floats.
Common questions
What is the formula linking density, mass and volume?
Density equals mass divided by volume. Rearranged, mass equals density times volume, and volume equals mass divided by density. Knowing any two lets you solve for the third.
What is the density of water?
Pure water is 1000 kg/m3, which is the same as 1.0 g/cm3 or 1.0 g/mL, at 4 degrees Celsius where it is densest. At room temperature it drops slightly to about 998 kg/m3.
How do I convert density from kg/m3 to g/cm3?
Divide by 1000. Copper at 8960 kg/m3 is 8.96 g/cm3. Going the other way, multiply g/cm3 by 1000 to get kg/m3. Mixing up these two units by a factor of 1000 is the most common density mistake.
