Density Calculator
Solve ρ = m / V for density, mass, or volume.
Keep mass and volume units consistent (e.g. g and cm³).
Density is mass divided by volume: ρ = m ÷ V. Rearrange it to find any of the three — m = ρV or V = m ÷ ρ. A 270 g aluminium block occupying 100 cm³ has a density of 270 ÷ 100 = 2.7 g/cm³, which is why aluminium sinks in water (1.0 g/cm³).
Mass packed into a volume
Density is how much mass occupies a given volume: ρ = m / V. It is why a kilogram of lead takes up far less space than a kilogram of feathers, and why some objects float while others sink. Because it is one equation with three variables, any two of them give you the third.
ρ = density (g/cm³), m = mass (g), V = volume (cm³)
Worked example
A block of aluminium has a mass of 270 g and a volume of 100 cm³. Find its density:
- 1 Write the density formula. ρ = m ÷ V, with mass in grams and volume in cm³.
- 2 Substitute the values. ρ = 270 g ÷ 100 cm³.
- 3 Compute the density. ρ = 2.7 g/cm³ — the textbook density of aluminium.
Densities of common materials
At roughly room temperature. Anything denser than its surrounding fluid sinks.
| Material | g/cm³ | kg/m³ |
|---|---|---|
| Cork | 0.24 | 240 |
| Ice | 0.92 | 920 |
| Water | 1.00 | 1000 |
| Aluminium | 2.70 | 2700 |
| Iron | 7.87 | 7870 |
| Lead | 11.34 | 11340 |
| Gold | 19.32 | 19320 |
Units, floating, and common mistakes
Keep units consistent. g/cm³ and kg/m³ are both standard, but never mix them: to convert g/cm³ to kg/m³, multiply by 1000 (water is 1 g/cm³ = 1000 kg/m³).
Why things float: an object floats when its density is less than the fluid around it, so it displaces enough fluid to support its own weight. Ice (0.92 g/cm³) floats on water (1.00 g/cm³); lead does not.
Common mistake: shape does not matter. Density depends only on total mass and total volume — a cube and a sphere of the same material have the same density.