Density, Mass and Volume
One formula ties all three together: density = mass ÷ volume (ρ = m/V). Rearrange it and you can find whichever quantity you are missing — mass = ρV, or volume = m/ρ. This is how you turn a weight into a volume, or check whether something will float.
The relationship
Density measures how much mass is packed into a given space. A cubic centimetre of lead weighs far more than a cubic centimetre of cork because lead is denser. The three quantities are locked together by a single equation:
where ρ (rho) is density, m is mass, and V is volume. Because it is one equation with three variables, knowing any two gives you the third.
The density triangle
The classic memory aid puts mass in the top of a triangle, with density and volume sharing the bottom. Cover the quantity you want with a finger, and the triangle shows the formula:
| Cover… | You get | Formula |
|---|---|---|
| Mass (top) | density × volume | m = ρ × V |
| Density (bottom left) | mass ÷ volume | ρ = m / V |
| Volume (bottom right) | mass ÷ density | V = m / ρ |
Finding volume from weight
This is the most useful rearrangement in practice. If you know how much something weighs and what it is made of, you can find its volume without measuring a single dimension.
Worked example. You have 500 g of aluminium (density 2.70 g/cm³). Its volume is:
The density–mass–volume calculator solves for whichever field you leave blank and includes a density table, so you do not need to look the figure up separately.
Common densities
| Material | Density (g/cm³) | Density (kg/m³) |
|---|---|---|
| Cork | 0.24 | 240 |
| Water (4 °C) | 1.00 | 1,000 |
| Aluminium | 2.70 | 2,700 |
| Steel | 7.85 | 7,850 |
| Lead | 11.34 | 11,340 |
| Gold | 19.32 | 19,320 |
Anything with a density below 1 g/cm³ floats on water; anything above sinks. That single comparison is why cork bobs and lead drops.
Keeping units straight
The three units must match. Use g with cm³ and g/cm³ together, or kg with m³ and kg/m³ together — never mix the two systems in one calculation. If your density is in g/cm³ but your mass is in kilograms, convert one first. Water is the easy reference point: 1 g/cm³ is the same density as 1,000 kg/m³.
Frequently asked questions
What is the formula linking density, mass and volume?
Density = mass ÷ volume, written ρ = m/V. Rearranged, mass = density × volume, and volume = mass ÷ density. Knowing any two lets you find the third.
How do you find volume from mass and density?
Divide the mass by the density: V = m ÷ ρ. For example, 500 g of a material with density 2.5 g/cm³ has a volume of 500 ÷ 2.5 = 200 cm³.
What is the density triangle?
A memory aid with mass on top and density and volume on the bottom. Cover the quantity you want: cover mass to see density × volume, or cover volume to see mass ÷ density.
What units are used for density?
Commonly g/cm³ or kg/m³. Water is 1 g/cm³ or 1,000 kg/m³. Keep mass and volume units consistent with the density unit you use.