Density, Mass and Volume Calculator
Enter any two of density, mass and volume and this calculator solves for the third. Choose between metric (kilograms and cubic metres) or imperial (pounds and cubic feet) units. You also get a step-by-step breakdown of the arithmetic, a bar chart comparing the three quantities in their natural units, and a reference table of densities for common materials.
Formula
Worked example
A block of pure water at 4 C has a mass of 1000 kg and occupies exactly 1 cubic metre. Density = 1000 kg / 1 m3 = 1000 kg/m3. To find the volume of 500 kg of the same water: V = 500 kg / 1000 kg/m3 = 0.5 m3. To find the mass of 2 m3: m = 1000 kg/m3 x 2 m3 = 2000 kg.
The density triangle: three formulas in one
Density, mass and volume are related by a single equation: density (rho) equals mass (m) divided by volume (V), written rho = m/V. Rearranging gives two more formulas - m = rho x V for mass, and V = m / rho for volume. These three rearrangements are often shown as a "density triangle" taught in school science. To use this calculator, choose which variable you are solving for, enter the other two, and the result appears instantly. The unit system selector lets you work in metric (kg, m3, kg/m3) or imperial (lb, ft3, lb/ft3) without any manual conversion.
Why density matters in everyday science and engineering
Density determines whether an object floats or sinks: any material less dense than water (1000 kg/m3) floats, and any denser material sinks. Steel ships float because the hollow hull contains air, so the average density of the whole ship-and-air system is below 1000 kg/m3. Engineers use density calculations constantly - to estimate the weight of a metal part from its dimensions, to work out how much liquid a container holds, or to check whether a material is suitable for a given application. In chemistry, density is used to convert between mass and volume when measuring liquids, since volumetric equipment is more accurate than balances for some substances. Geologists use density to identify minerals, jewellers use it to verify precious metals, and the food industry uses it to check the concentration of sugar solutions.
Densities of common substances (kg/m3)
| Substance | Density (kg/m3) | State |
|---|---|---|
| Air (sea level, 20 C) | 1.2 | Gas |
| Water (pure, 4 C) | 1000 | Liquid |
| Sea water (avg) | 1025 | Liquid |
| Concrete | 2300 | Solid |
| Aluminium | 2700 | Solid |
| Iron / Steel | 7870 | Solid |
| Copper | 8960 | Solid |
| Lead | 11340 | Solid |
| Gold | 19300 | Solid |
| Platinum | 21450 | Solid |
Values at standard conditions (roughly 20 C and 1 atm) unless noted. Gases change significantly with temperature and pressure.
Frequently asked questions
How do I calculate density?
Divide the mass of the object by the volume it occupies: density = mass / volume. For example, a 500 g rock that takes up 200 cm3 has a density of 500 / 200 = 2.5 g/cm3. Make sure mass and volume use compatible units so the density unit comes out correctly.
How do I find volume from mass and density?
Rearrange the formula to get V = m / rho. For instance, if you have 8 kg of aluminium (density 2700 kg/m3), the volume is 8 / 2700 = about 0.00296 m3, which is 2960 cm3 (or about 2.96 litres).
How do I find mass from density and volume?
Use m = rho x V. Multiply the density by the volume: a container of 0.5 m3 filled with sea water (density 1025 kg/m3) has a mass of 1025 x 0.5 = 512.5 kg.
Does temperature affect density?
Yes. Most substances expand when heated, so their volume increases while mass stays constant, reducing density. Water is an unusual exception - it reaches its maximum density at 4 degrees Celsius and is slightly less dense both above and below that temperature. For precise work, always note the temperature at which density was measured.
What is the density of water?
Pure water at 4 C has a density of exactly 1000 kg/m3 (or 1 g/cm3). At 20 C it is about 998 kg/m3. Sea water averages about 1025 kg/m3 because dissolved salts increase its mass without proportionally increasing its volume.