How to Calculate Mass from Density and Volume
Density describes how much mass is packed into a given volume. The relationship between density, mass and volume is defined as density equals mass divided by volume (rho = m / V). Rearranging this to solve for mass gives the formula used by this calculator: mass equals density multiplied by volume (m = rho x V). As long as you know the density of a substance and the volume you have, you can find the total mass.
The Formula
Mass = Density x Volume
For example, if you have 2 cubic metres of water, and water has a density of 1,000 kg/m3, the mass is 1,000 kg/m3 x 2 m3 = 2,000 kg (2 tonnes). This matches the calculator's default values above.
Keeping Units Consistent
The formula only works correctly if your density and volume units are compatible. This calculator handles the conversion automatically by converting whatever density unit you choose into kilograms per cubic metre, and whatever volume unit you choose into cubic metres, before multiplying them together. The common density unit conversions are:
| Density Unit | Equivalent in kg/m3 |
|---|
| 1 kg/m3 | 1 kg/m3 |
| 1 g/cm3 | 1,000 kg/m3 |
| 1 g/mL | 1,000 kg/m3 |
| 1 kg/L | 1,000 kg/m3 |
| 1 g/L | 1 kg/m3 |
Typical Densities of Common Materials
Water is the reference point most people know: 1,000 kg/m3 (or 1 g/cm3) at around 4 degrees Celsius, though it varies slightly with temperature. Denser materials like steel (7,850 kg/m3) and mercury (13,534 kg/m3) pack far more mass into the same volume. Lighter materials like air (about 1.2 kg/m3 at sea level) pack very little mass into a large volume. These reference values are useful for quick estimates, but for precise engineering or trade work, use the manufacturer's stated density for your specific material or product, since density varies with moisture content, temperature, alloy composition and manufacturing process.
Common Uses
- Estimating the weight of a volume of concrete, sand, aggregate or timber before ordering or transporting it
- Working out the mass of liquid in a tank, drum or container from its known volume
- Checking whether a load will exceed a vehicle's payload or a lifting device's rated capacity
- Science and engineering calculations involving fluids, materials and structural loads
Related Calculators
Sources: Standard physics definition of density (rho = m/V), as used in NCEA and university physics and engineering courses. Material density reference values are typical figures used in engineering handbooks and may vary by grade, temperature and moisture content.
This calculator provides an estimate based on the density value you enter or select. Actual material densities vary with temperature, pressure, moisture content and composition. For engineering, trade or legal purposes, confirm the exact density of your specific material or product.
