Calculator of Alexandria

Density calculator

Calculate density from mass and volume, or the mass or volume from density, in g/cm³, kg/m³, lb/ft³ and more.

Solve for

Formula

ρ=mV\rho = \frac{m}{V}
How it's derived

The formula

ρ=mV\rho = \frac{m}{V}

ρ\rho (the Greek letter rho) is density, mm is mass and VV is volume.

Where it comes from

Density is a definition, not a derived law. It answers “how much mass is packed into each unit of volume?” If 20 cm³ of a metal has a mass of 54 g, each cubic centimetre holds 54/20=2.754/20 = 2.7 g.

Because it’s a ratio, density doesn’t depend on how much material you have. A paper clip and a girder of the same steel have the same density. That makes it useful for identifying materials and for converting between mass and volume:

m=ρ Vm = \rho\,V V=mρV = \frac{m}{\rho}

Worked example

A block measures 20 cm³ and weighs 54 g:

ρ=54 g20 cm3=2.7 g/cm3\rho = \frac{54\ \text{g}}{20\ \text{cm}^3} = 2.7\ \text{g/cm}^3

That matches aluminium.

Converting units

The units look different but are simple multiples:

  • 1 g/cm3=1 g/mL=1 kg/L=1000 kg/m31\ \text{g/cm}^3 = 1\ \text{g/mL} = 1\ \text{kg/L} = 1000\ \text{kg/m}^3
  • Water is about 1.00 g/cm31.00\ \text{g/cm}^3 near room temperature, and 62.4 lb/ft362.4\ \text{lb/ft}^3.

Watch out for

  • Temperature. Most substances expand when heated, so density drops slightly. Water is densest at about 4 °C.
  • Porous or packed materials. Flour, soil and gravel have a “bulk density” that includes the air between grains. It’s much lower than the density of the solid itself.

Sources

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