This calculator finds the theoretical density of a crystalline solid from the properties of its unit cell, a key calculation in materials science and solid-state chemistry. Crystals are built from a repeating three-dimensional pattern, and the smallest repeating block is the unit cell. Remarkably, if you know just three things about that tiny cell, you can predict the density of the whole bulk material. Those three things are the number of atoms contained in the unit cell, which depends on the crystal structure, two for body-centred cubic, four for face-centred cubic, one for simple cubic, the molar mass of the element or compound, and the lattice parameter, the edge length of the cubic cell, usually measured in angstroms from X-ray diffraction. The density follows because the cell's mass, the atoms it contains divided by Avogadro's number, sits within its volume, the edge length cubed. This tool does the calculation. You enter the number of atoms per cell, the molar mass in grams per mole, and the lattice parameter in angstroms, and the calculator returns the density in grams per cubic centimetre and kilograms per cubic metre, along with the cell volume and the mass per cell. The results update as you type. Use it for materials science and chemistry study, to predict a material's density, or to check experimental results against theory. A powerful application: comparing the calculated density with a measured one reveals defects such as vacancies in the crystal, since missing atoms lower the real density below the ideal. As a check, entering the values for copper, a face-centred cubic metal, returns very close to its known density of about 8.96 grams per cubic centimetre.
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8.97 g/cm³
theoretical density
In kg/m³8,972
Cell volume4.705e-23 cm³
Mass per cell4.221e-22 g
Density = (Z x M) / (Avogadro x a³), with a in cm (1 Å = 10^-8 cm). Z is atoms per cell: 1 simple cubic, 2 BCC, 4 FCC. Avogadro = 6.022 x 10^23.
How it works
The mass of one unit cell is the number of atoms it contains times the molar mass, divided by Avogadro's number. The volume of the cubic cell is the lattice parameter cubed, after converting from angstroms to centimetres. Dividing the cell mass by the cell volume gives the theoretical density of the crystal.
Worked example
Copper has a face-centred cubic structure with 4 atoms per cell, a molar mass of 63.55 grams per mole and a lattice parameter of 3.61 angstroms. The cell volume is (3.61 times 10 to the minus 8 centimetres) cubed, about 4.705 times 10 to the minus 23 cubic centimetres. The density works out to about 8.97 grams per cubic centimetre, matching copper's known value.
