Skip to content
ENExplore Calculators

Unit Cell Density Calculator

Work out unit cell density instantly with clear inputs, formula shown and shareable results.

About Unit Cell Density Calculator

A crystal's density is the mass inside one unit cell divided by the cell's volume. The mass is the atoms per cell times the molar mass over the Avogadro constant; the volume is the cube of the edge. Copper with four atoms per face-centred cell, 63.55 g/mol and a 361.5 pm edge comes out at 8.93 g/cm3, matching the measured value.

Formulas

Cell mass

mass = Z x M / NA

Density

rho = Z x M / (NA x a^3)

Worked example

With the default values below, Unit Cell Density Calculator returns Crystal Density of 8.935. Change any input above and every figure here is recalculated in your browser.

Inputs used

Atoms per unit cell (Z)minimum 1
4
Molar massminimum 0 g/mol
63.55 g/mol
Cubic cell edge lengthminimum 0 pm
361.5 pm

Results

Crystal Density
8.935 g/cm3
Unit Cell Volume
4.7242 × 10⁻²³ cm3
Mass Of One Unit Cell
4.2211 × 10⁻²² g
Same Density In SI
8,935.1 kg/m3

Step by step

  1. 1Values used
  2. 2Cell mass
  3. 3Density
  4. 4Crystal Density= 8.935 g/cm3
  5. 5Unit Cell Volume= 0.0000 cm3
  6. 6Mass Of One Unit Cell= 0.0000 g
  7. 7Same Density In SI= 8,935.1 kg/m3

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is this called the X-ray density?

Because the edge length comes from diffraction. Comparing it to the measured bulk density reveals porosity or vacancies.

What Z should I use?

One for simple cubic, two for body-centred cubic, four for face-centred cubic, and eight for the diamond structure.

Related Calculators

Unit Cell Density Calculator | Calcrivo