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Crystal Lattice Parameter Calculator

Work out crystal lattice parameter instantly with clear inputs, formula shown and shareable results.

About Crystal Lattice Parameter Calculator

The lattice parameter follows from how the touching atoms are arranged along a cube direction: along the edge for simple cubic (a = 2r), along the body diagonal for body-centred cubic (a = 4r/sqrt3), and along the face diagonal for face-centred cubic (a = 4r/sqrt2). Copper's 128 pm radius therefore gives a 362 pm face-centred cell with the maximum 74% packing.

Formulas

Lattice parameter

SC: a = 2r; BCC: a = 4r/sqrt(3); FCC: a = 4r/sqrt(2)

Packing efficiency

packing = atoms x (4/3)pi.r^3 / a^3

Worked example

With the default values below, Crystal Lattice Parameter Calculator returns Lattice Parameter a of 362.04. Change any input above and every figure here is recalculated in your browser.

Inputs used

Atomic radiusminimum 0 pm
128 pm
Crystal structureone of Simple cubic, Body-centred cubic, Face-centred cubic
Face-centred cubic

Results

Lattice Parameter a
362.04 pm
Unit Cell Volume
4.7453 × 10¹ A^3
Packing Efficiency
74.05%
Atoms Per Unit Cell
4

Step by step

  1. 1Values used
  2. 2Lattice parameter
  3. 3Packing efficiency
  4. 4Lattice Parameter a= 362.04 pm
  5. 5Unit Cell Volume= 47.4531 A^3
  6. 6Packing Efficiency= 74.05
  7. 7Atoms Per Unit Cell= 4

Assumptions and limits

  • The result is derived only from the 2 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 face-centred cubic denser than body-centred?

Because the face diagonal packs four atomic radii into a shorter distance relative to the cell edge, giving 74% occupancy against 68%.

What is the densest possible packing?

74.05%, achieved by both face-centred cubic and hexagonal close packing. No arrangement of equal spheres beats it.

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