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Coordination Number Calculator

Work out coordination number instantly with clear inputs, formula shown and shareable results.

About Coordination Number Calculator

Coordination number counts the touching neighbours around one atom, and it is fixed by the lattice: six for simple cubic, eight for body-centred cubic, twelve for both close-packed structures and only four for diamond. Since neighbours touch, the centre-to-centre distance is twice the atomic radius regardless of structure - 256 pm for copper's 128 pm radius.

Formulas

Nearest neighbour distance

d = 2r for touching spheres

Structure relations

SC: CN 6; BCC: CN 8; FCC/HCP: CN 12; diamond: CN 4

Worked example

With the default values below, Coordination Number Calculator returns Coordination Number of 12. Change any input above and every figure here is recalculated in your browser.

Inputs used

Crystal structureone of Simple cubic, Body-centred cubic, Face-centred cubic / cubic close packed, Hexagonal close packed, Diamond cubic
Face-centred cubic / cubic close packed
Atomic radiusminimum 0 pm
128 pm

Results

Coordination Number
12
Atoms Per Unit Cell
4
Packing Efficiency
74.05%
Nearest Neighbour Distance
256.0 pm

Step by step

  1. 1Values used
  2. 2Nearest neighbour distance
  3. 3Structure relations
  4. 4Coordination Number= 12
  5. 5Atoms Per Unit Cell= 4
  6. 6Packing Efficiency= 74.05
  7. 7Nearest Neighbour Distance= 256.0 pm

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 2 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 do face-centred cubic and hexagonal close packing share a coordination number?

Both are close packings of spheres - six neighbours in the plane, three above and three below. They differ only in stacking sequence.

Why is diamond so open?

Because bonding is directional. Four covalent bonds at tetrahedral angles cannot be packed densely, leaving only 34% occupancy.

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