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Cubic Lattice Edge from Atomic Radius

Relate hard-sphere atomic radius to simple, body-centered or face-centered cubic cell edges.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Radius 1 Å gives a 2 Å simple-cubic edge.

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

Worked example

Enter these known values and leave the other values blank.

Lattice type
Simple cubic (SC)
Atomic radius (r)
1 Å
Lattice constant (a)
2 Å

Assumptions and limitations

  • The model treats equal atoms as contacting hard spheres in an ideal cubic cell. Atomic radius must refer to the same contact geometry as the lattice.
  • Simple cubic touches along an edge, BCC along the body diagonal and FCC along a face diagonal. Thermal expansion, bonding and distortions can change actual cell parameters.

Common questions

What does this model assume?

The model treats equal atoms as contacting hard spheres in an ideal cubic cell. Atomic radius must refer to the same contact geometry as the lattice.

Can I solve backward?

Clear the unknown value and enter compatible known values. Choices, one-way outputs and singular boundary cases cannot always be inverted.

References

Replace the captured explanatory image with a complete original text account of its formula, axes or contact geometry, preserving every identity and variant condition. No source arithmetic or data changes.

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