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Cubic Crystal Plane Spacing & Miller Indices

Calculate interplanar spacing for a cubic lattice from its lattice constant and signed integer Miller indices, with material presets.

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

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For a cubic lattice with a = 4 Å, the (200) plane spacing is 2 Å.

d(hkl) = a / √(h² + k² + l²)

Enter these known values and leave the other values blank.

The formula applies to cubic unit cells. Other crystal systems require their full lattice metric.
Miller indices are integers and cannot all be zero. Signed indices give the same spacing when their magnitudes match.
Material presets are rounded lattice constants without temperature or composition corrections. Use a measured value when those effects matter.
Spacing alone does not determine allowed diffraction reflections or their intensities. A computed inverse index must satisfy the integer guards.

The formula applies to cubic unit cells. Other crystal systems require their full lattice metric.

Bookify rejects the undefined all-zero Miller-index tuple while retaining signed integer indices.