Miller Indices Calculator
Calculate interplanar spacing d_hkl for cubic crystal systems from Miller indices and lattice constant.
Miller Indices Calculator
Miller indices $(hkl)$ label crystal planes in a lattice. For cubic crystal systems, the interplanar spacing between parallel planes is:
$$d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$$
where $a$ is the lattice constant in angstroms (Å). This spacing is used in X-ray diffraction, dislocation analysis, and nanofabrication.
Example: for copper ($a = 3.615$ Å) and plane (201), $d = 3.615 / \sqrt{2^2+0^2+1^2} \approx 0.8944$ Å.
See also the Lattice Energy Calculator and Molar Mass Calculator.
Frequently Asked Questions
What are Miller indices?
Miller indices are three integers (h, k, l) that describe the orientation of a crystal plane relative to the unit cell axes.
Which crystal systems does this formula cover?
This calculator uses the cubic form where all three lattice parameters are equal and angles are 90°. Other systems need different formulas.
How do I get Miller indices from intercepts?
Take reciprocals of the axis intercepts, clear fractions to integers, and use those as h, k, and l. Negative intercepts are shown with a bar over the index.
Why is interplanar distance important?
It links crystal structure to diffraction angles (Bragg's law) and helps analyze plastic deformation, thin films, and material orientation.
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