Miller Indices Calculator - Convert Crystal Plane Intercepts to (hkl)

Calculate Miller indices (hkl) from crystal plane intercepts. Fast, accurate converter for crystallography, XRD analysis, and materials science. Works for all crystal systems.

Miller Indices Calculator

Crystal Plane Intercepts

Enter the intercepts of the crystal plane with the x, y, and z axes. Use '∞' or 'infinity' for planes parallel to an axis.

Enter a number or ∞ for infinity (parallel to axis)

Enter a number or ∞ for infinity (parallel to axis)

Enter a number or ∞ for infinity (parallel to axis)

Miller Indices

The Miller indices for this plane are:

(1,1,1)
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Visualization

What are Miller Indices?

Miller indices are a notation system used in crystallography to specify planes and directions in crystal lattices.

To calculate Miller indices (h,k,l) from intercepts (a,b,c):

1. Take the reciprocals of the intercepts: (1/a, 1/b, 1/c) 2. Convert to the smallest set of integers with the same ratio 3. If a plane is parallel to an axis (intercept = infinity), its corresponding Miller index is 0

  • Negative indices are indicated with a bar over the number, e.g., (h̄,k,l)
  • The notation (hkl) represents a specific plane, while {hkl} represents a family of equivalent planes
  • Direction indices are written in square brackets [hkl], and families of directions are denoted by <hkl>
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Documentation

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