Miller Indices Explorer — Crystal Planes

Lattice Type

Miller Indices (h k l)

h 1

k 1

l 1

Layer offset n 0

Lattice parameter a (Å) 4.00

Plane Data

(1 1 1) plane

d-spacing d_hkl

0.00 Å

Family multiplicity

Axis intercepts (×a)

1, 1, 1

How it works

A crystal plane is labelled by its Miller indices (hkl): take the plane's intercepts on the a, b, c axes in units of the lattice parameter, invert each, and clear fractions. A plane through 1, 1, ∞ becomes (110); through 1, 1, 1 becomes (111).

Intercepts:  a/h,  a/k,  a/l   (∞ when an index is 0)
Cubic spacing:  d_hkl = a / √(h² + k² + l²)
Family {hkl}: all sign/permutation equivalents of (hkl)

h, k, l sliders — set the Miller indices; the shaded plane re-orients to satisfy h·x + k·y + l·z = n·d_hkl in units of the cell edge.
Layer offset n — steps the same family of parallel planes outward from the origin, spaced by d_hkl apart, showing that (hkl) names an infinite stack, not a single sheet.
Lattice parameter a — the real cell edge length; d_hkl is reported in Å using this value, the same quantity X-ray diffraction measures via Bragg's law λ = 2d sinθ.
Lattice type — Simple Cubic / BCC / FCC changes only which atoms sit in each cell (corner-only, +body-center, +face-centers); the plane geometry itself is a property of the indices and the cubic cell shape, not the basis.
Show plane family — draws every symmetry-equivalent plane of {hkl} at once, and the multiplicity readout counts how many there are (48 for a generic hkl in a cube, fewer when indices repeat or are zero).

Real-world relevance: Miller indices are how mineralogists and materials scientists name cleavage faces, growth facets and slip planes, and how every X-ray/electron diffraction pattern is indexed.

Atoms (hkl) plane

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