Miller Indices Calculator

Å
For cubic crystals, a = b = c.
Chemistry

Calculate the d-spacing (interplanar spacing) for a crystalline plane from Miller indices and lattice parameters.

Formula

d = a / √(h² + k² + l²) [cubic system]
  • Formula is for cubic (isometric) crystal system only (a = b = c, α = β = γ = 90°).
  • For other systems (tetragonal, hexagonal, orthorhombic), different formulas apply.
  • d-spacing is used in Bragg's Law: 2d sin(θ) = nλ for XRD analysis.
  • Copper Kα X-ray wavelength: λ = 1.5406 Å.

Copper (a=3.615 Å), plane (110)

Inputs
  • Miller Index h: 1
  • Miller Index k: 1
  • Miller Index l: 0
  • Lattice Parameter a: 3.615 Å

d = 3.615 / √(1+1+0) = 3.615 / 1.414 = 2.556 Å.

Frequently asked questions

What are Miller indices?
A notation system using three integers (h, k, l) to describe the orientation of crystal planes.
How is d-spacing used?
In Bragg's Law for X-ray diffraction to identify crystal structures: 2d sin(θ) = nλ.