Calculate cubic crystal lattice spacing d in Å from Miller indices and lattice constant, or from XRD peak 2θ and wavelength for cubic crystals.

Lattice Spacing Calculator

Get the d-spacing of a cubic crystal in under 10 seconds.

From hkl + a
From XRD peak (2θ)

Lattice Spacing Formula

The following equation is used to calculate the lattice spacing for a cubic crystal.

d_{hkl}=\frac{a}{\sqrt{h^{2}+k^{2}+l^{2}}}
  • Where dhkl is the lattice (interplanar) spacing for planes with Miller indices (hkl)
  • a is the (cubic) lattice constant
  • h, k, and l are the Miller indices

What is a Lattice Spacing?

Definition:

The crystal’s interplanar spacing, or lattice spacing (often called d-spacing), is the perpendicular distance between adjacent, parallel planes of atoms in a crystal. A family of parallel crystallographic planes is labeled by its Miller indices (hkl), which are derived from the plane’s intercepts with the crystallographic axes in the unit cell.

The spacing dhkl is a scalar distance. In reciprocal space, the planes are associated with a reciprocal lattice vector normal to the planes; using the common 2π convention, the magnitude satisfies |ghkl| = 2π/dhkl.

For a given crystal system, different (hkl) planes have different interplanar spacings. Smaller dhkl values mean the planes are closer together (often for higher-index planes), but atomic packing density depends on the full crystal structure and basis, not on a single plane spacing.

Interplanar spacings are commonly measured using X-ray, electron, or neutron diffraction. Diffraction peak positions are related to d through Bragg’s law, and collections of d-spacings are widely used to identify phases and determine lattice parameters.

Terms such as “close-packed” describe specific structures/stackings (for example, FCC or HCP) and are not determined solely by d-spacing. Likewise, whether a solid is metallic, ionic, or covalent depends primarily on bonding and electronic structure rather than interplanar spacing alone.