Calculate XRD d-spacing from 2θ, reverse a peak angle, or solve cubic hkl spacing with wavelength units, uncertainty, and peak-position sensitivity.

Enter the instrument angle 2θ, not Bragg θ.

Defaults to first order (n = 1).

Optional settings

Optional. The entire angular interval must stay above 0° and below 180°.

Lattice Spacing Formula

The following equation gives interplanar spacing for a cubic cell. The calculator also uses Bragg’s law, nλ = 2d sin θ, with the entered instrument angle 2θ divided by two. Inverse peak mode uses 2θ = 2 asin(nλ/(2d)); nλ > 2d has no real Bragg angle.

dₕₖₗ = (a) / (√(h² + k² + l²))
  • Where dhkl is the lattice (interplanar) spacing for planes with Miller indices (hkl)
  • a is the (cubic) lattice constant
  • h, k, and l are whole-number Miller indices; they cannot all be zero. Lattice constant and spacing have independent convertible units.

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. An optional angular tolerance is propagated at both endpoints, giving a generally asymmetric spacing interval. The ±1% sensitivity tables are illustrative changes, not measurement uncertainties. A geometric peak prediction does not test reflection extinctions, structure factors or experimental visibility.

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.