Chemistry
Miller Indices Calculator
Convert plane intercepts into Miller indices and find the spacing between planes in a cubic crystal.
Your inputs
Change any value to update the result instantly.
Spacing d(111)
233.7691 pm
In nanometres
0.2338 nm
h² + k² + l²
3
Plane
(1 1 1)
Bragg angle 2θ
38.478 degrees for first-order reflection
Intercept rule
Miller indices are the reciprocals of the axis intercepts, cleared of fractions
The d-spacing formula shown applies to cubic crystals only. Tetragonal, hexagonal and lower-symmetry systems each need their own expression. Copper Kα radiation is 154.06 pm.
What this calculator does
Converts Miller indices into interplanar spacing for a cubic crystal and the matching first-order Bragg angle.
What your result means
The distance between adjacent planes of that family, and the angle at which they diffract X-rays.
Formula and working
d_hkl = a / √(h² + k² + l²)
- 1
Collect the inputs
Lattice parameter a = 404.9 pm; Index h = 1; Index k = 1; Index l = 1; X-ray wavelength (0 to skip Bragg) = 154.06 pm
- 2
Apply the formula
d_hkl = a / √(h² + k² + l²)
- 3
Result
Spacing d(111) = 233.7691 pm
Frequently asked questions
Symbols and assumptions
- d_hkl
- Interplanar spacing
- a
- Lattice parameter
- h, k, l
- Miller indices
- λ
- X-ray wavelength
- • Cubic crystal system.
- • First-order reflection, n = 1, in the Bragg equation.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • Tetragonal, hexagonal and lower-symmetry systems each need a different d-spacing expression.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
Report a mistake or request an improvement
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