Bragg's Law Calculator

Your details

Choose which variable you want to calculate. The other three become inputs.
Unit used for both wavelength and d-spacing inputs and outputs.
X-ray wavelength. Cu Kα radiation is 154.18 pm (1.5418 Å).
pm
Distance between parallel lattice planes in the crystal. Typical values for X-ray diffraction are 50 to 500 pm.
pm
Positive integer representing the diffraction order. n = 1 is the first-order reflection, n = 2 is second-order, and so on.
ResultStandard XRD range
22.6717

The calculated unknown variable

Variable solvedBragg angle (°)
Bragg angle22.6717°
2θ (detector angle)45.3434°
Wavelength154.18pm
Interplanar spacing200pm
Diffraction order1
sin(θ)0.38545
Path difference (2d·sinθ)154.18pm
Maximum diffraction order2
22.6717 °
SAXS (<5°)<5Low angle5-15Standard XRD15-45High angle45-80Near grazing80+

Bragg reflection at θ = 22.6717° (2θ = 45.3434°)

  • The Bragg angle is 22.6717°, so an XRD detector placed at 2θ = 45.3434° captures this reflection.
  • Up to 2 diffraction orders can satisfy Bragg's condition for this wavelength and d-spacing (nλ ≤ 2d).
  • sin(θ) = 0.385450, confirming constructive interference: the path difference 2d·sinθ equals an integer multiple of the wavelength.

Next stepIn a powder XRD pattern, match your measured 2θ peaks to this value. Use the d-spacing to index Miller planes (hkl) and determine the crystal system.

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