Bragg's Law Calculator — X-ray Diffraction
Solve Bragg's diffraction equation for any unknown: enter the X-ray wavelength and Bragg angle to find lattice spacing d, or enter d and λ to find the diffraction angle. Outputs the Bragg angle θ, diffractometer angle 2θ, and sin θ.
Solve for
Å
°
Spacing between crystal lattice planes in ångströms
- 1
sin θ
sin(22.1°) = 0.37622 - 2
2 × sin θ
2 × 0.37622 = 0.75245 - 3
Interplanar spacing d = nλ ÷ (2 sin θ)
1 × 1.54 ÷ 0.75245 = 2.0467
How does this calculator work?
Bragg's law nλ = 2d·sin θ links X-ray wavelength λ, interplanar lattice spacing d, and the Bragg angle θ. For first-order diffraction (n = 1), d = λ / (2 sin θ). Enter any two of λ, d, and θ to solve for the third. Note: diffractometers report 2θ — halve the reading before entering it.
Formula
How this is calculated
When X-rays strike a crystal, beams reflected from successive parallel lattice planes interfere. Constructive interference — a detectable diffraction peak — occurs only when the path difference between beams from adjacent planes equals an integer multiple n of the wavelength λ. The extra path length is 2d·sin θ, where d is the interplanar spacing and θ is the glancing angle (Bragg angle) between the beam and the lattice plane. Setting these equal gives Bragg's law: nλ = 2d·sin θ.
In practice, n is almost always taken as 1 (first-order diffraction) because higher-order peaks are weak and often not distinguished from the first order of a harmonic spacing. The instrument reads 2θ (the angle between the incident and diffracted beams), not θ directly — so always halve the diffractometer reading before using this calculator. Wavelengths are typically given in ångströms: Cu Kα radiation (the most common laboratory source) has λ = 1.5406 Å; Mo Kα has λ = 0.7107 Å.
Bragg's law assumes elastic (coherent) scattering and ideal flat crystal planes. Real materials have peak broadening from finite crystallite size (Scherrer equation) and strain, but those corrections are outside the scope of this calculator.
Frequently asked questions
θ (the Bragg angle) is the glancing angle between the incoming X-ray beam and the crystal lattice plane. A diffractometer detector sits at twice this angle from the incident beam, so it reports 2θ. Always divide your instrument's peak position by 2 before entering it here as the Bragg angle.
The most common laboratory source is copper Kα radiation at λ = 1.5406 Å (or the weighted Kα₁/Kα₂ average of 1.5418 Å). Molybdenum Kα (0.7107 Å) is used for small-molecule crystal structures. Synchrotron sources use tunable wavelengths — check your beamline's reported λ.
Bragg's law gives the angular positions of diffraction peaks but not their intensities, which depend on the structure factor (atomic positions and scattering factors). It also assumes kinematic (single-scatter) diffraction; thick perfect crystals require dynamical diffraction theory. For amorphous, polycrystalline, or thin-film samples, additional corrections for preferred orientation, absorption, and instrumental broadening are needed.
Also known as
TG we-Calculate Editorial Team. (2026). Bragg's Law Calculator — X-ray Diffraction [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/braggs-law-calculator
TG we-Calculate Editorial Team. "Bragg's Law Calculator — X-ray Diffraction." TG we-Calculate. 2026. https://we-calculate.com/calculator/braggs-law-calculator.
TG we-Calculate Editorial Team, "Bragg's Law Calculator — X-ray Diffraction," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/braggs-law-calculator
@misc{wecalculate_braggs_law_calculator, title = {Bragg's Law Calculator — X-ray Diffraction}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/braggs-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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