Bragg's Law Calculator
X-ray diffraction with Bragg’s law — solve for the diffraction angle, d-spacing or wavelength given the other two and the order n, with the 2θ value diffractometers report.
How it works
n·λ = 2·d·sin θ; 2θ is the angle between incident and diffracted beams
X-rays reflecting from successive planes of atoms interfere constructively only when the extra path 2d·sinθ is a whole number of wavelengths. Each set of crystal planes therefore produces a peak at a characteristic angle, and measuring those angles with a known wavelength gives the plane spacings — the basis of powder diffraction, phase identification and the structure of DNA. Diffractometers report 2θ, so halve it before using the equation.
Worked example
Cu Kα (1.5406 Å) on silicon (111) planes with d = 3.1356 Å: sinθ = 0.2457, θ = 14.22°, 2θ = 28.44° — the familiar first silicon peak.
Frequently asked questions
Why does a peak vanish at higher order?
sinθ cannot exceed 1, so orders with n·λ > 2d are impossible; also structure-factor rules extinguish some reflections.
Does Bragg’s law work for electrons and neutrons?
Yes — any wave with a wavelength comparable to atomic spacing, including electrons in TEM.
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This calculator is for educational purposes. Double-check important results before acting on them.