X-Ray Wavelength Calculator Using Bragg's Law for Crystal Diffraction

What is Bragg's Law?

Bragg's Law describes how X-rays diffract off crystal planes to produce interference patterns. When X-rays strike a crystal at angle θ, they reflect off atomic planes separated by distance d. Constructive interference occurs at specific angles, producing maxima that reveal the crystal's atomic structure.

🔬 X-Ray Wavelength Calculator

Use our free calculator for instant, accurate results.

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📐 Formula

nλ = 2d × sin(θ)

n = diffraction order (integer), λ = X-ray wavelength (m), d = interplanar spacing (m), θ = Bragg angle (angle of incidence). Solved for any unknown.

📝 Worked Example

NaCl crystal, d = 2.82 Å = 2.82×10⁻¹⁰ m. First order (n=1) maximum at θ = 15.8°:
λ = 2 × 2.82×10⁻¹⁰ × sin(15.8°)
λ = 5.64×10⁻¹⁰ × 0.272 = 1.53×10⁻¹⁰ m = 1.53 Å

📝 How to Use the Calculator

Select UnknownChoose to solve for wavelength (λ), d-spacing, or Bragg angle (θ).

Enter Known ValuesInput the two known quantities with correct units.

Specify OrderEnter diffraction order n (usually 1 for first maximum).

CalculateView result and see how the crystal structure relates to the diffraction pattern.

❓ FAQ

Why are X-rays used for crystal structure analysis?

X-ray wavelengths (0.1–10 Å) are comparable to interatomic distances, producing measurable diffraction patterns. Visible light (500 nm) is too long.

What is X-ray powder diffraction (PXRD)?

A technique using polycrystalline powders instead of single crystals. Multiple crystal orientations produce a diffraction pattern of rings that identifies materials.

What is Bragg's Law?