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Bragg’s Law Calculator

Calculate diffraction angles, d-spacing, wavelengths, and generate XRD peak tables using nλ = 2d sinθ.

Interactive calculator

Bragg’s Law Calculator

Calculate Bragg diffraction angle, d-spacing, wavelength, diffraction order, and generate XRD peak tables using nλ = 2d sinθ.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: find angle, d-spacing, wavelength, order, or generate XRD tables.
  • Enter values in Å, nm, or pm for wavelength/spacing.
  • Results show both θ and 2θ (detector angle).

Table of Contents

Key Takeaways

  • Bragg’s law: nλ = 2d sinθ governs X-ray diffraction from crystal planes.
  • d-spacing is the distance between parallel crystal lattice planes.
  • Only certain angles produce constructive interference (diffraction peaks).
  • The diffraction order n must be a positive integer.
  • Cu Kα (1.5406 Å) is the most common lab X-ray source.
  • XRD is used to identify crystal structures, minerals, and proteins.

What Is Bragg’s Law?

Bragg’s law describes the conditions under which X-rays scattered from crystal lattice planes interfere constructively to produce intense diffraction peaks. It is the foundation of X-ray crystallography, enabling determination of atomic-scale crystal structures.

Bragg’s Equation

nλ=2dsin⁡θn\lambda = 2d\sin\theta

Where n is the diffraction order (positive integer), λ is the X-ray wavelength, d is the interplanar spacing, and θ is the angle between the incident X-ray beam and the lattice planes. Constructive interference occurs only when this equation is satisfied.

X-Ray Diffraction (XRD)

In an XRD experiment, a monochromatic X-ray beam strikes a crystal. The detector rotates to measure scattered intensity as a function of 2θ. Peaks in the diffraction pattern correspond to crystal planes satisfying Bragg’s law. The pattern is a fingerprint of the crystal structure.

Sourceλ (Å)Typical use
Cu Kα1.5406Routine analysis, powder XRD
Mo Kα0.7093Single-crystal, protein
Co Kα1.7889Fe-rich samples
Cr Kα2.2897Stress analysis

How to Use

  1. Select a mode: find angle, d-spacing, wavelength, order, or table.
  2. Enter known values. Use presets for common sources/crystals.
  3. Click Calculate. XRD table mode shows all orders up to n = 10.

Examples

Cu Kα on NaCl (d = 2.82 Å)

θ = arcsin(1.5406 / (2 × 2.82)) ≈ 15.86°, 2θ = 31.73°

Find d-spacing from peak

d = λ/(2 sin θ) = 1.5406/(2 sin 25°) ≈ 1.82 Å

FAQ

What is Bragg’s law?›

Bragg’s law (nλ = 2d sinθ) describes the condition for constructive interference of X-rays scattered from crystal lattice planes, where n is the order, λ is wavelength, d is interplanar spacing, and θ is the angle of incidence.

What is d-spacing?›

d-spacing is the perpendicular distance between adjacent parallel planes of atoms in a crystal lattice. It is characteristic of the crystal structure and the specific Miller indices (hkl) of the planes.

What X-ray sources are commonly used?›

Cu Kα (1.5406 Å), Mo Kα (0.7093 Å), Co Kα (1.7889 Å), and Fe Kα (1.9360 Å) are the most common laboratory X-ray sources.

Why does sinθ > 1 mean no peak?›

The sine function cannot exceed 1, so if nλ/(2d) > 1, no angle satisfies Bragg’s condition. This limits the number of observable diffraction orders.

What is the 2θ angle?›

In XRD measurements, the detector scans at angle 2θ from the incident beam. The Bragg angle θ is the angle between the incident beam and the crystal planes, so the scattering angle is 2θ.

Sources

  1. OpenStax – X-Ray Diffraction
  2. Wikipedia – Bragg’s Law
  3. NIST – Crystal Data
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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