Bragg's Law Calculator

About the Bragg's Law Calculator

The **Bragg's Law Calculator** solves the X-ray (or neutron, electron) diffraction equation nλ = 2d sin θ for any of the three unknowns: Bragg angle, d-spacing, or wavelength. It also computes higher-order reflections, the momentum transfer vector q, and X-ray photon energy — everything you need for interpreting diffraction patterns.

Bragg's Law is the cornerstone of crystallography — it relates the wavelength of incident radiation, the spacing between crystal planes, and the angles at which constructive interference (diffraction peaks) occur. William Lawrence Bragg and his father William Henry Bragg won the 1915 Nobel Prize for pioneering crystal-structure determination with X-rays.

Use the presets for common crystals (NaCl, Si, diamond, graphite) and X-ray sources (Cu Kα, Mo Kα, neutron), or enter custom parameters. The higher-order tables and source references make it easier to move between a quick angle check and a more realistic diffraction interpretation. That way the angle, wavelength, and spacing stay tied to the same crystallographic context instead of being handled as separate values. It also makes it easier to compare several peaks or source options without mixing angle conventions.

When This Page Helps

Bragg-angle calculations are easy to write down but surprisingly easy to mishandle when wavelength, order, and spacing all change at once. This calculator keeps the diffraction angle, d-spacing, wavelength, energy, and reciprocal-space quantity together so you can move between measurement and structure with fewer transcription mistakes. It is particularly helpful when comparing instrument readings against expected lattice spacings from a known crystal.

How to Use the Inputs

1. Select a crystal/source preset or enter d-spacing and wavelength manually.
2. Choose what to solve for: Bragg angle, d-spacing, or wavelength.
3. Set the diffraction order n (usually 1 for primary reflections).
4. Read the Bragg angle, 2θ, photon energy, and momentum transfer.
5. Review higher-order reflections and common X-ray lines in the tables.
6. Enter θ directly when solving for d-spacing or wavelength.

Example Calculation

Tips & Best Practices

• Cu Kα (1.5406 Å) is the most common lab X-ray source for powder XRD.
• For synchrotron work, λ is tunable — use the "solve for λ" mode to plan experiments.
• Higher-order peaks (n = 2, 3, ...) appear at larger angles and are weaker.
• Systematic absences (missing peaks) reveal the Bravais lattice type.
• Always check for Kβ contamination — a Ni filter removes Cu Kβ.

Keep Track Of Which Quantity Is Measured

In many diffraction problems, the instrument gives you 2θ while the equation is written in terms of θ. That single factor-of-two slip is one of the most common sources of wrong d-spacing results. Use the calculator to keep the measured detector angle and the Bragg angle clearly separated.

Order Matters, But First-Order Peaks Are Usually The Starting Point

Higher-order solutions can exist for the same wavelength and plane spacing, but they appear at different angles and are often weaker or absent depending on the structure factor and instrument setup. Checking multiple orders is useful, but starting with n = 1 usually gives the clearest connection between the measured line and the lattice spacing.

Units Connect The Physics

One strength of Bragg's Law is that it links angle, wavelength, spacing, photon energy, and reciprocal space in one compact relation. That also means unit slips can spread quickly. Keep angstroms, keV, and degrees consistent when moving between source data, instrument output, and structural interpretation.

Frequently Asked Questions

• What is Bragg's Law?

  Bragg's Law is the condition for constructive interference of waves scattered by regularly spaced crystal planes: nλ = 2d sin θ. It links the diffraction geometry directly to the lattice spacing.

• What is 2θ?

  The scattering angle measured by a detector in a diffractometer. It equals twice the Bragg angle θ, which is why the instrument angle and the Bragg angle are not the same quantity.

• When is there no diffraction?

  If nλ is larger than 2d, the required sine value would exceed 1 and no Bragg angle exists for that order. In practice that tells you the chosen wavelength and spacing cannot produce that reflection.

• What determines d-spacing?

  The crystal lattice parameters and the Miller indices (hkl) of the planes. For cubic: d = a / √(h²+k²+l²), so both lattice size and plane orientation matter.

• Can I use this for electron diffraction?

  Yes — use the de Broglie wavelength for electrons. At 200 kV, λ ≈ 0.025 Å.

• What is momentum transfer q?

  q is the magnitude of the scattering vector, which connects the measured diffraction angle to reciprocal-space coordinates. It is especially useful when comparing data across different wavelengths or instruments.