Calculate Bragg diffraction angle, d-spacing, or wavelength using nλ = 2d sin θ. Includes higher-order reflections, momentum transfer, and X-ray source reference.
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.
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.
Bragg's Law: nλ = 2d sin θ Solve for θ: θ = arcsin(nλ / 2d) Solve for d: d = nλ / (2 sin θ) Solve for λ: λ = 2d sin θ / n X-ray Energy: E (keV) = 12.398 / λ (Å) Momentum Transfer: q = 4π sin θ / λ
Result: θ = 15.86°, 2θ = 31.71°
NaCl has a (200) d-spacing of 2.82 Å. With Cu Kα X-rays (1.5406 Å), the first-order Bragg angle is about 15.86° (2θ = 31.71°).
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.
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.
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.
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.
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.
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.
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.
Yes — use the de Broglie wavelength for electrons. At 200 kV, λ ≈ 0.025 Å.
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.