Turn detector angles into q values within seconds. Choose wavelength, d-spacing, and output units easily. Use exports to share results with your team fast.
The scattering vector magnitude q (also called momentum transfer) is commonly defined as:
q = |kf − ki|λ: k = 2π/λq = 2k sin(θ) = (4π/λ) sin(θ)q = 2π/dHere 2θ is the measured scattering angle, and θ is half of it.
| Mode | λ | 2θ | d | q (1/Å) |
|---|---|---|---|---|
| λ and 2θ | 1.5406 Å | 30° | — | 2.112 |
| λ and 2θ | 1.5406 Å | 60° | — | 4.079 |
| λ and 2θ | 1.0000 Å | 20° | — | 2.182 |
| d-spacing | — | — | 3.135 Å | 2.005 |
Values are rounded for readability. Your results depend on units and rounding.
In elastic scattering, q is the magnitude of momentum transfer between the incoming and outgoing beams. It maps angle and wavelength into reciprocal space, where peaks relate directly to structure. Larger q corresponds to smaller real-space features, while smaller q emphasizes larger length scales. Many workflows report only |q|, but the underlying vector direction can matter for anisotropic samples.
Because q = (4π/λ)·sin(θ), the same angular step produces different q steps depending on λ and θ. Near low angles, sin(θ) changes slowly, so q spacing is tight. At higher angles, q grows faster, which can widen spacing between sampled reciprocal-space points. A helpful guide is dq/dθ = (4π/λ)·cos(θ), which shows why q resolution improves at small θ.
For Cu Kα radiation (λ = 1.5406 Å), a scan at 2θ = 30° gives q ≈ 2.11 1/Å. At 2θ = 60°, q rises to about 4.08 1/Å. These values match the example table and help validate instrument settings quickly.
When peaks are indexed by spacing, use q = 2π/d. Converting back, d = 2π/q gives an intuitive check: q = 2.00 1/Å corresponds to d ≈ 3.14 Å. This is useful for comparing diffraction peaks against reference patterns and lattice parameters.
In SAXS/SANS, data are often reported in 1/nm or 1/Å. A q-window like 0.05–5 1/nm probes features from roughly 125 nm down to 1.3 nm (using 2π/q). This calculator helps you translate detector angles and wavelength into the q-range your setup actually covers. It is also useful for checking whether beamstop geometry and minimum angle settings are limiting your lowest-q data.
The page also shows k = 2π/λ, θ, 2θ, and d derived from q. If k looks inconsistent with your wavelength, or if d is unrealistic for the material class, it usually indicates a unit mismatch. Keep q units consistent (1/Å for wide-angle, 1/nm for small-angle) when reporting, and record that choice in filenames, plot axes, and metadata.
Start by entering λ and your measured 2θ values, then export CSV for lab notes. For publications, keep a fixed significant-digit setting across all scans and report the same q units throughout. This keeps refinements, peak fitting, and model comparisons reproducible.
Most diffractometers report 2θ. Choose the “From wavelength and 2θ” mode and enter the displayed value. Use the θ mode only if your instrument or dataset already provides half-angle values.
It uses q = (4π/λ)·sin(θ) for elastic scattering and q = 2π/d when you provide a spacing. Both forms are shown in the Formula section for transparency.
Wide-angle diffraction commonly uses 1/Å. Small-angle scattering commonly uses 1/nm. Pick the unit that matches your plotting and fitting tools so you avoid conversion mistakes when sharing datasets.
d provides an immediate real-space interpretation: d = 2π/q. It helps you check whether a peak corresponds to an expected spacing range, such as atomic planes (Å scale) or larger nanostructures (nm scale).
Yes. Use the “From wavelength and q” mode. The calculator computes θ from sin(θ) = q/(2k) with k = 2π/λ, then reports θ and 2θ in degrees.
First confirm wavelength units and whether you entered θ versus 2θ. Next confirm the selected output unit. A single unit mismatch, especially Å vs nm, can shift q by a factor of ten.
Yes. CSV and PDF include the selected mode, the entered values with units, and the computed outputs. This makes it easy to attach a compact calculation record to lab notebooks or reports.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.