Calculator Inputs
Formula Used
Primary scattering-vector formula
q = (4π / λ) sin(θ)
Here, λ is wavelength and θ is half of the total scattering angle, so θ = (2θ)/2.
Relation with d-spacing
q = 2π / d
This is commonly used in diffraction, SAXS, and reciprocal-space analysis to convert between real-space periodicity and reciprocal-space magnitude.
Component form
|q| = √(qx² + qy² + qz²)
If you know vector components directly, the magnitude comes from the Euclidean norm, and the calculator also returns the in-plane term qxy.
How to Use This Calculator
- Choose the calculation mode that matches your known data.
- Enter wavelength and 2θ, or enter d-spacing, or enter q components.
- Pick the correct units before calculating.
- Use optional azimuth and elevation to estimate qx, qy, and qz from the magnitude modes.
- Click the calculate button to display results above the form.
- Review the summary table, component table, and the Plotly graph.
- Use the CSV or PDF buttons to save the result for reports or lab records.
Example Data Table
Example using λ = 1.5406 Å with several total scattering angles.
| Wavelength (Å) | 2θ (deg) | θ (deg) | q (1/Å) | d (Å) |
|---|---|---|---|---|
| 1.5406 | 10 | 5 | 0.711 | 8.833 |
| 1.5406 | 20 | 10 | 1.416 | 4.438 |
| 1.5406 | 30 | 15 | 2.112 | 2.975 |
| 1.5406 | 40 | 20 | 2.789 | 2.253 |
Frequently Asked Questions
1. What is the scattering vector q?
The scattering vector describes momentum transfer during scattering. Its magnitude links the experimental geometry to reciprocal space and directly connects to structural spacing through q = 2π/d.
2. Why does the calculator ask for 2θ instead of θ?
Many diffraction instruments report the total scattering angle as 2θ. The calculator automatically halves that value internally because the standard formula uses θ.
3. When should I use the d-spacing mode?
Use the d-spacing mode when you already know the lattice spacing or periodicity and want the reciprocal-space magnitude quickly. It is especially useful for indexing and back-checking diffraction peaks.
4. What unit is best for q?
In scattering work, q is often reported in 1/Å or 1/nm. The best unit depends on your field, instrument conventions, and how your reference data are published.
5. What do qx, qy, and qz represent?
They are Cartesian components of the scattering vector. These are useful in oriented samples, detector mapping, grazing-incidence experiments, and anisotropic reciprocal-space analysis.
6. Why can a wavelength make a d-spacing angle unreachable?
For a fixed wavelength, Bragg geometry requires sin(θ) ≤ 1. If the implied value exceeds one, no real scattering angle satisfies that combination, so the geometry is not physically reachable.
7. What does the graph show?
The graph shows how q changes with 2θ for a given wavelength, or how q changes with d-spacing when wavelength is not supplied. In component mode, it shows the component magnitudes.
8. Can I use this for SAXS, WAXS, and diffraction?
Yes. The relationships used here are standard across many elastic scattering workflows. Just make sure your wavelength, angles, and reported units match your instrument conventions.