Bragg Angle Calculator
Choose a mode, enter known values, then calculate the missing quantity using Bragg’s law.
Example Data Table
These sample rows show typical first- and second-order diffraction cases using Bragg’s law.
| Material Case | Wavelength λ (Å) | Spacing d (Å) | Order n | Bragg Angle θ (deg) | Scattering Angle 2θ (deg) |
|---|---|---|---|---|---|
| Cu Kα on d = 2.0000 Å | 1.5406 | 2.0000 | 1 | 22.6531 | 45.3061 |
| Mo Kα on d = 1.5000 Å | 0.7107 | 1.5000 | 1 | 13.7036 | 27.4073 |
| Cu Kα on d = 3.1355 Å | 1.5406 | 3.1355 | 1 | 14.2215 | 28.4429 |
| Second-order reflection example | 1.5406 | 2.5000 | 2 | 38.0421 | 76.0842 |
Formula Used
Bragg diffraction relates crystal plane spacing, wavelength, diffraction order, and reflection angle. The calculator uses SI units internally, then converts the results back to your selected display units.
A real Bragg reflection requires the ratio nλ/(2d) to stay between 0 and 1. If that condition fails, the calculator reports that no physical Bragg angle exists.
How to Use This Calculator
- Select the quantity you want to solve.
- Enter the known wavelength, spacing, order, or angle values.
- Choose suitable units for wavelength, spacing, and angle.
- Set the decimal precision and the maximum order for the sweep chart.
- Press the calculate button to place the result above the form.
- Review the summary, plot, and valid order sweep table.
- Download the CSV file for spreadsheet work.
- Use the PDF button for a shareable report.
Frequently Asked Questions
1) What is the Bragg angle?
It is the angle where waves scattered from adjacent crystal planes reinforce each other constructively. The calculator reports θ, while many instruments display the doubled value, 2θ.
2) Why are some inputs rejected?
Bragg’s law requires nλ/(2d) to remain above 0 and not exceed 1. If the ratio falls outside that range, the arcsine step has no real physical diffraction solution.
3) When should I use radians?
Use radians when your source equations, scripts, or measurement workflow already use radian values. The calculator still returns both degrees and radians for easy checking.
4) Is diffraction order always an integer?
Physical reflection orders are integers. In order mode, the calculator also shows the exact theoretical value and the nearest valid integer so you can compare measured geometry.
5) What does 2θ represent?
2θ is the full scattering angle between the incoming beam and the detected reflected beam. Powder diffraction patterns are commonly plotted against 2θ instead of θ.
6) Which units can I enter?
Wavelength and spacing support angstroms, nanometers, picometers, and meters. All lengths are converted internally to meters before the final display values are generated.
7) How should I choose the maximum order?
Choose a small number for quick checking or a larger number when comparing several reflections. The calculator automatically stops once the next order becomes physically impossible.
8) Can I export the results?
Yes. CSV is useful for spreadsheet analysis, while PDF is better for sharing or printing. Both exports include the calculation summary and the valid order sweep table.