Bragg Law Calculator

Explore diffraction geometry with clean inputs and validation. Switch units easily and visualize peak behavior. Built for students, labs, and accurate crystal spacing studies.

Calculator Input

Choose one unknown quantity, then enter the remaining values. The form stays stacked on the page, while the inputs adapt responsively.

Example Data Table

Case Order n Wavelength λ Spacing d Bragg Angle θ Computed Highlight
Cu Kα on crystal plane 1 1.5406 Å 2.0000 Å 22.65° Condition nearly satisfied for first-order reflection
Find spacing from XRD peak 1 0.15406 nm Unknown 30.00° d ≈ 0.15406 nm
Find angle for known crystal 2 1.20 Å 3.00 Å Unknown θ determined from inverse sine relation
Estimate order from measured peak Unknown 1.00 Å 2.50 Å 23.58° n expected close to an integer maximum

Formula Used

Bragg’s law describes constructive interference from crystal planes:

nλ = 2d sin(θ)

Solve wavelength
λ = 2d sin(θ) / n
Solve spacing
d = nλ / [2 sin(θ)]
Solve angle
θ = sin-1(nλ / 2d)
Solve order
n = 2d sin(θ) / λ

θ is the Bragg angle between the incident beam and the reflecting plane. Many diffractometers display 2θ, so be careful when entering measured values.

How to Use This Calculator

  1. Select which Bragg-law quantity you want to solve.
  2. Enter the remaining known values.
  3. Choose the correct wavelength and spacing units.
  4. Use θ, not 2θ, in the angle field.
  5. Press the calculate button.
  6. Review the primary result, supporting values, and graph.
  7. Export the solved data as CSV or PDF if needed.

FAQs

1) What does Bragg’s law calculate?

It links diffraction order, wavelength, lattice spacing, and Bragg angle for constructive interference from parallel crystal planes. It is widely used in X-ray diffraction analysis.

2) Should I enter θ or 2θ?

Enter θ only. Many XRD instruments report 2θ on plots, so divide the measured peak position by two before using this calculator.

3) Can the diffraction order be non-integer?

Mathematically, the formula can return a non-integer value. Physically, strong diffraction maxima are associated with integer orders, so the calculator shows the nearest integer and the difference.

4) Why do I get no real angle?

A real Bragg angle needs nλ/(2d) to be between zero and one. If the ratio exceeds one, the chosen wavelength, spacing, or order cannot produce a valid reflection.

5) Which wavelength unit should I use?

Use the same unit that matches your source data. Ångström and nanometer inputs are common for X-ray work, while the calculator automatically handles unit conversion internally.

6) What is interplanar spacing?

Interplanar spacing, d, is the perpendicular distance between adjacent crystal planes that reflect the incoming radiation under the Bragg condition.

7) What does the graph represent?

The graph is a simple normalized peak centered at the solved Bragg angle. It visually highlights the angular region where constructive diffraction is strongest.

8) Can I use this for teaching and lab reports?

Yes. It is suitable for classroom demonstrations, crystal spacing checks, quick XRD calculations, and exporting summary results for worksheets or reports.

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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.