When X-rays reflect from layers of atoms in a crystal, they interfere constructively only at angles that satisfy Bragg’s law. William and Lawrence Bragg used it in 1913 to determine crystal structures – later including DNA and proteins.
How to use the Bragg’s Law Calculator
- Find
- Order n
- Wavelength λ
- Interplanar distance d
- Incidence angle θ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose what to find and enter the other values. θ is the glancing angle between the beam and the crystal planes (not the normal).
Inputs explained
| Field | What to enter |
|---|---|
| Find | Choose one: Wavelength λ, Interplanar distance d, Angle θ |
| Order n | A number |
| Wavelength λ | Units: nm, Å, pm, m |
| Interplanar distance d | Units: nm, Å, pm, m |
| Incidence angle θ | Units: °, rad, arcmin, arcsec, mrad |
What each result means
- Wavelength λ = 2×[Interplanar distance d]×sin(rad([Incidence angle θ]))÷[Order n]
- Interplanar distance d = [Order n]×[Wavelength λ]÷(2×sin(rad([Incidence angle θ])))
- Angle θ = deg(asin([Order n]×[Wavelength λ]÷(2×[Interplanar distance d])))
Example values
How the main result changes when Order n changes and everything else stays at the example values above:
| Order n | Wavelength λ (nm) |
|---|---|
| 1 | 0.1537 |
| 1.25 | 0.123 |
| 1.5 | 0.1025 |
| 2 | 0.0769 |
Formula
n·λ = 2·d·sin θ
Worked example
Inputs — Find: Wavelength λ; Order n: 1; Interplanar distance d: 0.2 nm; Incidence angle θ: 22.6 °.
Results — Wavelength λ = 0.153718 nm.
Key terms
- Interplanar spacing
- Distance between parallel planes of atoms.
Frequently asked questions
What is Bragg's law used for?
X-ray crystallography – finding atomic spacings and crystal structures.
Why must the waves be X-rays?
Their wavelengths (≈0.1 nm) match the spacing of atomic planes.
What is the diffraction order?
The number of whole wavelengths of path difference.
What if nλ > 2d?
No diffraction peak is possible for that order.