Bragg's Law Calculator
Diffraction angle from lattice spacing, wavelength and order, plus the 2-theta value read off a diffractometer.
Results
What this tool does
William and Lawrence Bragg, father and son, worked out in 1913 that a crystal reflects X-rays strongly only at angles where waves scattered from successive planes of atoms come back exactly in step. That single condition turned crystals into rulers: measure the angle, know the wavelength, and the spacing between atomic planes falls out. It won them the Nobel Prize in 1915, and Lawrence remains the youngest science laureate ever at twenty-five.
Formula
n lambda = 2 d sin(theta)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dd | Lattice plane spacing | nm |
lm | Wavelength | nm |
nn | Diffraction order | — |
TH | Bragg angle | ° |
T2 | 2-theta | ° |
SN | Sine of the angle | — |
MO | Highest usable order | — |
Worked example
- Lattice plane spacing0.2 nm
- Wavelength0.154 nm
- Diffraction order1
- Bragg angle22.6437 °
- 2-theta45.2875 °
- Sine of the angle0.385000
- Highest usable order2
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
Frequently asked questions
Why is there a longest usable wavelength?
Because the sine of an angle cannot exceed one. If the wavelength is more than twice the plane spacing, there is no angle at all that satisfies the condition and the crystal simply cannot diffract that radiation. It is exactly why X-rays, with wavelengths comparable to atomic spacings, are the tool of choice and visible light is useless for the job.