Free · Optics and light calculators 🔍

Bragg Diffraction Angle & Lattice Spacing

Calculate Bragg angle, wavelength, lattice spacing or positive integer diffraction order using the principal physical angle.

Calculator inputs

Loading calculator…

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

For first order, wavelength 100 pm and plane spacing 100 pm give a Bragg angle of 30°. The corresponding scattering angle 2θ is 60°.

Order × wavelength = 2 × plane spacing × sine(Bragg angle)

Enter these known values and leave the other values blank.

Wavelength and lattice spacing are positive. Order is a positive whole number satisfying order × wavelength ≤ 2 × spacing.
The displayed angle is θ between the incident beam and lattice planes. Instruments may instead report the scattering angle 2θ.
The inverse sine uses the physical principal range greater than zero through 90°.
The relation gives the geometric diffraction condition; crystal selection rules and intensity are not modeled.

No. This field takes θ. Divide a reported 2θ angle by two before entering it.

If order times wavelength exceeds twice the spacing, the required sine would exceed one.

Bookify restricts the Bragg angle to its positive principal physical range through ninety degrees.