FREE ONLINE TOOL · XRD ANALYSIS

XRD Crystallite Size Calculator

Enter 2θ and FWHM to estimate apparent crystallite size in nm

Free to use No installation Instant result
Scherrer equation D = Kλ / (β cosθ) β = FWHM · θ = 2θ / 2

Enter peak data

Example values loaded

Angle at the peak maximum, for example 38.18°

Width at half the peak height, for example 0.42°

Cu Kα₁ defaults to 1.5406 Å

A common shape factor is 0.9

Estimated result Apparent crystallite size
20.0 nm

This is an apparent crystallite size. Instrumental broadening and microstrain are not removed.

D = Kλ / (β cosθ). The calculator converts FWHM from degrees to radians and uses θ = 2θ / 2.

Frequently asked questions

Is crystallite size the same as SEM particle size?

Not necessarily. The Scherrer equation estimates the coherently diffracting crystallite size. One particle seen in SEM can contain multiple crystallites, so different values are expected.

Should FWHM be entered in degrees or radians?

Enter the FWHM shown by your XRD software in degrees. This calculator converts it to radians inside the equation.

Can I use only one XRD peak?

Yes, for a quick apparent-size estimate. To separate crystallite size from microstrain, use two or more peaks for Williamson-Hall analysis and report how instrumental broadening was handled.