What does a Williamson-Hall plot separate?

It uses peak broadening trends across diffraction angle to estimate size broadening and strain broadening with a linear fit.

Do I need instrument broadening?

Use an instrument FWHM value when available. The calculator subtracts it in quadrature before the fit.

Why might the fit quality be poor?

Peak fitting, anisotropic strain, texture, phase overlap, and incorrect peak selection can all weaken the linear trend.

ToolsConductScience tool

XRDFree in-browser calculator

Williamson-Hall Calculator.

Paste XRD peak positions and FWHM values to estimate microstrain, crystallite size, and regression fit quality. For materials research, education, and protocol documentation only. Not a certified inspection, compliance, asset-integrity, or final acceptance tool.

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Validated2026-05-24

CitableMethods and citation included

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Try it out

Load example Williamson-Hall data to see the full workflow

Peak broadening data

Wavelength

Shape factor K

Instrument FWHM

deg

Peak rows: two-theta FWHM

Results

Crystallite size

79.046 nm

Microstrain slope

0.002121

Intercept

0.001754

R squared

0.9624

Review notes

Williamson-Hall analysis is sensitive to peak fitting, broadening correction, and chosen peaks.

Methods note

Uses beta cos(theta) = K lambda / D + 4 epsilon sin(theta). Corrected beta is calculated in radians after optional instrument broadening correction.

Scope and limitations

For materials research, education, and protocol documentation only. Not a certified inspection, compliance, asset-integrity, or final acceptance tool.

Results are deterministic calculations from the values entered here. Review units, assumptions, and measurement quality before using outputs in reports or protocols.

Method

Uses the tool-specific formulas and assumptions shown in the calculator output.

Validated

Last validated 2026-05-24. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.

How to cite

How to Cite

Williamson-Hall Calculator (1.2.0). ConductScience, Inc. 2026. Available at: https://conductscience.com/tools/williamson-hall-calculator

For materials research, education, and protocol documentation only. Not a certified inspection, compliance, asset-integrity, or final acceptance tool.

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