Particle Size Estimator Calculator

Calculator Inputs

Estimation Method

Choose the chemistry model that best fits your available data.

Shape factor K

X-ray wavelength (nm)

Instrument broadening (deg)

2θ peak positions

Use comma or space separated peak positions.

FWHM values (deg)

Enter one FWHM value for each peak.

Fluid viscosity (Pa·s)

Particle density (g/cm³)

Fluid density (g/cm³)

Settling distance (cm)

Settling times (s)

Each time value creates one equivalent diameter estimate.

Particle density (g/cm³)

Specific surface area values (m²/g)

Higher surface area usually indicates smaller particles.

Advanced chemistry estimation Three supported models Export ready results

Example Data Table

Method	Input Set	Representative Values	Estimated Size
Scherrer XRD	Peak 1	2θ = 28.4°, FWHM = 0.22°, λ = 0.15406 nm	≈ 37.39 nm
Stokes Settling	Trial 1	μ = 0.001 Pa·s, time = 12 s, distance = 10 cm	≈ 144.95 µm
Surface Area	Sample 1	SSA = 8.5 m²/g, density = 2.50 g/cm³	≈ 282.35 µm

These rows are illustrative examples for learning and validation.

Formula Used

1) Scherrer Equation

D = (K × λ) / (β × cosθ)

D is crystallite size, K is shape factor, λ is wavelength, β is corrected line broadening in radians, and θ is the Bragg angle. This method estimates coherent domain size from XRD peak broadening.

2) Stokes Settling Diameter

d = √[(18μv) / ((ρ_p - ρ_f)g)]

d is equivalent diameter, μ is fluid viscosity, v is settling velocity, ρp is particle density, ρf is fluid density, and g is gravitational acceleration. This works best for small spherical particles under laminar settling.

3) Surface Area Diameter

d(µm) = 6000 / (SSA × ρ)

d is equivalent spherical diameter in microns, SSA is specific surface area in m²/g, and ρ is particle density in g/cm³. This model assumes nonporous spherical particles.

How to Use This Calculator

Choose the estimation method that matches your laboratory data source.
Enter the required chemistry inputs for the selected method.
Use comma separated series when you have multiple peaks, trials, or samples.
Click Estimate Particle Size to show results above the form.
Review the detailed output table and the Plotly graph.
Download CSV for spreadsheet work or PDF for reporting.
Compare methods carefully because each model reflects different physical assumptions.

FAQs

1. What does this calculator estimate?

It estimates particle or crystallite size from chemistry data using diffraction broadening, settling behavior, or specific surface area values.

2. Which method should I choose?

Choose Scherrer for XRD peak broadening, Stokes for sedimentation experiments, and surface area mode when BET-style area measurements are available.

3. Why are results from different methods not identical?

Each method measures a different physical meaning of size. Crystallite size, hydrodynamic settling size, and equivalent spherical surface area size often differ.

4. Does Scherrer size equal true particle diameter?

Not always. Scherrer usually estimates crystallite domain size, which can be smaller than the overall particle size when particles contain multiple domains.

5. When is the Stokes model reliable?

It is most reliable for small, nearly spherical particles settling in laminar flow, where aggregation and turbulence are limited.

6. Why is density required for surface area sizing?

Density links mass-based surface area to geometric diameter. Without density, the calculator cannot convert SSA into an equivalent spherical size.

7. What does relative spread mean here?

Relative spread is a coefficient-of-variation style indicator. It shows how strongly your estimated sizes vary across the supplied peaks, trials, or samples.

8. Can I use exported files in reports?

Yes. The CSV file works well for spreadsheet analysis, and the PDF export gives a quick summary suitable for lab notes or presentations.