Porod Invariant Calculator

Compute invariant using q and intensity pairs quickly. Add Guinier and Porod tails when needed. See results above, then download clean tables anytime instantly.

Calculator Inputs
Use the responsive fields below. Large screens show three columns.
Used for display and PDF/CSV exports.
Invariant units follow q and intensity units.
Corrected intensity is I(q) − background.
If provided, uploaded file overrides textarea.
Auto-fit uses first N positive corrected points.
Auto-tail uses median of I·q⁴ over last M points.
Guinier form: I = I0·exp(−q²Rg²/3).
Porod form: I ≈ K·q⁻⁴.
Trapezoid is robust for uneven q spacing.
Overrides Guinier auto-fit when combined with Rg.
Rg uses the same length unit as q⁻¹.
Overrides tail estimate when Porod tail is enabled.
Enables two-phase φ and S/V estimates.
Displayed with contrast-based outputs.
Accepted separators: comma, semicolon, tab, or spaces. Lines starting with # are ignored.

Example Data Table

This sample resembles decaying intensity with q. Replace with your measured dataset.
q I(q) q²·I(q)
0.020120.00.0480
0.03078.50.0707
0.04055.40.0886
0.06030.10.1084
0.10012.70.1270
0.2003.50.1400

Formula Used

The Porod invariant aggregates scattering power across all length scales:

  • Invariant definition: Q = ∫ q² I(q) dq
  • Low-q extrapolation (optional): I(q)=I0·exp(−q²Rg²/3)
  • High-q tail (optional): I(q)≈K·q⁻⁴, giving Q_high=K/qmax
  • Two-phase relation (optional): Q=2π²(Δρ)²φ(1−φ)

Use extrapolation only when your data supports the assumed regime.

How to Use This Calculator

  1. Paste your q, I(q) pairs or upload a CSV file.
  2. Enter a background level if your intensity needs subtraction.
  3. Enable Guinier extrapolation if you have reliable low-q data.
  4. Enable Porod tail if your high-q region follows a q⁻⁴ trend.
  5. Optionally enter Δρ to estimate two-phase volume fraction and S/V.
  6. Press Calculate. Results appear above the form.
  7. Use Download CSV or Download PDF for exports.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.