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Van der Pauw resistivity, done right.

Solve the transcendental Van der Pauw equation to extract sheet resistance and resistivity from two four-probe measurements on a thin film of any shape. Single sample or thousands at a time.

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1e-10
solver tolerance
100%
in-browser, no upload
∞
samples per batch
The equation

There is no closed-form solution for Rs. We iterate on z = 1/Rs until the residual |Δz/z| drops below 10⁻¹⁰.

Input
RA, RB, thickness
Output
Rs, ρ, σ

Single-sample calculator

Enter your two four-probe resistance measurements and the film thickness. Results update live.

Measurements

Display resistivity in
Sample shape (illustration only)
Configuration shown

Results

Sheet resistance
— Ω/sq
Resistivity ρ
— Ω·cm
Conductivity σ
—
Symmetry
—
Iterations
—
Residual
—

Convergence trace

—

Log-scale residual |Δz/z| per iteration. The solver halts when this falls below 10⁻¹⁰.

Sample geometry

Van der Pauw’s theorem holds for any simply-connected, thin, uniform sample with point contacts on its perimeter. The cloverleaf geometry minimizes contact-finite-size error.

Batch processing

Upload an Excel (.xlsx) or CSV file with Ra and Rb columns. We compute Rs and ρ for every row, locally, in your browser.

Drop your file here
or click to browse · .xlsx, .xls, .csv accepted

How it works

  1. 1 Your file is parsed entirely in this browser. Nothing is uploaded.
  2. 2 Columns named Ra and Rb are matched (case-insensitive; underscores and dashes ignored).
  3. 3 Each row is solved with tolerance 10⁻¹². Rs and ρ are added as new columns.
  4. 4 Download a new .xlsx with results plus a “Run info” sheet capturing the thickness and timestamp.

The Van der Pauw method

A four-point technique for measuring the resistivity of a thin, uniform, simply-connected sample of arbitrary shape — derived by Leo J. van der Pauw at Philips Research in 1958.

1 · Procedure

Place four small ohmic contacts on the perimeter of a thin, simply-connected sample. Number them 1, 2, 3, 4 in order. Make two resistance measurements:

  • RA = V43 / I12 — current through 1→2, voltage between 4 and 3.
  • RB = V14 / I23 — current through 2→3, voltage between 1 and 4.

The sheet resistance Rs satisfies van der Pauw’s relation:

There is no closed-form inverse, so we solve numerically. Once Rs is known, the resistivity for a film of thickness t is simply ρ = Rs · t.

2 · The symmetric limit

When RA = RB ≡ R, the equation collapses to 2 exp(−π R / Rs) = 1, so:

This is the famous Van der Pauw constant π/ln 2 ≈ 4.5324. It is the only case with a closed-form solution.

3 · Numerical method

Let z = 1/Rs. Starting from the symmetric guess z₀ = 2 ln 2 / (π (RA + RB)), we iterate:

This is a damped Newton step with very fast quadratic convergence — typically ten to fifteen iterations suffice for double-precision residuals.

About this tool

The original Van der Pauw calculator was written as an R Shiny app by Dr. Aous Abdo in 2018, building on the NIST C reference implementation. This is the 2026 rebuild — a fully static, in-browser TypeScript port with a stricter solver, batch processing, and a from-scratch UI.

It runs as a static site on GitHub Pages, costs nothing, and respects your data: no telemetry, no analytics, no uploads. Everything happens in this tab.

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