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Pt100 RTD (Callendar–Van Dusen)

Convert Pt100/Pt1000 resistance to temperature and back using the IEC 60751 Callendar–Van Dusen coefficients.

Inputt ≥ 0: R(t) = R₀·(1 + A·t + B·t²) , t < 0: R(t) = R₀·(1 + A·t + B·t² + C·(t−100)·t³) , A = 3.9083×10⁻³, B = −5.775×10⁻⁷, C = −4.183×10⁻¹²

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The engineering

The Callendar–Van Dusen equation is the standard model for how a platinum RTD's resistance tracks temperature. Above 0 °C it is a simple quadratic in t, so resistance-to-temperature inverts in closed form; below 0 °C the extra cubic C-term makes it a quartic, so this card runs a quick Newton iteration to invert it. The coefficients A, B, C are the IEC 60751 values for standard (α = 0.00385) platinum.

The classic sanity check: a Pt100 reads exactly 100 Ω at 0 °C and about 138.51 Ω at 100 °C — roughly 0.385 Ω per °C near room temperature. Scale everything by R₀, so a Pt1000 just multiplies those numbers by ten. If your reading looks off by a few tenths of an ohm, suspect lead-wire resistance before you doubt the probe — always use 3- or 4-wire hookup for anything past bench accuracy.

Where this math comes from

Hugh Longbourne Callendar characterized the platinum resistance thermometer in the 1880s while at the Cavendish Laboratory, showing platinum's resistance-temperature curve was smooth and repeatable enough to serve as a practical thermometric standard. His quadratic fit handled the range above freezing well.

M. S. Van Dusen added the cubic correction term in 1925 to make the fit hold below 0 °C, where the simple quadratic drifts. The combined equation carried the platinum RTD into the modern era and now anchors IEC 60751, which pins the A, B, C coefficients and the ±tolerance classes this card assumes.

  1. 1887Hugh L. CallendarEstablishes the platinum resistance thermometer and its quadratic R–t fit.
  2. 1925M. S. Van DusenAdds the cubic term extending the fit below 0 °C.
  3. 1990ITS-90International Temperature Scale ties platinum thermometry to defined fixed points.
  4. 2008IEC 60751Standardizes the α = 0.00385 coefficients and RTD tolerance classes used here.

See the full timeline of the math behind every calculator →

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