RTD calculator

The Callendar-Van Dusen equation

R(t) = R0 * (1 + A*t + B*t^2)                        0 to 850 °C
R(t) = R0 * (1 + A*t + B*t^2 + C*(t - 100)*t^3)      -200 to 0 °C

A = 3.9083e-3    B = -5.775e-7    C = -4.183e-12

These are the IEC 60751 coefficients for industrial platinum RTDs with α = 0.00385, the curve nearly every Pt100 and Pt1000 on the market follows. α is the average slope between 0 and 100 °C relative to R0: (138.51 − 100) / (100 × 100) = 0.003851 per °C. R0 is the resistance at 0 °C, so a Pt1000 is ten times a Pt100 at every temperature.

Above 0 °C the equation is quadratic and inverts in closed form:

t = (-A + sqrt(A^2 - 4*B*(1 - R/R0))) / (2*B)

Below 0 °C the C term makes it a quartic, so the calculator starts from the quadratic estimate and refines it with Newton’s method. Both directions agree with the published tables:

Worked example: Pt100 at 100 °C on a 2-wire hookup

At 100 °C a Pt100 is 138.51 Ω, and its slope there is 100 × (A + 2B × 100) = 0.3793 Ω/°C. Wire it with two leads of 0.25 Ω each and the DAQ sees 139.01 Ω, which reads 1.32 °C high. A Class A sensor at 100 °C is specified to ±0.35 °C (±0.133 Ω), so the leads add four times the sensor’s own tolerance. A 3-wire or 4-wire connection removes most or all of that error. With a Pt1000 the same 0.5 Ω of lead resistance is a tenth as large relative to the sensor, about 0.13 °C.

IEC 60751 tolerance classes

These are the thermometer classes from IEC 60751:2008. The standard also defines classes for bare measuring resistors, labeled W 0.1 to W 0.6 for wire-wound and F 0.1 to F 0.6 for film, with the same formulas and somewhat different validity ranges. Check which one a sensor’s datasheet quotes, since a Class A film element is not rated at 400 °C even though the formula still gives a number.

Common mistakes

• Using a linear α approximation. R = R0 (1 + 0.00385 t) reads a Pt100 at 247.09 Ω as 382 °C when the true temperature is 400 °C.
• Ignoring lead resistance on 2-wire Pt100 circuits, as in the example above.
• Driving too much excitation current. The sensor dissipates I²R and warms itself, so use the smallest current your DAQ can resolve, typically 1 mA or less for a Pt100.
• Mixing curves. Some older sensors follow α = 0.003916 or 0.003926 curves with different coefficients, and this calculator only covers the IEC 60751 curve.
• Measuring with too coarse an input range. A Pt100 changes only 0.38 Ω per °C, so with 1 mA of excitation that is 0.38 mV per °C. See ADC resolution vs accuracy for how range and noise limit what you can resolve.

Thermocouples have their own thermocouple calculator, and the thermocouple measurement guide covers wiring and measurement practice.