Thermocouple calculator

NIST ITS-90 reference functions

A thermocouple produces a voltage set by the temperature difference between its hot (measuring) junction and its cold (reference) junction, where the thermocouple wires meet copper at your DAQ’s terminals. NIST Monograph 175 defines a reference function for each letter type that gives the EMF in millivolts for a hot junction at t °C with the reference junction at 0 °C:

E(t) = c0 + c1*t + c2*t^2 + ... + cn*t^n                    all types
E(t) = sum(ci * t^i) + a0 * exp(a1 * (t - a2)^2)            type K, 0 to 1372 °C

Each type has two or three temperature sub-ranges with their own coefficients. For voltage to temperature NIST publishes inverse polynomials, t = d0 + d1·E + d2·E² + ..., fitted over sub-ranges with a stated error. For type K from 0 to 500 °C the inverse stays within −0.05 to +0.04 °C of the reference function. This calculator uses the reference functions for temperature to voltage and the NIST inverse polynomials for voltage to temperature. Where no inverse exists, such as type K below −200 °C, it solves the reference function numerically and says so under the result.

Cold junction compensation

E_total = E_measured + E(T_cj)
T_hot   = inverse(E_total)

The voltage at your DAQ reflects only the difference between the two junctions. To recover the hot junction temperature, convert the cold junction temperature to an EMF with the reference function, add it to the measured voltage, then invert the total. Converting the measured voltage to a temperature and adding the cold junction temperature gives the wrong answer, because the curve isn’t linear.

Worked example: type K with the terminals at 25 °C

The DAQ reads 3.096 mV and the cold junction sensor on the terminal block reads 25.0 °C. The type K reference function gives E(25 °C) = 1.000 mV, so the total is 4.096 mV, which inverts to 100.0 °C. Adding temperatures instead gives 75.9 °C + 25.0 °C = 100.9 °C, almost a degree high. The error grows with temperature. A 20.000 mV reading with the junction at 35 °C is really 517.9 °C, and the shortcut says 519.9 °C.

NIST defines each curve over a wider range than the type is used for in service. Type B produces almost no voltage near room temperature, so its cold junction barely affects the reading and the type is only useful well above 250 °C.

Common mistakes

• Measuring cold junction temperature somewhere other than at the junction itself. If the CJC sensor sits a few centimeters from the screw terminals and a fan blows across the block, the error passes straight into the reading at about 1 °C per °C.
• Using a wide input range. A 16-bit DAQ on ±10 V has a 305 µV LSB, which is about 7.5 °C for type K. Use the smallest range the device offers, or a thermocouple input such as the MCC USB-TC or NI 9211.
• Reversing polarity. In the ANSI color code the red lead is negative. A reversed thermocouple moves the wrong way as the hot end heats, reading below the cold junction temperature.
• Assuming a constant 41 µV/°C for type K. That linear shortcut drifts by several degrees over a few hundred degrees of span.
• Splicing with copper wire. Every junction of dissimilar metals is another thermocouple, so extend with thermocouple or extension-grade wire of the same type.

The thermocouple measurement guide covers wiring and hardware choices. DAQAtlas, which is in development, includes a simulated MCC USB-TC, so you can set up thermocouple channels, alarms and a dashboard before the hardware arrives.