Thermocouple calculator: type K, J, T, E and more
Type the voltage your meter or amplifier reads and the temperature at the terminals, and get the hot-junction temperature with the cold junction compensated in volts. Or go the other way, from a hot temperature to the millivolts you should see.
The voltages are the NIST ITS-90 reference functions. Types K, J, T and E are checked against the NIST tables to within 0.6 µV, and N, R, S and B use the same reference functions. The wire is the limit: see the tolerance of the wire you buy and the accuracy of the cold-junction sensor.
Sources: NIST ITS-90 thermocouple database and reference functions (NIST Monograph 175, Burns and others, 1993), through the thermocouple-converter library (MIT licence). Wire tolerance: ASTM E230 standard limits.
The formula
T_hot = T( V_read + E(T_cold) ) E(T) = NIST ITS-90 voltage of the type at T, reference junction at 0 °C °C per LSB = (Vref / 2^bits) / (gain · Seebeck)
When to use it
Reading a thermocouple with a bench meter or your own amplifier and ADC: checking a type K reading, working out what the firmware must add for the cold junction, or sizing the gain so one count is a fraction of a degree. A thermocouple makes a voltage from the temperature difference between the hot junction and its own terminals, so the terminal temperature has to be measured as well, usually with a thermistor or a sensor chip beside the terminals.
Pitfalls
- Compensate in volts, never in degrees. Convert the terminal temperature to its voltage, add that to the reading, then convert the sum. Adding the terminal temperature to the temperature the reading gives on its own is wrong because the curve is not a straight line: for type K at 1000 °C with the terminals at 50 °C the sum is about 1.6 °C low.
- Standard-grade thermocouple wire (ASTM E230 standard limits for types K and J) is good to ±2.2 °C or ±0.75 %, whichever is greater. That is larger than any rounding here, so the calculation is more precise than the wire.
- Measure the cold junction where the thermocouple wire ends and copper begins, and keep that block at one temperature. Air moving across a terminal block, or a hot part beside it, gives an error the sensor chip cannot see.
- The signal is tiny. A type K thermocouple makes about 41 µV per °C near 100 °C, so 1 µV of amplifier offset is about 0.024 °C. Pick an amplifier for low offset and low drift, and keep the leads short and twisted.
- Use extension wire and connectors of the same type. A copper or mismatched connector in the run adds another junction and another voltage.
- Outside the NIST range for the type the calculator shows a message and no number. Out-of-range values are not extrapolated.
Need a thermocouple or thermistor front end designed into your product, with the cold-junction sensing and firmware?