Thermocouple Calculator (Type K Voltage and Temperature)
Thermocouple Calculator (Type K Voltage and Temperature)
Both directions on the NIST ITS-90 reference functions — temperature to millivolts and millivolts back to temperature — for type K, J and T, with the exponential term above 0 °C that most pages leave out, and with cold-junction compensation as a first-class input rather than an afterthought. It is the step that ruins more thermocouple builds than any other, and it works on voltages, not on temperatures.
Thermocouple
a type K junction at 100 °C with the terminal block at 25 °C
The ITS-90 reference functions, and cold-junction compensation
- E(t)
- the EMF a junction at t produces against a reference junction at 0 °C, in millivolts — a polynomial of degree 9 to 14 depending on the type and the range
- a₀, a₁, a₂
- type K only, above 0 °C: 0.118598, −1.18343×10⁻⁴ and 126.9686. The bump this adds peaks near 127 °C and is worth about 0.1 mV
- E(t_cold)
- the voltage the cold junction would have produced at ITS OWN temperature. Adding it back is cold-junction compensation
- E⁻¹
- NIST’s inverse polynomial, good to about ±0.05 °C, refined here by one Newton step against E(t)
Worked example
a type K junction at 100 °C with the terminal block at 25 °C
E(100 °C) from the ITS-90 function = 4.0962 mV against a 0 °C reference
E(25 °C) = 1.0002 mV — what the cold junction itself contributes, with the opposite sign
The meter therefore reads 4.0962 − 1.0002 = 3.096 mV
Going back the other way: 3.0960 + 1.0002 = 4.0962 mV, and the inverse function returns 100.000 °C
Do it wrongly — take the temperature for 3.0960 mV and add 25 — and you get 75.89 + 25 = 100.89 °C. Here that is only 0.89 °C out; at −100 °C with a 50 °C block the same mistake is 31.41 °C out
The sensitivity here is 41.37 µV/°C, so a microvolt of amplifier offset is 24.2 millidegrees
The three types, where they are used and what they give
| Type | Materials | Range (ITS-90) | µV/°C at 25 °C | mV at 100 °C | Notes |
|---|---|---|---|---|---|
| K | chromel / alumel | −270 to 1372 °C | 40.52 | 4.096 | the default choice; cheap, wide, and the most nearly linear of the three |
| J | iron / constantan | −210 to 1200 °C | 51.75 | 5.269 | the largest output per degree; the iron leg rusts, so not for damp or oxidising service above 760 °C |
| T | copper / constantan | −270 to 400 °C | 40.68 | 4.279 | the best of the three at cryogenic and sub-zero temperatures, and tolerant of moisture |
IEC 60584-1 tolerance classes
| Type | Class 1 | Class 2 | Class 3 |
|---|---|---|---|
| K | ±1.5 °C or ±0.004|t|, −40 to 1000 °C | ±2.5 °C or ±0.0075|t|, −40 to 1200 °C | ±2.5 °C or ±0.015|t|, −200 to 40 °C |
| J | ±1.5 °C or ±0.004|t|, −40 to 750 °C | ±2.5 °C or ±0.0075|t|, −40 to 750 °C | not defined |
| T | ±0.5 °C or ±0.004|t|, −40 to 350 °C | ±1.0 °C or ±0.0075|t|, −40 to 350 °C | ±1.0 °C or ±0.015|t|, −200 to 40 °C |
Reading a thermocouple properly
Two wires of different alloys joined at one end produce a voltage that depends on the temperature of the join — a few tens of microvolts per degree. What they actually produce is a voltage that depends on the temperature difference between the join and wherever the two wires stop being different, and that is the fact everything else on this page follows from. The published tables give the EMF against a reference junction held at 0 °C, because that is a temperature you can make with ice and water and nothing else.
Cold-junction compensation, and why it adds voltages. Your terminal block is not at 0 °C. Where the thermocouple wire meets copper — at the connector, the terminal strip, the screw terminals on the module — a second junction forms, and it produces its own EMF in the opposite direction. So the meter reads E(thot) − E(tcold), not E(thot). To recover the hot junction you measure the block’s temperature with something else (a thermistor or a semiconductor sensor), look up the voltage that temperature would have produced, add it to what the meter read, and convert the sum. Add voltages, then convert. Converting first and adding temperatures is the mistake, and it is wrong by exactly the curvature of the E(t) curve between the two points. At 100 °C with a 25 °C block, type K is straight enough that it costs only 0.89 °C and the error hides; at −100 °C with a 50 °C block it costs 31.41 °C on type K, 23.31 °C on type J and 38.59 °C on type T. Leaving the compensation out altogether is worse still and much more obvious: a 100 °C junction reads 75.89 °C.
The exponential term. Above 0 °C the ITS-90 reference function for type K is not a polynomial. NIST adds a term a₀·exp(a₁(t − a₂)²), a Gaussian bump centred near 127 °C, because the alloy has a magnetic ordering transition there that no reasonable polynomial fits. Most calculators and a great many firmware libraries quietly drop it, which costs up to about 0.1 mV — around two and a half degrees at the peak, right in the middle of the range most people use. It is included here, and every coefficient was checked against NIST Monograph 175’s printed tables before this page was written: fifteen temperatures for type K, ten for type J and seven for type T, all agreeing to within the tables’ own rounding.
Going the other way. NIST publishes inverse polynomials, one per voltage sub-range, accurate to about ±0.05 °C. This page evaluates those and then takes one Newton step against the direct function, which removes that residual entirely — round-tripping any temperature in range returns it to better than a thousandth of a degree. That precision is not the point, though. The tolerance table below is: a class 2 type K probe is ±2.5 °C as supplied, so the arithmetic was never the limiting factor. What limits a real thermocouple measurement is the cold-junction sensor’s own accuracy, the thermal gradient across the terminal block, the amplifier’s input offset voltage and its drift — at 41 µV/°C, ten microvolts of offset is a quarter of a degree — and, in the field, the extension wire. Extension wire must be of the same type as the thermocouple, or of matched compensating alloy; splice copper in anywhere warm and you have created a junction you are not measuring.
Thermocouple or RTD? Honestly: if the temperature is below about 500 °C and you can afford four wires, use a platinum RTD. A class A PT100 is ±0.15 °C at 0 °C against ±1.5 °C for a class 1 type K, its output is a resistance rather than tens of microvolts so the amplifier is far less critical, it needs no cold junction at all, and it is far more repeatable. The thermocouple wins on range — nothing else reaches 1372 °C on two cheap wires — on response time, because the junction can be tiny and has no self-heating, on ruggedness and vibration tolerance, and on cost per metre. It also fails safe in a useful way: a broken thermocouple reads open circuit, which is easy to detect. Whatever the sensor, the signal ends at a converter, so check what your reading is worth in codes with the ADC resolution calculator, and for the other two common sensors see the NTC thermistor calculator and the 4–20 mA loop calculator.
Frequently asked questions
How do you convert a thermocouple voltage to temperature?
Add back the voltage the cold junction would produce at its own temperature, then run the total through the inverse reference function. For type K at a 25 °C terminal block, a meter reading of 3.0961 mV becomes 3.0961 + 1.0002 = 4.0962 mV, which is 100 °C.
What is cold junction compensation?
Correcting for the fact that the terminal block where thermocouple wire meets copper is not at 0 °C. Measure that block’s temperature with another sensor, convert it to the voltage it would produce, and add that voltage to the meter reading before converting. Adding temperatures instead of voltages is the classic mistake.
Why can’t I just add the cold junction temperature to my reading?
Because the voltage-to-temperature relation is not a straight line, so the two operations do not commute. On type K near 100 °C the curve is straight enough that the error hides; at −100 °C with a 50 °C block the same shortcut is 31.41 °C out.
What is the output of a type K thermocouple per degree?
About 41 µV/°C near room temperature — 40.52 µV/°C at 25 °C rising to 41.37 µV/°C at 100 °C — falling to 39 µV/°C at 1000 °C and to 15 µV/°C at −200 °C. It is the most nearly linear of the common types, which is most of why it is the default.
How accurate is a type K thermocouple?
IEC 60584-1 class 1 is the greater of ±1.5 °C and ±0.004|t|, class 2 the greater of ±2.5 °C and ±0.0075|t|. That is the wire alone: your cold-junction sensor, the gradient across the terminal block and the amplifier’s offset all add to it.
Should I use a thermocouple or a PT100?
Below about 500 °C, a PT100 — it is roughly ten times more accurate, needs no cold junction, and its output is a resistance rather than microvolts. Above that, or where you need a fast response, a tiny sensor, ruggedness or low cost per metre, a thermocouple.
Related calculators
References
- NIST ITS-90 Thermocouple Database (Standard Reference Database 60), based on Burns GW, Scroger MG, Strouse GF et al. Temperature-Electromotive Force Reference Functions and Tables for the Letter-Designated Thermocouple Types Based on the ITS-90, NIST Monograph 175, 1993. Direct coefficients for types K, J and T with type K’s exponential term a₀ = 0.118597600000, a₁ = −0.118343200000×10⁻³, a₂ = 0.126968600000×10³; inverse coefficients with stated errors of ±0.02 to ±0.06 °C.
- IEC 60584-1:2013. Thermocouples — Part 1: EMF specifications and tolerances. Class 1 the greater of ±1.5 °C and ±0.004|t| (±0.5 °C for type T), class 2 the greater of ±2.5 °C and ±0.0075|t| (±1.0 °C for type T), class 3 the greater of ±2.5 °C and ±0.015|t| over −200 to +40 °C. Tolerance figures quoted here from supplier summaries of the standard, cross-checked between two independent sources; the standard itself is not freely available.
- Analog Devices. MT-032 Tutorial: Thermocouples, by Walt Kester. The thermocouple loop, why the connection to copper forms a second junction, and practical cold-junction compensation in a signal chain.