Thermocouple Calculator (Type K, J, T, E, N)
Convert thermocouple voltage to temperature and back for types K, J, T, E and N using the NIST ITS-90 tables, with cold-junction compensation.
About thermocouples
E(t) = Σ cᵢ·tⁱ · measured = E(hot) − E(cold)
Two dissimilar metals joined together develop a voltage that depends on temperature — the Seebeck effect. A thermocouple exploits it with a pair of junctions, so what a meter reads is the difference between the measuring junction and the reference junction where the wires meet the instrument. This calculator uses the NIST ITS-90 reference functions for the five base-metal types, and shows the cold-junction step explicitly rather than folding it away.
How it works
The published tables give EMF against temperature for a reference junction held at exactly 0 °C. Your reference junction is not at 0 °C — it is at whatever your terminal block happens to be — so a correction is needed in both directions. Going from temperature to voltage, the calculator computes the table EMF for the hot junction and subtracts the table EMF for the cold junction; the difference is what a meter would actually show. Going from voltage to temperature, it adds the cold junction's EMF back on before looking the total up, which is exactly what the compensation circuit inside an instrument does.
The conversion itself is a polynomial fit — up to fifteen terms for type T below zero — and the reverse direction is solved numerically rather than with a second approximating polynomial, so a value converted one way and back returns exactly where it started.
Worked example
A type K probe in a 300 °C oven, with the instrument sitting on a bench at 25 °C. The table says 300 °C is 12.209 mV and 25 °C is 1.000 mV, so the meter sees the difference: 11.209 mV. Feed that raw figure back through the table as though the reference were an ice bath and it converts to about 275 °C — the reading is low by very nearly the temperature of the room. Add the millivolt back first and 300 °C returns.
Common mistakes
Forgetting compensation entirely is the big one, and it produces the signature error above: a reading low by roughly room temperature, which drifts as the room warms up. Extending with copper wire creates two new junctions partway along the cable and injects an error that depends on the temperature of the splice.Reversing the polarity gives a reading that falls as the process heats. And letting the terminal block sit in a gradient— near a hot regulator, or in the path of a fan — breaks the assumption that both terminals are at the single temperature your compensation sensor is measuring.
What this does not cover
Only the base-metal types K, J, T, E and N are here. The noble-metal types R, S and B use separate reference functions and are rare outside furnace and calibration work. More importantly, this is the idealconversion: it assumes wire that matches its standard exactly, and real thermocouples carry a tolerance class on top — commonly ±1.5 °C or ±0.4% of reading for class 1 type K, whichever is larger. Ageing, contamination and mechanical work all shift a thermocouple away from its table over time, which is why critical measurements are recalibrated rather than trusted indefinitely. The figures here are the standard, not a promise about the particular probe in your hand.
Related
For accurate work below about 600 °C aplatinum RTD is the better sensor, and an NTC thermistor is cheaper still for narrow ranges near ambient — including the job of measuring your own cold junction. Thesensor front-end calculatorcovers the amplifier that has to turn microvolts into something an ADC can read.
Common questions
- Why does a thermocouple need a second temperature to work?
- Because it never measures one temperature — it measures a difference. Joining two dissimilar metals produces a voltage that depends on the temperature gradient along the wires, so the pair of junctions gives you the difference between the hot end and wherever the wires meet the instrument. That second point is the cold junction or reference junction. Published tables assume it sits at exactly 0 °C, which historically meant an ice bath. Yours is at room temperature, so its own contribution has to be measured with a separate sensor and added back — that is cold-junction compensation, and it is why every thermocouple instrument contains a thermistor or a semiconductor temperature sensor at the terminal block.
- What happens if I ignore cold-junction compensation?
- You under-read by roughly the temperature of your terminal block. Measure a 300 °C junction with the meter at 25 °C and the raw voltage converts to about 275 °C. The error is not exactly the reference temperature, because the curve is not perfectly straight, but it is close enough that a reading suspiciously low by about room temperature is the first thing to suspect. This is the single most common thermocouple mistake, and it is easy to make when reading a raw ADC value from a thermocouple amplifier that does not compensate internally.
- Which thermocouple type should I use?
- Type K unless you have a reason otherwise — it is the widest-range, cheapest and most available, which is why it is the default on nearly every instrument. Choose type T for sub-zero and cryogenic work, type E when you want the most millivolts per degree and so the best resolution from a given ADC, type J for older industrial plant that already uses it, and type N where long-term stability matters more than availability, since it drifts far less than K at high temperature.
- Can I extend a thermocouple with ordinary copper wire?
- No, and this catches people out regularly. Every junction between dissimilar metals in the circuit produces its own voltage. Splicing copper onto a type K cable creates a new pair of junctions partway along, and unless that splice happens to be at the same temperature as the instrument terminals, it adds an error you cannot see or correct. Extend with matching thermocouple wire or with the cheaper alloy-matched extension grade cable, and keep the polarity right — reversing the leads is a classic fault that makes the reading move the wrong way as the process heats up.
- Why is the voltage so small?
- Because the Seebeck effect is weak. Type K gives about 41 µV per degree, so a junction at 25 °C above its reference produces around one millivolt — roughly a thousandth of what a typical ADC input range covers. That is why thermocouples need a dedicated amplifier, why microvolt-level offsets and thermal EMFs in the front end matter, and why a noisy ground can move a reading by degrees. The sensitivity figure shown above is the number to design that front end around.
- Is a thermocouple more accurate than a PT100?
- No. A platinum RTD is considerably more accurate and more repeatable over the range where both work, which is why RTDs are used for calibration and precision measurement. Thermocouples win on range, ruggedness, cost, size and speed: they reach temperatures that would destroy an RTD, survive vibration, can be made tiny enough to respond in milliseconds, and cost very little. Choose an RTD when you need accuracy under about 600 °C, and a thermocouple when you need range or toughness.