Thermocouple millivolt to temperature calculator
Convert between millivolts and temperature for type K, T, J, N and E using the NIST ITS-90 reference functions, with proper cold-junction compensation and IEC 60584-1 tolerance classes.
A thermocouple measures the difference between its two junctions. The reference-junction emf is added back to your reading before conversion — adding the reference temperature to a converted reading gives a different, wrong answer, because the curve is not linear.
Result
| Class | Tolerance at 300.0 °C | In millivolts |
|---|---|---|
| 1 | ±1.50 °C | ±0.0622 mV |
| 2 | ±2.50 °C | ±0.1036 mV |
| 3 | not defined here | — |
Tolerance is a manufacturing limit on unused wire, not a measurement uncertainty. A calibration replaces it.
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Type K reference points (vs 0 °C)
A worked example
A type K thermocouple is read on a millivolt meter that shows 4.096 mV. The terminals, where the thermocouple wire meets copper, are at 22.5 °C.
What you start with
- Thermocouple type
- K
- Measured emf
- 4.096 mV
- Cold junction temperature
- 22.5 °C
The arithmetic
- 01
Find the emf type K would give at the cold junction temperature against an ice point.
E(22.5 °C) = 0.8991 mV
- 02
Add it to the measured emf to get the emf referenced to 0 °C.
4.096 + 0.8991 = 4.9951 mV
- 03
Invert the ITS-90 reference function for type K.
4.9951 mV → 121.836 °C
121.836 °C. Taking the 4.096 mV straight to a table instead gives 99.994 °C.
The error from skipping compensation is 21.84 °C, not 22.5 °C. Cold junction compensation is not "add the room temperature" — you add the voltage that the room temperature is worth, and because the Seebeck coefficient changes with temperature the two answers differ by two-thirds of a degree here and by more at higher readings. Anyone who checks compensation by seeing whether the correction looks like room temperature will accept a wrong instrument.
How the calculation works
- 01Emf against a 0 °C reference junction from the NIST ITS-90 Thermocouple Database (Monograph 175) polynomials for each type, including the exponential term type K adds above 0 °C.
- 02Cold-junction compensation done in emf, not in degrees: E(t_junction) = E_measured + E(t_reference), then the sum is inverted.
- 03Inversion is performed on the reference function itself (bisection then Newton), so the reverse direction agrees with the forward one exactly, including at branch boundaries.
- 04Tolerance classes from IEC 60584-1, stated as the greater of the fixed limit and the proportional term, over each class's defined range.
Limitations
- These are the standard reference functions for new, nominal wire. A calibrated thermocouple has its own deviation from them, on its certificate — use that for measurement.
- It does not model the errors that dominate thermocouple work in practice: inhomogeneity along the wire, extension-lead mismatch, junction contamination or drift after thermal cycling.
- Tolerance is not uncertainty. A class 1 type K is not a ±1.5 °C measurement until the whole chain, reference junction included, has been accounted for.
Frequently asked questions
- How do I convert thermocouple millivolts to temperature?
- Add the emf of your reference junction to the measured voltage, then invert the type's reference function. If your meter's terminals are at 25 °C and you read 12.209 mV on a type K, the junction emf is 12.209 + 1.000 = 13.209 mV, which is 324 °C — not 300 °C, and not 300 + 25.
- Why can I not just add the cold-junction temperature to the answer?
- Because the emf-temperature relationship is not linear. Adding degrees instead of millivolts introduces an error that grows with the difference between the two junctions, and it is a common source of a few degrees of unexplained bias.
- What is 0 mV on a thermocouple?
- The junction is at the same temperature as the reference junction. With an ice-point reference that means 0 °C; with the meter's terminals as the reference it means the junction is at terminal temperature. A thermocouple never measures an absolute temperature by itself.
- Which thermocouple type should I use?
- Type T below 0 °C — it is the best behaved of the common types in cold-chain and cryogenic work. Type K for general-purpose wide-range use. Type N where you would use K but need stability at high temperature. Type E when you want the largest output per degree. Type J mainly where existing plant already uses it.
- What is the difference between class 1 and class 2?
- IEC 60584-1 tolerance bands on the wire. For type K, class 1 is the greater of ±1.5 °C and ±0.004|t|; class 2 is the greater of ±2.5 °C and ±0.0075|t|. At 1000 °C that is ±4 °C against ±7.5 °C. Class 3 covers sub-zero use for the types that define it.
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Thermocouple types and tolerance classes (IEC 60584)
Types K, J, T, N and E each have a defined EMF curve and tolerance classes 1, 2 and 3. The tolerance applies to new wire, not to a year-old thermocouple.
How thermocouples are calibrated
Comparison against a reference in a bath or furnace, with the reference junction realised. Ignore it on a type K at 420 °C and you read 398 °C.
Uncertainty budget for a thermocouple calibration
Inhomogeneity, reference junction and extension leads join the comparison budget. At 400 °C on a type K, inhomogeneity alone carries 85 % of the variance.
Selecting a reference thermometer
Pick a reference for stability first and certificate uncertainty second: one that drifts between its own calibrations is worse than a larger honest number.
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