When to use
When reading a type K thermocouple with a multimeter or calibrator and you need the process temperature; when checking a transmitter or input card against the EMF measured at its terminals; when building the calibration sheet for a type K loop; and when chasing a suspicious reading (reversed polarity, wrong extension cable, forgotten cold junction).
The math in three steps
A thermocouple does not measure temperature: it measures the difference in temperature between the measuring junction (in the process) and the cold junction (at the instrument terminals). So converting millivolts to temperature on a type K is always:
- measure the EMF at the terminals,
E_measured(mV); - compute the cold junction EMF with the type K function itself,
E(t_ref), and add it:E(t_hot) = E_measured + E(t_ref); - invert the reference function:
t = E^-1(E(t_hot)).
The calculator above does all three. In the starting example — 15.000 mV with terminals at 25 °C — the cold junction contributes 1.0002 mV, the sum is 16.0002 mV and the temperature is 390.60 °C. Converting the 15.000 mV directly would give 366.84 °C.
Type K thermocouple table (reference junction at 0 °C)
Values computed from the ITS-90 reference function — the same one the calculator runs. To use it with the cold junction away from 0 °C, first add the terminal EMF (for example 1.0002 mV at 25 °C).
| Temperature (°C) | EMF (mV) | Seebeck (µV/°C) |
|---|---|---|
| −200 | −5.8914 | 15.26 |
| 0 | 0.0000 | 39.45 |
| 25 | 1.0002 | 40.52 |
| 100 | 4.0962 | 41.37 |
| 200 | 8.1385 | 39.97 |
| 400 | 16.3971 | 42.24 |
| 600 | 24.9055 | 42.51 |
| 800 | 33.2754 | 41.00 |
| 1000 | 41.2756 | 38.98 |
| 1200 | 48.8382 | 36.49 |
| 1372 | 54.8864 | 33.88 |
The full table, at any step, comes out of the calculator’s bench sheet (CSV button).
The ITS-90 inverse, range by range
Besides the direct function E(t), NIST publishes inverse polynomials t(E) for type K in three voltage windows:
- −5.891 to 0 mV (−200 to 0 °C), stated error −0.02 to +0.04 °C;
- 0 to 20.644 mV (0 to 500 °C), error −0.05 to +0.04 °C;
- 20.644 to 54.886 mV (500 to 1372 °C), error −0.05 to +0.06 °C.
Below −200 °C (down to −270 °C, −6.458 mV) there is no published inverse. Since the standard defines the direct function, the calculator uses the inverse only as a starting point and converges with Newton on E(t) — in the tails without an inverse, the seed comes from bisection. The result closes the round trip, which the inverse alone does not guarantee.
Cold junction: where almost every field error starts
With an ice bath, the reference junction sits at 0 °C and the terminal reading is already the absolute EMF — just invert it. With internal compensation (CJC), the instrument measures its own terminals and adds the term. Anyone checking a transmitter with a multimeter is in the second case without noticing: the multimeter reads the terminals, and the terminal temperature has to enter the math.
Two details change the number: the cold junction temperature is the one at the terminals, not the room (inside a closed panel it is usually much higher); and if there is copper cable between head and panel, the cold junction becomes the head — whose temperature nobody measures.
Polarity and extension cable
Chromel is positive and Alumel negative (and slightly magnetic). In the ANSI colour code red is always negative; in IEC 60584-3 type K uses green for positive and white for negative. Reversed polarity makes the reading move against the process temperature. Extension or compensating cable must be type K (KX, KCA, KCB): another type, or copper, creates an extra junction at every splice with a thermal gradient.
Other types and RTDs
For types J, T, N, E, R, S and B, for the reverse direction (temperature → mV, to simulate with a calibrator) and for Pt100/Pt1000, use the general thermocouple and RTD conversion page — the calculator is the same.
Formulas and fundamentals
E(t_hot) = E_measured + E(t_ref) A voltmeter at the terminals sees the difference between the two junctions. To get the measuring-junction EMF referenced to 0 °C, add the cold junction EMF — computed with the type K function at the terminal temperature. Only then convert to degrees. With an ice bath, E(t_ref) = 0.
E(t) = c1*t + c2*t^2 + ... + c10*t^10 E in mV, t in °C. Degree-10 polynomial with no exponential term; c1 = 0.039450128025 mV/°C.
E(t) = c0 + c1*t + ... + c9*t^9 + a0*exp(a1*(t - a2)^2) Degree-9 polynomial plus the Gaussian term for the magnetic anomaly of Chromel near 127 °C. c0 = −0.017600413686 mV exists to be cancelled by the exponential term at t = 0 — implementing the sum alone creates a step at zero.
t = d0 + d1*E + d2*E^2 + ... + dn*E^n Three windows: −5.891 to 0 mV (−200 to 0 °C, stated error −0.02 to +0.04 °C); 0 to 20.644 mV (0 to 500 °C, −0.05 to +0.04 °C); 20.644 to 54.886 mV (500 to 1372 °C, −0.05 to +0.06 °C). No published inverse below −200 °C. The calculator uses the inverse only as a seed and converges with Newton on the direct function, which is what the standard defines.
S(t) = dE/dt [µV/°C] Turns a reading uncertainty in mV into an uncertainty in degrees. For type K it stays near 40 µV/°C over most of the range — each µV is worth about 25 m°C.
Standards & methods
- ITS-90 · NIST Monograph 175 — type K reference function and inverse
- NIST Temperature Scale Database (SRD 60), Version 3.0 — DOI 10.18434/T4S888
- IEC 60584-1 — thermocouple reference functions and tolerances
- IEC 60584-3 — extension and compensating cables, colour code
Typical reference values
| Quantity | Typical range | Note |
|---|---|---|
| Type K reference function range | −270 to 1372 °C | −6.458 to 54.886 mV; the NIST inverse only covers −200 to 1372 °C |
| E(25 °C) — typical panel cold junction | 1.0002 mV | what you add to the reading when the terminals sit at 25 °C |
| E(100 °C) | 4.0962 mV | Seebeck at the point 41.37 µV/°C |
| E(1000 °C) | 41.2756 mV | Seebeck at the point 38.98 µV/°C — the curve is already flattening |
| NIST inverse polynomial error | up to ±0.06 °C | which is why the calculator iterates on the direct function |
Worked example
15.000 mV on a type K thermocouple with terminals at 25 °C
Inputs
- Thermocouple type
- K Chromel/Alumel
- EMF measured at the terminals
- 15.000 mV
- Cold junction (terminal) temperature
- 25.0 °C
Results
- E(t_ref) — cold junction EMF
- 1.0002 mV
- E(t_hot) = 15.000 + 1.0002
- 16.0002 mV
- Measuring junction temperature
- 390.60 °C
- Sensitivity at the point
- 42.18 µV/°C
- If the cold junction were ignored
- 366.84 °C (error of −23.75 °C)
Adding the 1.0002 mV of the terminals puts the measuring junction at 16.0002 mV referenced to 0 °C, which the type K function inverts to 390.60 °C (the NIST inverse polynomial seed landed 0.001 °C from the root; three Newton iterations closed the residual). The 42.18 µV/°C sensitivity means each µV of multimeter uncertainty is worth 23.7 m°C. Converting the 15.000 mV without compensating the cold junction would give 366.84 °C — the error is practically the terminal temperature itself, the classic symptom of a forgotten CJC.
Common mistakes
- Ignoring the cold junction. Looking the terminal voltage up in the table is only right with the reference junction at 0 °C. In the example below, 15.000 mV with terminals at 25 °C is 390.60 °C; converted without compensation it reads 366.84 °C — a 23.75 °C error, almost exactly the terminal temperature.
- Subtracting the cold junction instead of adding it. In the mV → °C direction the cold junction term enters with a POSITIVE sign: what the reading lacks is precisely the EMF between 0 °C and the terminal temperature. Subtracting doubles the error instead of fixing it.
- Reversed polarity. With the wires swapped the terminal voltage changes sign: the reading goes DOWN as the process heats, and with a hot process it falls out of the type K range, which ends at −6.458 mV. In the ANSI code the red conductor is always negative; in IEC 60584-3 type K uses green for positive and white for negative. Alumel (negative) is slightly magnetic — a magnet settles it.
- Using extension cable of another type, or copper, between head and panel. With copper, the cold junction becomes the sensor head, whose temperature the instrument does not measure; with type J cable, every stretch with a thermal gradient adds the Seebeck difference between the two pairs. The error moves with the weather and no bench calibration reproduces it.
- Linearizing with a fixed factor (mV ÷ 0.041). Type K sensitivity goes from 39.45 µV/°C at 0 °C to 42.63 µV/°C at 500 °C and 36.49 µV/°C at 1200 °C; a straight line is only right near the point it was taken from.
- Measuring room temperature instead of terminal temperature. The cold junction is wherever the thermocouple alloy meets copper — inside a closed panel that is usually several degrees above the room.
Frequently asked questions
How many mV does a type K thermocouple give at 100 °C?
4.0962 mV with the reference junction at 0 °C. With the cold junction at 25 °C the terminals read the difference, 4.0962 − 1.0002 = 3.0960 mV, and that is what a calibrator must inject to simulate 100 °C on an instrument with CJC.
Can I use the type K table if the cold junction is not at 0 °C?
Yes, with one extra step. The table is always referenced to 0 °C. First look up the EMF of the terminal temperature in the same table and ADD it to the reading; then look up the temperature for that sum. Using the raw reading is off by roughly the terminal temperature.
Why doesn't the calculator just use the NIST inverse polynomial?
Because it approximates the direct function, with a stated error of up to 0.06 °C for type K, and it does not exist below −200 °C. The calculator uses the inverse as a starting point and iterates on the direct function until the residual drops below double precision — the round trip closes.
What is the temperature range of a type K thermocouple?
The ITS-90 reference function spans −270 to 1372 °C (−6.458 to 54.886 mV). In practice the usable range depends on wire gauge and sheath; above about 1000 °C in a reducing atmosphere type K drifts and type N is usually the better choice.
Why does type K have an exponential term?
Chromel goes through magnetic ordering near 127 °C, and the curve picks up an inflection there that a degree-nine polynomial cannot reproduce. NIST adds a Gaussian term valid from 0 to 1372 °C; leaving it out costs about 2.6 °C at 100 °C.
Does it work for other types (J, T, N, E, R, S, B)?
Yes. The calculator is the same one as on the general thermocouple and RTD conversion page: just change the type in the selector. This page simply opens on type K, in the mV → °C direction.
Glossary
- Cold junction (reference junction)
- Where the thermocouple wires meet the instrument's copper — usually the terminals of the transmitter or input card. Its temperature must be known.
- CJC
- Cold Junction Compensation: the instrument measures its own terminal temperature and adds the matching EMF before converting.
- EMF
- Thermoelectric electromotive force, in mV — always a difference between two junctions.
- Chromel / Alumel
- The type K alloys: Chromel (nickel-chromium) is positive, Alumel (nickel-aluminium) is negative and slightly magnetic.
- Extension / compensating cable
- Cable whose alloys match the type K thermoelectric response (KX, KCA, KCB) and carry the cold junction to the instrument. It must be the same type and respect polarity.
- Seebeck coefficient
- The thermocouple sensitivity dE/dt at a point, in µV/°C.