Thermocouple Calculator (mV ↔ °C)

About the Thermocouple Calculator (mV ↔ °C)

Turn the millivolts a thermocouple gives into the temperature of its hot junction, or a temperature into the voltage a meter will read, for the eight letter types: B, E, J, K, N, R, S and T. The conversion uses the reference functions of the NIST ITS-90 Thermocouple Database, the same polynomials IEC 60584-1 publishes, and solves them exactly instead of using the shorter inverse polynomials, which can be 0.05 °C out.

Type the cold-junction temperature (where the thermocouple wires meet the copper of the meter) and the calculator applies cold-junction compensation the right way: by voltage, not by adding temperatures. Each result also shows the voltage referred to 0 °C, the sensitivity of the pair at that temperature, the IEC 60584-1 class 1 and class 2 tolerances there, and a reference table for the type in °C, °F or kelvin.

Without a pass, the free preview runs on your own reading: it shows the notes that apply and the temperatures of the reference table’s first rows, with the temperature or voltage you convert, every other figure and the working hidden; the full result, Copy result and the CSV table come with a Pro pass.

How cold-junction compensation works

A thermocouple measures the difference between its two junctions. The meter sees E_measured = E(t_hot) − E(t_cj), where E(t) is the type’s reference voltage at t with the reference junction at 0 °C. So the calculator first works out E(t_cj), adds it to the reading to get the voltage referred to 0 °C, and then finds the temperature with that voltage.

The relation is not a straight line, so adding the cold-junction temperature to a converted reading is wrong: the error grows with the difference in sensitivity between the two temperatures. Type B is the exception in practice: between 0 °C and 50 °C it makes almost no voltage (E(25 °C) is −0.0025 mV), so its cold junction hardly matters.

The reference functions

• Voltage from temperature: E = Σ cᵢ·tⁱ over two or three temperature subranges per type, with the coefficients of the NIST ITS-90 database (download page); type K adds a0·e^(a1·(t − a2)²) above 0 °C.
• Temperature from voltage: NIST also publishes inverse polynomials t = Σ dᵢ·Eⁱ that agree with the reference functions to a few hundredths of a degree. The calculator starts from them and refines the answer with Newton’s method on the reference function until it matches to better than a millionth of a degree, and shows the inverse polynomial’s own value beside it.
• Sensitivity: S = dE/dt, the Seebeck coefficient of the pair. At 25 °C it is about 61 µV/°C for type E, 52 for J, 41 for K and T, 27 for N and 6 for R and S.
• Ranges: K −270 °C to 1372 °C, J −210 °C to 1200 °C, T −270 °C to 400 °C, E −270 °C to 1000 °C, N −270 °C to 1300 °C, R and S −50 °C to 1768.1 °C, B 0 °C to 1820 °C.

The method and data are described in NIST Monograph 175.

Tolerance classes (IEC 60584-1)

The tolerance is the largest difference the standard allows between new, as-delivered thermocouple wire and the reference function; where two limits are given, the larger applies.

• Types K and N: class 1 ±1.5 °C or ±0.004·|t| from −40 °C to 1000 °C; class 2 ±2.5 °C or ±0.0075·|t| from −40 °C to 1200 °C.
• Type J: class 1 ±1.5 °C or ±0.004·|t|, class 2 ±2.5 °C or ±0.0075·|t|, both from −40 °C to 750 °C.
• Type E: class 1 ±1.5 °C or ±0.004·|t| from −40 °C to 800 °C; class 2 ±2.5 °C or ±0.0075·|t| from −40 °C to 900 °C.
• Type T: class 1 ±0.5 °C or ±0.004·|t|, class 2 ±1 °C or ±0.0075·|t|, both from −40 °C to 350 °C.
• Types R and S: class 1 ±1 °C from 0 °C to 1100 °C and ±[1 °C + 0.003·(t − 1100 °C)] up to 1600 °C; class 2 ±1.5 °C or ±0.0025·t from 0 °C to 1600 °C.
• Type B: no class 1; class 2 ±1.5 °C or ±0.0025·t from 600 °C to 1700 °C.

The standard also has a class 3, which this calculator does not show; for types T, E, K and N it reaches down to −200 °C and needs specially selected material.

Limitations

• The reference functions describe ideal wire. Real wire differs from them within its tolerance class, and drifts with time at high temperature; for better accuracy, calibrate the probe and apply its own correction.
• The cold-junction temperature must be the temperature of the junction itself: an error in it goes almost one-for-one into the result.
• Extension and compensating cables must match the thermocouple type; a copper cable or a wrong connector creates new junctions the calculator cannot know about.
• Type B gives almost no voltage below 50 °C, so voltages that low are not converted; it is meant for about 600 °C and above.

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