A thermocouple produces a small voltage proportional to the temperature difference between its measurement (“hot”) junction and reference (“cold”) junction (this is the Seebeck effect). Calculating or converting this voltage involves a few steps:

1. Determine the type of thermocouple and obtain reference data: Each thermocouple type (K, J, T, E, etc.) has a well-characterized voltage-vs-temperature response (often provided by NIST tables or polynomial equations). You’ll need the data or formula for your thermocouple type to relate voltage to temperature.
2. Measure the cold junction (reference) temperature: Unless your reference junction is exactly 0 °C (ice point), you must compensate for the fact that the reference end is not at 0 °C. Modern instruments have a built-in cold junction sensor to measure the terminal temperature.
3. Find the reference junction equivalent voltage: Using the thermocouple’s table, find what voltage would be generated by that type of thermocouple at the reference junction temperature. For example, if using a Type K and your reference is 25 °C, the table might say this corresponds to about 1.00 mV. This is often called V_ref.
4. Measure the thermocouple’s output voltage (relative to reference): Let’s call this V_D. This is the raw reading from the thermocouple wires.
5. Add the voltages (cold-junction compensation): The effective thermocouple voltage as if the reference were 0 °C is V_t = V_D + V_ref. In other words, we mentally “move” the reference to 0 °C by adding the reference junction’s equivalent voltage.
6. Convert total voltage to temperature: Now using the Type’s standard curve, find the temperature that corresponds to the voltage V_t. That will be the measured temperature at the hot junction.

For example, suppose you have a Type K thermocouple: the reference junction is at 22 °C (which, for Type K, is ~0.87 mV from the table) and the measured voltage from the thermocouple is 3.41 mV. Adding them gives V_t = 3.41 + 0.87 = 4.28 mV. Looking up 4.28 mV in the Type K table (or using the polynomial), you find that it corresponds to about 100 °C. This would mean the hot junction is ~100 °C. Many DAQ devices do all this internally: the cold junction sensor reading is used to automatically apply the compensation and convert the thermocouple voltage to a temperature reading. If doing it manually, use official thermocouple tables for accuracy, especially for higher temperatures where the voltage-temperature relationship is non-linear.

Thermocouple types (J, K, T, E, N, etc.) can be identified in a few ways, most commonly by the color coding of their wires or connectors, and by the magnetic/physical properties of the wires:
ANSI color code (North America): In ANSI/ASTM standards, red is the negative lead for all thermocouple types. The positive lead has a distinctive color for each type:

• Type K: Positive wire is yellow, negative wire is red. (Type K = Chromel/Alumel; the Alumel negative is magnetic.)
• Type J: Positive wire is white, negative wire red. (J = Iron/Constantan; the iron positive is magnetic.)
• Type T: Positive wire is blue, negative wire red.
• Type E: Positive wire is purple (sometimes violet), negative wire red.
• Type N: Positive wire is orange, negative wire red.
• (Type S/R: often black or green overall, with wire colors varying by manufacturer; Type B: usually gray overall in ANSI).

For example, a thermocouple with one yellow and one red lead is Type K, whereas one with blue and red leads is Type T.
IEC color code (Europe): Uses different colors (e.g., Type K positive is green in IEC, Type T positive is brown, etc., and negative is white in many cases). So be aware of the standard in use; often the overall cable jacket has a color too (IEC Type K jacket is green, Type J is black, Type T is brown, etc.).
Check markings: Some thermocouple connectors or cables have the type letter embossed or printed on them. For example, miniature thermocouple connectors are often color-coded (yellow connector for Type K, etc.) and may have the letter on the plastic.
Material/magnetic test: Type J has a magnetic iron wire; Type K’s Nickel-Chromium/Nickel-Alumel are partially magnetic (the Alumel is magnetic, Chromel is not). Type T’s copper wire is obviously copper-colored and non-magnetic, etc. This can sometimes help distinguish (e.g., if one wire is magnetic and one isn’t, that could indicate Type K). However, using color codes is simpler and more reliable.
Suppose the thermocouple wires have lost their insulation or have no obvious color. In that case, you might perform a calibration test: connect the pair to a thermometer reader and see the voltage generated at known temperatures, then compare with standard tables. The voltage response (Seebeck coefficient) differs by type (e.g., Type K ~41 µV/°C around room temp, Type T ~42 µV/°C, Type J ~52 µV/°C at 0–100 °C). This requires sensitive equipment, but it can identify the type by the voltage curve.
In summary, the easiest way is by insulation color coding per standards – for instance, a yellow/red thermocouple is Type K, white/red is Type J, blue/red is Type T, purple/red is Type E, orange/red is Type N in the ANSI system. Always ensure you know which standard is being used, and when replacing or extending thermocouples, match the type exactly (you must use thermocouple-grade extension wire of the same type for accuracy).