Thermocouple Voltage Formulas

Thermocouple formulas: the voltage from the temperature difference, the reference junction compensation and the temperature from a measured voltage.

The formulas

S is the Seebeck coefficient in µV per °C, Thot the temperature at the measuring junction and Tref the temperature at the reference (cold) junction, where the thermocouple wire meets the copper of the instrument. A thermocouple measures the difference, so the reference temperature must be measured and added, which is the cold junction compensation. The straight-line model with S = 41 µV/°C is a rough fit for a type K over a limited range. The real response is not a straight line, so a real instrument uses the standard tables or polynomials for the type (IEC 60584), and this page is only an estimate.

Worked example: a reading of 2.05 mV with the reference at 25 °C

1. Thot = 2.05 × 1000 / 41 + 25 = 75 °C

Worked example: the voltage at 150 °C with the reference at 20 °C

1. V = 41 × (150 − 20) / 1000 = 5.33 mV

Approximate voltage by temperature difference (S = 41 µV/°C)

Frequently asked questions

Why is a reference junction needed?

The voltage depends on the difference between the two junctions. Without the reference temperature the absolute temperature at the tip is unknown.

Can I use ordinary copper wire?

Not for the whole run. Use thermocouple wire or compensating cable of the same type up to the instrument, because a different metal adds a junction of its own.

Is the straight-line model accurate?

Only over a narrow range. Use the standard tables or the instrument's linearisation over a wide range.

How small is the signal?

A few tens of microvolts per degree, so the amplifier needs a low offset and the wiring needs shielding.

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