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Thermocouple Seebeck Voltage

A thermocouple is made of two different metals joined at a point. When that junction is heated or cooled, it produces a small voltage. The voltage equals the Seebeck coefficient of the metal pair multiplied by the temperature difference between the hot junction and the cold reference junction. This effect is used to measure temperature in ovens, engines, and industrial processes. Different metal pairs have different Seebeck coefficients, giving different voltage ranges.

Written by the Vorzep Team

Instrumentation Temperature Sensing

Thermocouple Seebeck Voltage Calculator

A thermocouple makes a small voltage proportional to the temperature difference between its hot and cold junctions. Enter any two of V, Seebeck coefficient S and ΔT and the third is solved. Choose a thermocouple type, add a cold-junction temperature, amplifier gain and ADC details to see the hot-junction temperature and the temperature resolution of your measuring chain.

V = S · ΔTΔT = Thot − TcoldVpile = N · S · ΔT
Solve for
Thermocouple type (sets S)
Cold-junction temperature
°C
Enter a number.
Junction pairs in series (thermopile)
×
1 or more.
Amplifier gain
×
Above 0.
ADC resolution
bits
1 to 32.
ADC reference voltage
V
Above 0.
—
Temperature difference |ΔT|
03006009001200 °C
—

Step-by-step solution

Measurement chain and related values

Thermocouple circuit

Two dissimilar metals are joined at the hot junction. The voltage between the open ends depends on the temperature difference to the cold junction.

Voltage versus temperature difference

Reference data

Common thermocouple types (approximate)
TypeMetalsS (µV/°C)Typical range
Voltage at your S and number of pairs
ΔTVoltage (mV)After gain (V)Hot junction (cold at your Tc)
Nonlinearity: published voltages vs the linear estimate (cold junction at 0 °C)
TypeTemperaturePublished V (mV)Average S = V/ΔT (µV/°C)

Average S changes with temperature. The published values are rounded reference values (NIST ITS-90 tables). Use the full tables or polynomials for real work.

FAQ

What is the Seebeck effect?

When two different conductors are joined and their junctions are at different temperatures, a voltage appears between the ends. The Seebeck coefficient S is the voltage per degree of temperature difference, typically 6 to 70 µV/°C for standard thermocouples.

Why does the cold junction matter?

A thermocouple measures a temperature difference, not an absolute temperature. To get the hot-junction temperature you must know the reference (cold-junction) temperature, add ΔT to it, or compensate electronically. Using this tool, Thot = Tcold + ΔT.

Is the response really linear?

Only approximately. S changes with temperature, so a single S value is accurate over a narrow range. Real instruments use standard polynomial or table conversions. The nonlinearity table shows how the average S drifts.

How small a temperature change can I resolve?

One ADC step equals Vref / 2bits at the input, divided by the amplifier gain. Dividing by S gives the smallest temperature step, for example about 0.2 °C for a 12-bit, 3.3 V ADC with gain 100 and a type K couple. Noise and amplifier offset set the real limit.

Educational tool only. This applies the linear Seebeck relation with a constant coefficient. Real thermocouple readings need cold-junction compensation, standard conversion tables, correct extension wire, and attention to noise, grounding and wire tolerance. Do not rely on these estimates for safety-critical temperature control.

Variables

Symbol Quantity Unit
V Seebeck voltage (thermocouple output) µV
S Seebeck coefficient (thermopower) µV/°C
ΔT Temperature difference (hot junction – cold junction) °C

What it means

The Seebeck effect generates a voltage V between two junctions of dissimilar metals when there is a temperature difference ΔT between them. The voltage is given by V = S·ΔT, where S is the Seebeck coefficient (material‑dependent). Thermocouples are widely used as temperature sensors because they are rugged, low‑cost, and have a wide range. The output voltage is small (typically µV/°C) and must be amplified. The relationship is approximately linear, but corrections are needed for high accuracy. Example: A type‑K thermocouple has a Seebeck coefficient of about 40 µV/°C. For a 100°C temperature difference, V = 40e-6 * 100 = 4 mV. This signal is measured to determine the temperature.

Worked example

Thermocouple Seebeck Voltage – Practical Example

Real‑World
Scenario: A Type‑K thermocouple has Seebeck coefficient S ≈ 41 µV/°C. If the temperature difference is 100 °C, what is the output voltage?
ParameterValue
S41 µV/°C
ΔT100 °C
FormulaV = S·ΔT
1V = 41 × 100 = 4100 µV = 4.1 mV
Final Design V = 4.1 mV ✓ Thermocouple output
Why: The voltage is proportional to the temperature difference – this is the basis of thermocouple thermometry.

Common mistakes

Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.

Applications

Thermocouple Seebeck voltage V = S·ΔT generates a voltage proportional to the temperature difference between two junctions. This is the basis of thermocouple temperature measurement. Engineers use thermocouples in industrial process control, HVAC, and automotive applications. The Seebeck coefficient S determines sensitivity. Understanding this formula is essential for selecting and calibrating thermocouples.

  • Temperature measurement in industrial and laboratory settings
  • Process control and monitoring
  • Automotive exhaust and engine temperature sensing
  • HVAC temperature regulation
  • Educational understanding of thermoelectric effects

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  • Published July 10, 2026
  • Last updated August 9, 2026