Thermocouple Cold Junction Compensation

T_hot = T_cjc + V / S

Quick answer

This calculator solves T_hot = T_cjc + V_measured / S for Hot Junction Temp. With Cold Junction Temp 110 °C, Thermocouple Voltage 100 µV, Seebeck Coefficient 10 µV/°C, the result is 120 °C. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Hot Junction Temp (°C)
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Formula

T_hot = T_cjc + V_measured / S

Description

A thermocouple measures temperature difference between its hot junction (measurement point) and cold junction (connection to the measurement instrument). Cold junction compensation (CJC) adds the known cold junction temperature to the temperature indicated by the thermocouple voltage to obtain the absolute hot junction temperature. The Seebeck coefficient relates the voltage to the temperature difference and varies by thermocouple type. This linearized formula is a good approximation over limited ranges but polynomial correction is needed for high accuracy.

Variables

  • T_hot — Actual temperature at the measurement point (°C)
  • T_cjc — Cold junction temperature measured by a separate sensor (°C)
  • V — Thermocouple output voltage (µV)
  • S — Seebeck coefficient (µV/°C)

Practical Notes

Common Seebeck coefficients at room temperature: Type K (chromel-alumel) ≈ 41 µV/°C, Type J (iron-constantan) ≈ 52 µV/°C, Type T (copper-constantan) ≈ 43 µV/°C. Dedicated thermocouple ICs like MAX31855 and ADS1118 handle CJC and linearization internally. For precision measurements, use NIST thermocouple reference tables with polynomial fitting.

Symbols and units

Symbol Meaning Default unit Accepted units
T_hot Hot Junction Temp °C °C
T_cjc Cold Junction Temp °C °C
V Thermocouple Voltage µV pV, nV, µV, mV, V, kV
S Seebeck Coefficient µV/°C µV/°C, mV/°C, V/°C

Step by step

  1. 1. What you know: Cold Junction Temp 110 °C, Thermocouple Voltage 100 µV, Seebeck Coefficient 10 µV/°C
  2. 2. The relation: T_hot = T_cjc + V_measured / S
  3. 3. Substitute: T_cjc = 110 °C, V = 100 µV, S = 10 µV/°C
  4. 4. Result: Hot Junction Temp = 120 °C

Worked examples

Minimum range

Given: Cold Junction Temp 5.5 °C, Thermocouple Voltage 1 µV, Seebeck Coefficient 0.1 µV/°C

Result: Hot Junction Temp = 15.5 °C

Low range

Given: Cold Junction Temp 55 °C, Thermocouple Voltage 10 µV, Seebeck Coefficient 1 µV/°C

Result: Hot Junction Temp = 65 °C

Typical

Given: Cold Junction Temp 110 °C, Thermocouple Voltage 100 µV, Seebeck Coefficient 10 µV/°C

Result: Hot Junction Temp = 120 °C

High range

Given: Cold Junction Temp 187 °C, Thermocouple Voltage 0.8 mV, Seebeck Coefficient 100 µV/°C

Result: Hot Junction Temp = 195 °C

Maximum range

Given: Cold Junction Temp 1870 °C, Thermocouple Voltage 8 mV, Seebeck Coefficient 1 mV/°C

Result: Hot Junction Temp = 1878 °C

Solving for each variable

Solve for Hot Junction Temp

Cold Junction Temp 5.5 °C, Thermocouple Voltage 1 µV, Seebeck Coefficient 0.1 µV/°C → 15.5 °C

Solve for Cold Junction Temp

Hot Junction Temp 2.5 °C, Thermocouple Voltage 1 µV, Seebeck Coefficient 0.1 µV/°C → -7.5 °C

Solve for Thermocouple Voltage

Hot Junction Temp 2.5 °C, Cold Junction Temp 5.5 °C, Seebeck Coefficient 0.1 µV/°C → -0.3 µV

Solve for Seebeck Coefficient

Hot Junction Temp 2.5 °C, Cold Junction Temp 5.5 °C, Thermocouple Voltage 1 µV → -0.3333 µV/°C

How Hot Junction Temp changes with Cold Junction Temp

Cold Junction Temp (input) Hot Junction Temp (result)
24.2 °C 34.2 °C
60.5 °C 70.5 °C
121 °C 131 °C
181.5 °C 191.5 °C
242 °C 252 °C
363 °C 373 °C
484 °C 494 °C
968 °C 978 °C
1694 °C 1704 °C
2420 °C 2430 °C

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Frequently asked questions

How do you calculate Thermocouple Cold Junction Compensation?

Use T_hot = T_cjc + V_measured / S. With Cold Junction Temp 110 °C, Thermocouple Voltage 100 µV, Seebeck Coefficient 10 µV/°C, Hot Junction Temp works out to 120 °C.

What is the formula for Thermocouple Cold Junction Compensation?

The formula is T_hot = T_cjc + V_measured / S. A thermocouple measures temperature difference between its hot junction (measurement point) and cold junction (connection to the measurement instrument).

How do you find Cold Junction Temp when you know the other values?

Rearrange for Cold Junction Temp: with Hot Junction Temp 2.5 °C, Thermocouple Voltage 1 µV, Seebeck Coefficient 0.1 µV/°C, Cold Junction Temp is -7.5 °C.

How do you find Thermocouple Voltage when you know the other values?

Rearrange for Thermocouple Voltage: with Hot Junction Temp 2.5 °C, Cold Junction Temp 5.5 °C, Seebeck Coefficient 0.1 µV/°C, Thermocouple Voltage is -0.3 µV.

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