RFrftools.io
Sensor

Thermocouple Voltage & Temperature

Calculate thermocouple EMF voltage from hot junction temperature and cold junction compensation for Type K, J, T, and E thermocouples.

Loading calculator...

Formula

E = S × (T_hot − T_cold)

Reference: NIST Monograph 175

S— Seebeck coefficient (K: 41 μV/°C) (μV/°C)
T— Temperature (°C)

How It Works

A thermocouple generates a thermoelectric EMF (electromotive force) proportional to the temperature difference between a hot junction and a cold (reference) junction via the Seebeck effect. The output voltage is E = S × (T_hot − T_cold), where S is the Seebeck coefficient in μV/°C. Each thermocouple type has a characteristic Seebeck coefficient: Type K (Chromel–Alumel) ≈ 41 μV/°C, Type J (Iron–Constantan) ≈ 51 μV/°C, Type T (Copper–Constantan) ≈ 43 μV/°C, and Type E (Chromel–Constantan) ≈ 68 μV/°C. In practice, the cold junction is not at 0 °C — it is at the measurement instrument terminal temperature. Cold junction compensation (CJC) adds or subtracts the cold-junction voltage correction to produce the correct measurement. NIST polynomial tables provide more accurate (non-linear) conversions over full thermocouple ranges; the linear Seebeck approximation used here is accurate to ±1–3% over moderate temperature ranges.

Worked Example

Problem
A Type K thermocouple has its hot junction at 350 °C and cold junction at 23 °C. What is the measured voltage, and what is the cold junction correction needed?
Solution
1. Type K Seebeck coefficient S = 41 μV/°C 2. ΔT = T_hot − T_cold = 350 − 23 = 327 °C 3. Measured EMF: E = 41 × 327 = 13,407 μV ≈ 13.4 mV 4. Cold junction correction: E_cjc = 41 × 23 = 943 μV ≈ 0.94 mV 5. True hot-junction voltage (ref 0 °C): 13.4 + 0.94 = 14.35 mV Result: The thermocouple output is 13.4 mV; the CJC correction adds 0.94 mV to reference to 0 °C.

Practical Tips

  • ✓Use the same type of extension wire as the thermocouple (Type K extension with Type K thermocouple) to avoid introducing additional Seebeck junctions at connections.
  • ✓An INA118 or AD8495 instrumentation amplifier with built-in cold-junction compensation simplifies thermocouple signal conditioning significantly.
  • ✓For temperatures above 1000 °C, Type K accuracy degrades due to preferential oxidation of aluminium; Type R or S (platinum-based) provide better accuracy at high temperatures.

Common Mistakes

  • ✗Ignoring cold junction compensation — if the terminal strip is at 30 °C instead of 0 °C, the error in a Type K measurement is 30 × 41 = 1230 μV, equivalent to a 30 °C temperature error.
  • ✗Using the wrong thermocouple type in lookup tables — Type K and Type J cables look similar; using J calibration on K wire introduces errors of up to 50 °C at high temperatures.
  • ✗Routing thermocouple extension wire near high-current conductors — the millivolt signals are easily corrupted by inductive coupling; always use twisted shielded thermocouple extension wire.

Frequently Asked Questions

Thermocouples measure the temperature difference between the hot and cold junctions, not absolute temperature. If the cold junction (at the instrumentation terminal) is not at the reference temperature (usually 0 °C), the reading includes an offset error. CJC measures the terminal temperature and subtracts the corresponding voltage contribution to recover the true hot-junction temperature.
Type K is the most widely used thermocouple covering −200 °C to +1372 °C with good sensitivity (41 μV/°C) and reasonable cost. Type T is preferred for low temperatures (−200 °C to +350 °C) due to better accuracy and oxidation resistance in moist environments.
The linear approximation is accurate to ±2–3% over a ±100 °C range around a reference point. For precision measurements or wide temperature ranges, use the NIST polynomial tables (NIST Monograph 175), which model non-linearity to ±0.02 °C.

Related Calculators

Sensor

PT100 Resistance

Calculate PT100 or PT1000 RTD resistance at any temperature using the ITS-90 Callendar-Van Dusen equation.

Sensor

RTD Temperature

Calculate temperature from PT100 or PT1000 RTD (Resistance Temperature Detector) measured resistance using the linear Callendar-Van Dusen approximation.

Sensor

NTC Thermistor

Calculate temperature from NTC thermistor resistance using the Steinhart-Hart beta equation. Useful for PT100/PT1000 and generic NTC thermistors.

Sensor

Wheatstone Bridge

Calculate Wheatstone bridge output voltage, balance condition, and sensitivity. Used for strain gauges, RTDs, and precision resistance measurements.

Sensor

Hall Effect Sensor

Calculate Hall voltage, Hall coefficient, and sensitivity for Hall effect sensors. Useful for magnetic field measurement, current sensing, and position detection.

Sensor

Strain Gauge Bridge

Calculate Wheatstone bridge output voltage for strain gauges. Supports quarter, half, and full bridge configurations for structural monitoring and load cell design.