# Type T Thermocouple Calibration

Calibrate and convert type T thermocouple voltage to temperature accurately using rational polynomial function equations.

If you are using the Thermocouple Wildcard, type T voltage measurements are automatically converted to temperatures for you.

If you are using other hardware and are looking for equations to accurately convert type T thermocouple to voltage, we hope the type T thermocouple calibration equations and coefficients on this page will be helpful.

Functions for voltage to temperature conversion often use high-order polynomials. For example, the National Institute of Standards and Technology ITS-90 database of thermocouple values publishes a high order polynomial formula with coefficients for voltage-to-temperature conversion.

However, their high order polynomials are often not very accurate – they show systematic errors because the polynomial functions weave around the desired data, as shown by these curve fits to Type K thermocouple data.

The data can be fit with much lower errors using rational polynomial functions. This page provides those functions and coefficients so you can convert thermocouple voltage to temperature (for measurement) and temperature to voltage (for cold junction compensation) accurately and efficiently.

The rational polynomial coefficients for type T thermocouples provided here exhibit an order of magnitude lower errors than the type T NIST ITS-90 thermocouple coefficients, for both direct and inverse conversion.

## Type T calibration equation

A rational polynomial function approximation for Type T thermocouple data is used for computing temperature from measured thermocouple voltage (potential). The calibration function uses a ratio of two smaller order polynomials rather than one large order polynomial. Using a least squares curve fitting procedure we fit the National Institute of Standards and Technology (NIST) type T thermocouple data with a function of the following form,

where T is the thermocouple temperature (in °C), V is the thermocouple voltage (in millivolts), and To, Vo, and the pi and qi are coefficients. The function uses a ratio of two polynomials, P/Q, in this case a fourth order to a third order polynomial. The second form of the equation emphasizes the most efficient order of operations.

The coefficients, To, Vo, pi and qi were found by performing a least squares curve fit to the NIST data for type T thermocouples. The full temperature range is broken into several sub-ranges, and a different set of coefficients used for each. The coefficients, fitted data and charts of residual errors may be found in this Excel spreadsheet of thermocouple data.

The following table contains calibration coefficients for Type T thermocouple wire. The graph shows residual errors after calibrating the thermocouple with a rational function of polynomials. Most of the residual error results from rounding of the NIST provided voltage values to the nearest microvolt. The rational function approximation interpolates the data well so that computed values of temperature are more accurate than the residuals plots would indicate.

The following table is of calibration coefficients for Type T thermocouple wires.

 Range Voltage: Temperature: Coefficients -6.18 to -4.648 mV -4.648 to 0 mV 0 to 9.288 mV 9.288 to 20.872 mV -250 to -150°C -150 to 0°C 0 to 200°C 200 to 400°C `-1.9243000E+02` `-6.0000000E+01` `1.3500000E+02` `3.0000000E+02` `-5.4798963E+00` `-2.1528350E+00` `5.9588600E+00` `1.4861780E+01` `5.9572141E+01` `3.0449332E+01` `2.0325591E+01` `1.7214707E+01` `1.9675733E+00` `-1.2946560E+00` `3.3013079E+00` `-9.3862713E-01` `-7.8176011E+01` `-3.0500735E+00` `1.2638462E-01` `-7.3509066E-02` `-1.0963280E+01` `-1.9226856E-01` `-8.2883695E-04` `2.9576140E-04` `2.7498092E-01` `6.9877863E-03` `1.7595577E-01` `-4.8095795E-02` `-1.3768944E+00` `-1.0596207E-01` `7.9740521E-03` `-4.7352054E-03` `-4.5209805E-01` `-1.0774995E-02` `0.0` `0.0`

## Type T thermocouple accuracy and calibration error

The following graph shows residual errors after the calibration with a rational polynomial function.

Most of the residual error in the above graph results from rounding of the NIST provided voltage values to the nearest microvolt. You can see the rounding errors as aliasing or Moiré patterns in the data.

The rational function approximation interpolates the type T data well so that computed values of temperature are more accurate than the residuals plots would indicate.

## Computing type T cold junction voltages

Your type T thermocouple may be terminated at a cold junction temperature other than 0°C. If so, you must measure the temperature of the cold junction using another sensor, perhaps a thermistor. You can then compute a cold junction voltage from that measured temperature, and use it to compensate the type T thermocouple voltage before converting the thermocouple voltage to a temperature.

In that case you need the inverse transform, that is, an equation for converting temperature into voltage. You don't need a valid equation for a wide temperature range as the cold junction is likely to be placed at ambient temperature. Usually a range of -20 to +70°C is sufficient.

To convert temperature to voltage, you can again use a rational function approximation of the form,

where TCJ is the cold junction temperature, VCJ is the computed cold junction voltage, and the T0, V0, pi and qi are coefficients.

To learn more about cold junction compensation you can consult How To Do Cold Junction Compensation, and you can find the coefficients here:

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