NIST has ITS-90 Thermocouple Database with full description if thermocouple related values. Here we are reproducing only data relevant to type T thermocouple.
There are two Matlab scripts suitable to convert from temperature to thermoelectric voltage and back. They are available at matlab drive
There are also local copies of these scripts t_inC_to_mV.m and mV_to_t_inC.m.
Here is a quick examples of their use
>> Tin = [-200, -100, -20, 0, 10, 20]; % array of temperatures in degrees C
>> Tref = 22; % Temperature of the reference point
>> % Converting temperature to Thermoelectric voltage in mV
>> V = t_inC_to_mV(Tin, Tref)
V =
6.4733 4.2489 1.6271 0.8703 0.4793 0.0807
>> % Converting Thermoelectric voltage back to corresponding temperature
>> T = mV_to_t_inC(V, Tref)
T =
-200.0005 -100.0002 -20.0001 -0.0001 9.9999 19.9999Note that temperatures T and Tin agree to +/- 0.001 degrees.
Note that this table assumes that the reference end of the thermocouple is held at 0°C. If the reference is kept at another temperature use the adjusted formula V = V(T) − V(Tref), where T is temperature of the thermocouple, Tref is temperature of the reference end, and V is voltage taken from the table below. To get more understanding of this, review https://en.wikipedia.org/wiki/Thermocouple.
Table data source last checked on 2020/09/01.
°C 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
Thermoelectric Voltage in mV
-270 -6.258
-260 -6.232 -6.236 -6.239 -6.242 -6.245 -6.248 -6.251 -6.253 -6.255 -6.256 -6.258
-250 -6.180 -6.187 -6.193 -6.198 -6.204 -6.209 -6.214 -6.219 -6.223 -6.228 -6.232
-240 -6.105 -6.114 -6.122 -6.130 -6.138 -6.146 -6.153 -6.160 -6.167 -6.174 -6.180
-230 -6.007 -6.017 -6.028 -6.038 -6.049 -6.059 -6.068 -6.078 -6.087 -6.096 -6.105
-220 -5.888 -5.901 -5.914 -5.926 -5.938 -5.950 -5.962 -5.973 -5.985 -5.996 -6.007
-210 -5.753 -5.767 -5.782 -5.795 -5.809 -5.823 -5.836 -5.850 -5.863 -5.876 -5.888
-200 -5.603 -5.619 -5.634 -5.650 -5.665 -5.680 -5.695 -5.710 -5.724 -5.739 -5.753
-190 -5.439 -5.456 -5.473 -5.489 -5.506 -5.523 -5.539 -5.555 -5.571 -5.587 -5.603
-180 -5.261 -5.279 -5.297 -5.316 -5.334 -5.351 -5.369 -5.387 -5.404 -5.421 -5.439
-170 -5.070 -5.089 -5.109 -5.128 -5.148 -5.167 -5.186 -5.205 -5.224 -5.242 -5.261
-160 -4.865 -4.886 -4.907 -4.928 -4.949 -4.969 -4.989 -5.010 -5.030 -5.050 -5.070
-150 -4.648 -4.671 -4.693 -4.715 -4.737 -4.759 -4.780 -4.802 -4.823 -4.844 -4.865
-140 -4.419 -4.443 -4.466 -4.489 -4.512 -4.535 -4.558 -4.581 -4.604 -4.626 -4.648
-130 -4.177 -4.202 -4.226 -4.251 -4.275 -4.300 -4.324 -4.348 -4.372 -4.395 -4.419
-120 -3.923 -3.949 -3.975 -4.000 -4.026 -4.052 -4.077 -4.102 -4.127 -4.152 -4.177
-110 -3.657 -3.684 -3.711 -3.738 -3.765 -3.791 -3.818 -3.844 -3.871 -3.897 -3.923
-100 -3.379 -3.407 -3.435 -3.463 -3.491 -3.519 -3.547 -3.574 -3.602 -3.629 -3.657
-90 -3.089 -3.118 -3.148 -3.177 -3.206 -3.235 -3.264 -3.293 -3.322 -3.350 -3.379
-80 -2.788 -2.818 -2.849 -2.879 -2.910 -2.940 -2.970 -3.000 -3.030 -3.059 -3.089
-70 -2.476 -2.507 -2.539 -2.571 -2.602 -2.633 -2.664 -2.695 -2.726 -2.757 -2.788
-60 -2.153 -2.186 -2.218 -2.251 -2.283 -2.316 -2.348 -2.380 -2.412 -2.444 -2.476
-50 -1.819 -1.853 -1.887 -1.920 -1.954 -1.987 -2.021 -2.054 -2.087 -2.120 -2.153
-40 -1.475 -1.510 -1.545 -1.579 -1.614 -1.648 -1.683 -1.717 -1.751 -1.785 -1.819
-30 -1.121 -1.157 -1.192 -1.228 -1.264 -1.299 -1.335 -1.370 -1.405 -1.440 -1.475
-20 -0.757 -0.794 -0.830 -0.867 -0.904 -0.940 -0.976 -1.013 -1.049 -1.085 -1.121
-10 -0.383 -0.421 -0.459 -0.496 -0.534 -0.571 -0.608 -0.646 -0.683 -0.720 -0.757
0 0.000 -0.039 -0.077 -0.116 -0.154 -0.193 -0.231 -0.269 -0.307 -0.345 -0.383
°C 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
ITS-90 Table for type T thermocouple
°C 0 1 2 3 4 5 6 7 8 9 10
Thermoelectric Voltage in mV
0 0.000 0.039 0.078 0.117 0.156 0.195 0.234 0.273 0.312 0.352 0.391
10 0.391 0.431 0.470 0.510 0.549 0.589 0.629 0.669 0.709 0.749 0.790
20 0.790 0.830 0.870 0.911 0.951 0.992 1.033 1.074 1.114 1.155 1.196
30 1.196 1.238 1.279 1.320 1.362 1.403 1.445 1.486 1.528 1.570 1.612
40 1.612 1.654 1.696 1.738 1.780 1.823 1.865 1.908 1.950 1.993 2.036
50 2.036 2.079 2.122 2.165 2.208 2.251 2.294 2.338 2.381 2.425 2.468
60 2.468 2.512 2.556 2.600 2.643 2.687 2.732 2.776 2.820 2.864 2.909
70 2.909 2.953 2.998 3.043 3.087 3.132 3.177 3.222 3.267 3.312 3.358
80 3.358 3.403 3.448 3.494 3.539 3.585 3.631 3.677 3.722 3.768 3.814
90 3.814 3.860 3.907 3.953 3.999 4.046 4.092 4.138 4.185 4.232 4.279
100 4.279 4.325 4.372 4.419 4.466 4.513 4.561 4.608 4.655 4.702 4.750
110 4.750 4.798 4.845 4.893 4.941 4.988 5.036 5.084 5.132 5.180 5.228
120 5.228 5.277 5.325 5.373 5.422 5.470 5.519 5.567 5.616 5.665 5.714
130 5.714 5.763 5.812 5.861 5.910 5.959 6.008 6.057 6.107 6.156 6.206
140 6.206 6.255 6.305 6.355 6.404 6.454 6.504 6.554 6.604 6.654 6.704
150 6.704 6.754 6.805 6.855 6.905 6.956 7.006 7.057 7.107 7.158 7.209
160 7.209 7.260 7.310 7.361 7.412 7.463 7.515 7.566 7.617 7.668 7.720
170 7.720 7.771 7.823 7.874 7.926 7.977 8.029 8.081 8.133 8.185 8.237
180 8.237 8.289 8.341 8.393 8.445 8.497 8.550 8.602 8.654 8.707 8.759
190 8.759 8.812 8.865 8.917 8.970 9.023 9.076 9.129 9.182 9.235 9.288
200 9.288 9.341 9.395 9.448 9.501 9.555 9.608 9.662 9.715 9.769 9.822
210 9.822 9.876 9.930 9.984 10.038 10.092 10.146 10.200 10.254 10.308 10.362
220 10.362 10.417 10.471 10.525 10.580 10.634 10.689 10.743 10.798 10.853 10.907
230 10.907 10.962 11.017 11.072 11.127 11.182 11.237 11.292 11.347 11.403 11.458
240 11.458 11.513 11.569 11.624 11.680 11.735 11.791 11.846 11.902 11.958 12.013
250 12.013 12.069 12.125 12.181 12.237 12.293 12.349 12.405 12.461 12.518 12.574
260 12.574 12.630 12.687 12.743 12.799 12.856 12.912 12.969 13.026 13.082 13.139
270 13.139 13.196 13.253 13.310 13.366 13.423 13.480 13.537 13.595 13.652 13.709
280 13.709 13.766 13.823 13.881 13.938 13.995 14.053 14.110 14.168 14.226 14.283
290 14.283 14.341 14.399 14.456 14.514 14.572 14.630 14.688 14.746 14.804 14.862
300 14.862 14.920 14.978 15.036 15.095 15.153 15.211 15.270 15.328 15.386 15.445
310 15.445 15.503 15.562 15.621 15.679 15.738 15.797 15.856 15.914 15.973 16.032
320 16.032 16.091 16.150 16.209 16.268 16.327 16.387 16.446 16.505 16.564 16.624
330 16.624 16.683 16.742 16.802 16.861 16.921 16.980 17.040 17.100 17.159 17.219
340 17.219 17.279 17.339 17.399 17.458 17.518 17.578 17.638 17.698 17.759 17.819
350 17.819 17.879 17.939 17.999 18.060 18.120 18.180 18.241 18.301 18.362 18.422
360 18.422 18.483 18.543 18.604 18.665 18.725 18.786 18.847 18.908 18.969 19.030
370 19.030 19.091 19.152 19.213 19.274 19.335 19.396 19.457 19.518 19.579 19.641
380 19.641 19.702 19.763 19.825 19.886 19.947 20.009 20.070 20.132 20.193 20.255
390 20.255 20.317 20.378 20.440 20.502 20.563 20.625 20.687 20.748 20.810 20.872
400 20.872
°C 0 1 2 3 4 5 6 7 8 9 10
************************************
* This section contains coefficients for type T thermocouples for
* the two subranges of temperature listed below. The coefficients
* are in units of °C and mV and are listed in the order of constant
* term up to the highest order. The equation is of the form
* E = sum(i=0 to n) c_i t^i.
*
* Temperature Range (°C)
* -270.000 to 0.000
* 0.000 °C to 400.000
************************************
name: reference function on ITS-90
type: T
temperature units: °C
emf units: mV
range: -270.000, 0.000, 14
0.000000000000E+00
0.387481063640E-01
0.441944343470E-04
0.118443231050E-06
0.200329735540E-07
0.901380195590E-09
0.226511565930E-10
0.360711542050E-12
0.384939398830E-14
0.282135219250E-16
0.142515947790E-18
0.487686622860E-21
0.107955392700E-23
0.139450270620E-26
0.797951539270E-30
range: 0.000, 400.000, 8
0.000000000000E+00
0.387481063640E-01
0.332922278800E-04
0.206182434040E-06
-0.218822568460E-08
0.109968809280E-10
-0.308157587720E-13
0.454791352900E-16
-0.275129016730E-19
************************************
* This section contains coefficients of approximate inverse
* functions for type T thermocouples for the subranges of
* temperature and voltage listed below. The range of errors of
* the approximate inverse function for each subrange is also given.
* The coefficients are in units of °C and mV and are listed in
* the order of constant term up to the highest order.
* The equation is of the form t_90 = d_0 + d_1*E + d_2*E^2 + ...
* + d_n*E^n,
* where E is in mV and t_90 is in °C.
*
* Temperature Voltage Error
* range range range
* (°C) (mV) (° C)
* -200. to 0. -5.603 to 0.000 -0.02 to 0.04
* .0 to 400. 0.000 to 20.872 -0.03 to 0.03
********************************************************
Inverse coefficients for type T:
Temperature -200. 0.
Range: 0. 400.
Voltage -5.603 0.000
Range: 0.000 20.872
0.0000000E+00 0.000000E+00
2.5949192E+01 2.592800E+01
-2.1316967E-01 -7.602961E-01
7.9018692E-01 4.637791E-02
4.2527777E-01 -2.165394E-03
1.3304473E-01 6.048144E-05
2.0241446E-02 -7.293422E-07
1.2668171E-03 0.000000E+00
Error -0.02 -0.03
Range: 0.04 0.03