This is in a sense the reciprocal or converse function of the equation for converting voltage to temperature:

For all types of thermocouples (except K at t>0°C), we have:

$$ V(mV) = \mathop \sum \limits_{i = 0}^n {\left( {{t_{90}}} \right)^i} $$

For type K thermocouples at temperatures above 0°C, we have:

$$ T\left( {^\circ C} \right) = {T_{inf}}\left( {^\circ C} \right) + \frac{{V – {V_{inf}}}}{{{V_{sup}} – {V_{inf}}}} $$

Ci = Coefficients from C0 to Cn

t90 = Temperature of the thermocouple in °C

a0 to a2 = Specific coefficients of exponentiation only for type K thermocouples and temperatures above 0 °C

e= natural logarithm constant: 2.71828…

Example of coefficients for type K thermocouples
Temperature (°C)-270 to 00 to 1372
c00-0.176004136860e-1
c10.394501280250e-10.389212049750e-1
c20.236223735980e-40.185587700320e-4
c3-0.328589067840e-6-0.994575928740e-7
c4-0.499048287770e-80.318409457190e-9
c5-0.675090591730e-10-0.560728448890e-12
c6-0.574103274280e-120.560750590590e-15
c7-0.310888728940e-14-0.320207200030e-18
c8-0.104516093650e-160.971511471520e-22
c9-0.198892668780e-19-0.121047212750e-25
c10-0.163226974860e-22 
Exponential coefficients for temperatures above 0 °C
a00.1185976
a1-0.1183432e-3
a20.1269686e+3


VOLTAGE OF DIFFERENT THERMOCOUPLES FOR A TEMPERATURE OF 350 °C

Voltage calculated in mV
TypeBy ITS-90 tableVoltageDifference in %
B 0,596 0,596-0,018
E24,96424,9640,001
J19,09019,0900,002
K14,29314,2930,001
N11,13611,1360,002
R 2,896 2,8960,007
S 2,786 2,786-0,008
T17,81917,819-0,002