{"id":3242,"date":"2023-05-02T06:36:57","date_gmt":"2023-05-02T06:36:57","guid":{"rendered":"https:\/\/thermibel.be\/faq\/how-do-you-convert-voltage-to-temperature\/"},"modified":"2023-06-27T12:09:35","modified_gmt":"2023-06-27T12:09:35","slug":"how-do-you-convert-voltage-to-temperature","status":"publish","type":"faq","link":"https:\/\/thermibel.be\/en\/faq\/how-do-you-convert-voltage-to-temperature\/","title":{"rendered":"How do you convert voltage to temperature?"},"content":{"rendered":"\n

Now that we have used either software compensation or hardware compensation to obtain a reference junction at 0\u00b0C, we must now convert the voltage measured V to temperature.<\/p>\n\n\n\n

Unfortunately, the relationships between thermocouple voltage and temperature are not linear.<\/u><\/p>\n\n\n

\n
\"Figure<\/figure>\n<\/div>\n\n\n

Figure 4. Thermocouple voltage as a function of temperature<\/p>\n\n\n\n

Type<\/td>Metal A (+)<\/td>Metal B (-)<\/td><\/tr>
E<\/td>Chromel<\/td>Constantan<\/td><\/tr>
J<\/td>Iron<\/td>Constantan<\/td><\/tr>
K<\/td>Chromel<\/td>Alumel<\/td><\/tr>
R<\/td>Platinum<\/td>Platinum
13% Rhodium<\/td><\/tr>
S<\/td>Platinum<\/td>Platinum
10% Rhodium<\/td><\/tr>
T<\/td>Copper<\/td>Constantan<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

In order to obtain a better picture of this non-linearity, let\u2019s look at the Seebeck coefficient as a function of temperature:<\/strong><\/p>\n\n\n

\n
\"Figure<\/figure>\n<\/div>\n\n\n

Figure 5. Seebeck coefficient as a function of temperature for different types of thermocouples<\/p>\n\n\n\n

Note that the type K thermocouple has a section which is almost linear between 0\u00b0C et 1000\u00b0C with a Seebeck coefficient \u03b1 fluctuating around 40 \u00b5V\/\u00b0C. Therefore this type of thermocouple can be used directly with a voltmeter multiplier and reference 0\u00b0C to obtain the temperature with moderate accuracy. <\/p>\n\n\n\n

Calculation using tables<\/strong><\/p>\n\n\n\n

After reading the voltage value V, for example 8.35687 mV, with a type K thermocouple (Chromel\/Alumel), let\u2019s look in the ITS-90 table:<\/p>\n\n\n\n

ITS-90 table for Type K Thermocouple
Thermoelectric voltage in mV<\/strong><\/td><\/tr>
\u00b0C<\/td>0<\/td>1<\/td>2<\/td>3<\/td>4<\/td>5<\/td>6<\/td>7<\/td>8<\/td>9<\/td>10<\/td><\/tr>
190<\/td>7.739<\/td>7.779<\/td>7.819<\/td>7.859<\/td>7.899<\/td>7.939<\/td>7.979<\/td>8.019<\/td>8.059<\/td>8.099<\/td>8.138<\/td><\/tr>
200<\/td>8.138<\/td>8.178<\/td>8.218<\/td>8.258<\/td>8.298<\/td>8.338<\/td>8.378<\/td>8.418<\/td>8.458<\/td>8.499<\/td>8.539<\/td><\/tr>
210<\/td>8.539<\/td>8.579<\/td>8.619<\/td>8.659<\/td>8.699<\/td>8.739<\/td>8.779<\/td>8.819<\/td>8.860<\/td>8.900<\/td>8.940<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

We can see that this value is between Tinf 205 \u00b0C (8.338 mV) and Tsup 206 \u00b0C (8.378 mV). Let\u2019s make a calculation by interpolation between the values 205 and 206 \u00b0C: <\/p>\n\n\n\n

8.35687 – 8.338 = 0.01887 mV (remaining voltage above 205 \u00b0C)

8.378 – 8.338 = 0.040 mV for a difference of 1 \u00b0C

0.01887 \/ 0.040 = 0.471 \u00b0C in addition

The temperature is therefore 205 + 0.471 = 205.471 \u00b0C<\/strong>

In summary, the equation is:<\/p>\n\n\n\n

= 205 + [(8.35687 – 8.338) \/ (8.378 – 8.338)] = 205.471 \u00b0C

Or:
$$ T\\left( {^\\circ C} \\right) = {T_{inf}}\\left( {^\\circ C} \\right) + \\frac{{V – {V_{inf}}}}{{{V_{sup}} – {V_{inf}}}} $$<\/p>\n\n\n\n

Calculation by polynomial equation<\/strong><\/p>\n\n\n\n

It is possible to calculate the temperature from the thermoelectric voltage by means of a polynomial equation:
$$ {T_{90}} = {c_0} + {c_1}V + {c_2}{V^2} + \\cdots + {c_n}{V^n} $$<\/p>\n\n\n\n

T90 = Temperature in \u00b0C<\/p>\n\n\n\n

V = Thermoelectric voltage in mV<\/p>\n\n\n\n

c = Polynomial coefficients<\/p>\n\n\n\n

n = Maximum order of the polynomial equation<\/p>\n\n\n\n

<\/p>\n\n\n\n

Example of coefficients for type K thermocouples<\/strong><\/td><\/tr>
Temperature (\u00b0C)<\/td>-200 to 0<\/td>0 to 500<\/td>500 to 1372<\/td><\/tr>
Voltage (mV)<\/td>-5.891 to 0.000<\/td>0.000 to 20.644<\/td>20.644 to 54.886<\/td><\/tr>
c0<\/sub><\/td>0<\/td>0.000000E+00<\/td>-1.318058E+02<\/td><\/tr>
c1<\/sub><\/td>2.5173462E+01<\/td>2.508355E+01<\/td>4.830222E+01<\/td><\/tr>
c2<\/sub><\/td>-1.1662878E+00<\/td>7.860106E-02<\/td>-1.646031E+00<\/td><\/tr>
c3<\/sub><\/td>-1.0833638E+00<\/td>-2.503131E-01<\/td>5.464731E-02<\/td><\/tr>
c4<\/sub><\/td>-8.9773540E-01<\/td>8.315270E-02<\/td>-9.650715E-04<\/td><\/tr>
c5<\/sub><\/td>-3.7342377E-01<\/td>-1.228034E-02<\/td>8.802193E-06<\/td><\/tr>
c6<\/sub><\/td>-8.6632643E-02<\/td>9.804036E-04<\/td>-3.110810E-08<\/td><\/tr>
c7<\/sub><\/td>-1.0450598E-02<\/td>-4.413030E-05<\/td>0<\/td><\/tr>
c8<\/sub><\/td>-5.1920577E-04<\/td>1.057734E-06<\/td>0<\/td><\/tr>
c9<\/sub><\/td>0<\/td>-1.052755E-08<\/td>0<\/td><\/tr>
Error (\u00b0C)<\/td>-0.02 to 0.04<\/td>-0.05 to 0.04<\/td>-0.05 to 0.06<\/td><\/tr>
The coefficients for other types of thermocouples are given in appendices at the end of the ITS-90 tables<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"featured_media":0,"template":"","format":"standard","class_list":["post-3242","faq","type-faq","status-publish","format-standard","hentry"],"acf":[],"aioseo_notices":[],"yoast_head":"\nHow do you convert voltage to temperature? - Thermibel<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/thermibel.be\/en\/faq\/how-do-you-convert-voltage-to-temperature\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How do you convert voltage to temperature? - Thermibel\" \/>\n<meta property=\"og:description\" content=\"Now that we have used either software compensation or hardware compensation to obtain a reference junction at 0\u00b0C, we must now convert the voltage measured V to temperature. 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