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THERMOCOUPLES

NFPA TIE ROD PNEUMATIC

AND HYDRAULIC CYLINDERS

LINEAR VALVE ACTUATORS

RTD’S 101

RTD Temperature Calculations


Callendar-Van-Dusen (CVD) Equation


The relationship between the temperature and ohmic value of RTD’s were calculated by Callendar, and later on, refined by Van Dusen; this is why the equation is named Callendar-Van Dusen.



With RT = resistance at T°C , R0 = resistance at 0°C, = temperature coefficient at 0°C in //°C, = linearisation coefficient, = second coefficient of linearisation for negatives temperature values ( = 0 for T > 0°C).

This equation has been transformed in order to be used easily with the coefficients A, B and C given by the standard DIN 43760 (IEC 751) and the component technicals specifications with the following conversions:


With the following conversions:



Different Coefficients for (alpha)
CoefficientValueValueValue
α0,0038500,0039260,003911
δ1,4999  
β0,10863  
A3,9083e-33,9848e-33,9692e-3
B-5,775e-7-5,870e-7-5,8495e-7
C-4,18301e-12-4,000e-12-4,2325e-12

These three values represent the three principal specifications for RTD’s.
  • 0,003850 //°C: Standard DIN 43760, IEC 751, named Europeen Industrial Standard.
  • 0,003926 //°C: Require pur platinum (99,999%), named U.S. Industrial Standard.
  • 0,3911 //°C: Often named U.S. Industrial Standard.


The Callendar-Van Dusen equation permits a good linearity of RTD’s, ±0.01°C between -100°C and +100°C but the error increases rapidly with high temperatures. Furthermore, this equation calculates the resistance with temperature change; which is the opposite of the most current uses : Temperature with resistance change.


To convert the resistance value of the RTD to temperature, we are obliged to use a quad equation to the 2nd degree, which is, in sort, the reciprocal of the Callendar-Van Dusen equation, but iniquely for temperatures superior to 0°C.


For temperatures inferior to 0 C, the Callendar-Van Dusen equation is too complex to reslove and the the use of successive approximations is necessary:



The following table propose calculated values with the Callendar-Van Dusen equation.


Temperatures from resistance
Resistance () CVD Equation (°C)Error (%)
10.00-219.5390.056
15.00-208.1140.073
20.00-196.5720.032
25.00-184.9180.024
30.00-173.1580.023
50.00-125.6020.383
75.00-63.329-0.010
100.000.000 
102.005.121-0.024
103.007.685-0.022
107.7919.991-0.012
115.5439.998-0.009
120.0051.566-0.010
123.2459.995-0.011
130.9080.008-0.012
150.00130.447-0.017
175.00197.673-0.021
200.00266.348-0.027
210.00294.246-0.029
220.00322.397-0.031
250.00408.450-0.045
275.00482.109-0.048
300.00557.688-0.055
310.00588.491-0.058
399.00879.278-0.095


We can see that the gaps of the Callendar-Van Dusen equation are limited and are found around 0,05% and 0,1% for higher temperatures.