Technical information

Callendar-Van Dusen equations for the calibration of platinum
resistance thermometers
WIKA data sheet IN 00.29

The accuracy of a platinum resistance thermometer (PRT)
can be improved by the calculation of coefficients.
PRTs are usually calibrated at several temperature points ina temperature range requested by the user. Generally, thethermometer is not used at the exact calibration points, butalso in between. This is why the user ofter requests a continuous description of the correlation between temperature andresistance over the complete temperature range used.

In most cases, this is achieved by the specification of amathematical equation that describes the measured temperature points as an approximation.
Also widely used is the Callendar-van Dusen equation (CvD)
which is used in DIN EN IEC 60751 as well in order to illustrate the so-called DIN characteristic curve.
In case of moderate requirements for measurement uncertainty, it is suitable for common Pt100 models across a wide
temperature range.

The coefficients A, B, C and the conversion into α, δ, βThe relationship between resistance and temperature forplatinum RTDs can be described by a polynomial.
In the early days of thermometry, Hugh Longbourne
Callendar (1863 - 1930), British physicist, used a simple
quadratic equation. Milton S. van Dusen, American chemist,
later found that a third order term was required to adequately
describe the relationship for temperatures below 0 °C. This
gave rise to the Callendar-van Dusen equations still valid
today:For t > 0 °C:
Rt = R0 (1 + At + Bt²)
For t < 0 °C:
Rt = R0 (1 + At + Bt² + C (t - 100) t³)
Legend:t = temperature in °C
Rt = resistance at temperature t
R0 = resistance at 0 °C

WIKA data sheet IN 00.29 ∙ 08/2014

These equations were used to establish the internationaltemperature scale of 1927 (ITS-27) between 1927 and 1990.
Since 1990 a more sophisticated equation has been usedat national standards level (as described in the internationaltemperature scale of 1990 (ITS-90)), but the Callendar-van
Dusen equations are still widely used with industrial PRTs.
Historically, the equations were written in an alternative butequivalent form:
For t > 0 °C:

t t 
Rt = R 0  1 + α  t + δ 1
100100For t < 0 °C:

 t 3 t t t 
Rt = R 0  1 + α  t + δ1+β 1
100 100 100   
 100  

Although this looks more complex than the version using A,
B and C coefficients, it is easier to derive the coefficientsfrom calibration data. This form was therefore favoured before
calculators and computers were available. It is still often used
today, especially in the USA.

Page 1 of 2
Similar technical information:
Usage limitations and accuracies of platinum resistance thermometers per EN 60751: 2008;
see IN 00.17

These forms of the equation are equivalent and it is a simple
matter to convert the coefficients from one form into theother:δ 
A=α  1+

100


B=-αδ
104

C=-αβ
108

Alternatively, for less accurate temperature measurement
generic values can be used. With generic coefficients, theaccuracy of the temperature measurement depends on anumber of factors, the most important being the purity of theplatinum.
The purity of the platinum is indicated by the α value, whichis easily determined as the average slope of the line between
the ice and steam points on the resistance-temperature
curve:
α=R100 °C - R0 °C
100 ∙ R0 °C

α = A + 100B
δ=

-104 ∙ B(A + 100B)

β=-108 ∙ C=(A + 100B)=-104 ∙ Bα-108 ∙ Cα

For best accuracy, a PRT should be individually calibrated togenerate the A, B, C or α, δ, β coefficients.

Typically, industrial PRTs have a nominal alpha value of
α = 3.85 ∙ 10-3 per °C.
For this grade of PRT, standard EN 60751:1995 provides
values for the coefficients of:
A = 3.9083 ∙ 10-3 °C-1
B = -5.775 ∙ 10-7 °C-2
C = -4.183 ∙ 10-12 °C-4
The converted values are as follows:
α = 3.85 ∙ 10-3 °C-1
δ = 1.500 °C
β = 0.1086

Page 2 of 2

WIKA data sheet IN 00.29 ∙ 08/2014

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info@wika.dewww.wika.de08/2014 GB© 2014 WIKA Alexander Wiegand SE & Co. KG, all rights reserved.
The specifications given in this document represent the state of engineering at the time of publishing.
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