# 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) | |||

Coefficient | Value | Value | Value |

α | 0,003850 | 0,003926 | 0,003911 |

δ | 1,4999 | ||

β | 0,10863 | ||

A | 3,9083e^{-3} | 3,9848e^{-3} | 3,9692e^{-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 | -219.539 | 0.056 |

15.00 | -208.114 | 0.073 |

20.00 | -196.572 | 0.032 |

25.00 | -184.918 | 0.024 |

30.00 | -173.158 | 0.023 |

50.00 | -125.602 | 0.383 |

75.00 | -63.329 | -0.010 |

100.00 | 0.000 | |

102.00 | 5.121 | -0.024 |

103.00 | 7.685 | -0.022 |

107.79 | 19.991 | -0.012 |

115.54 | 39.998 | -0.009 |

120.00 | 51.566 | -0.010 |

123.24 | 59.995 | -0.011 |

130.90 | 80.008 | -0.012 |

150.00 | 130.447 | -0.017 |

175.00 | 197.673 | -0.021 |

200.00 | 266.348 | -0.027 |

210.00 | 294.246 | -0.029 |

220.00 | 322.397 | -0.031 |

250.00 | 408.450 | -0.045 |

275.00 | 482.109 | -0.048 |

300.00 | 557.688 | -0.055 |

310.00 | 588.491 | -0.058 |

399.00 | 879.278 | -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.