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RTD PT100 Resistance to Temperature

High-accuracy IEC 60751 conversion of RTD PT100 resistance values directly into Celsius/Fahrenheit.

Sensor Parameters

Ω
18.52 Ω (-200°C) 390.48 Ω (850°C)

Temperature Output

0.00 °C
32.00 °F
info
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Introduction to Pt100 and IEC 60751

The Pt100 Resistance Temperature Detector (RTD) is one of the most widely used temperature sensors in industrial automation due to its high accuracy, stability, and repeatability. “Pt” refers to platinum, and “100” indicates that its resistance at 0 °C is exactly 100 Ω. The universally accepted standard governing the resistance-to-temperature relationship of a standard platinum RTD is the IEC 60751 (equivalent to DIN EN 60751).

For automation engineers designing signal conditioning circuits or implementing PLC scaling logic, understanding the exact mathematical models behind this standard is crucial.

The Callendar-Van Dusen Equation

The IEC 60751 standard relies on the Callendar-Van Dusen (CVD) equation. This empirical formula defines the relationship between the resistance of the platinum element and its temperature. The equation has two variations depending on whether the measured temperature (t) is above or below 0 °C.

Calculating Resistance from Temperature

1. For Temperatures ≥ 0 °C

When the temperature is positive, the relationship is defined by a second-order polynomial (quadratic equation):

Rt = R0(1 + A t + B t2)

2. For Temperatures < 0 °C

When the temperature drops below zero, the sensor exhibits additional non-linearity. A third-order term is introduced to compensate:

Rt = R0[1 + A t + B t2 + C(t - 100)t3]

Standard IEC 60751 Coefficients

To implement these equations, the standard specifies the following constants for industrial-grade platinum (often referred to as having a temperature coefficient α = 0.00385 Ω/Ω/°C):

  • R0 = 100 Ω (Resistance at 0 °C)
  • A = 3.9083 × 10-3 °C-1
  • B = -5.775 × 10-7 °C-2
  • C = -4.183 × 10-12 °C-4 (Used only when t < 0 °C)

Converting Resistance to Temperature

In most industrial control systems (such as a DCS or PLC analog input module), the hardware measures the sensor’s resistance (Rt) and must calculate the corresponding temperature (t). This requires the mathematical inversion of the Callendar-Van Dusen equation.

1. Temperature Calculation for ≥ 0 °C

For temperatures above 0 °C (where Rt ≥ 100 Ω), we can solve the quadratic equation using the standard quadratic formula:

t = (-A + √(A2 - 4B(1 - Rt/R0))) / (2B)

This explicit algebraic solution is easy to implement in structured text or C-based microcontroller code.

2. Temperature Calculation for < 0 °C

For temperatures below 0 °C (where Rt < 100 Ω), the inclusion of the t4 term (expanded from C(t-100)t3) means there is no simple algebraic inverse. In digital automation systems, temperature is typically determined using one of the following methods:

  • Newton-Raphson Iteration: A numerical root-finding algorithm that rapidly converges on the exact temperature.
  • Polynomial Approximation: Using a pre-calculated best-fit polynomial designed explicitly to calculate temperature from resistance.
  • Look-up Tables (LUT): Interpolating between standardized resistance-temperature points.

Converting Celsius to Fahrenheit

The Callendar-Van Dusen equations are inherently based on the Celsius scale. If your control loop or HMI requires Fahrenheit, you must first calculate the temperature in Celsius and then apply the standard unit conversion:

T°F = (T°C × 9/5) + 32

Conclusion

Implementing the exact IEC 60751 formulas ensures maximum accuracy across the entire operational range of a Pt100 sensor. While hardware transmitters often handle these conversions internally, deep knowledge of the underlying equations is essential when developing custom instrumentation, writing software drivers, or troubleshooting high-precision automation systems.