The Pt100 follows the famous Callendar–Van Dusen equation, used in almost all precision temperature measurement instruments:

R(T) = R₀ [1 + A·T + B·T² + C·(T − 100)·T³]

at :

• R₀ = 100 Ω (resistance to 0 °C)

• A = 3,9083 × 10⁻³

• B = −5,775 × 10⁻⁷

• C = −4,183 × 10⁻¹² (for T < 0 °C)

For T ≥ 0 °C, the CCC component becomes negligible.

🔹 Example 1 : calculation of resistance at 100 °C

We seek the resistance of the pt100 at 100°C :

R(100) = 100 × [1 + 3,9083 × 10⁻³ × 100 − 5,775 × 10⁻⁷ × 100²]

R(100) = 100 × (1 + 0,39083 − 0,005775)

R(100) = 100 × 1,385055 = 138,51 Ω

✅ Result : at 100 °C, the resistance of the Pt100 is approximately 138.5 Ω.

🔹 Example 2: calculating the temperature from a measured resistance

We measure R = 118.1 Ω. What is the temperature ?

T = (−A + √(A² − 4B(1 − R/R₀))) / (2B)

T = (−3,9083 × 10⁻³ + √[(3,9083 × 10⁻³)² − 4 × (−5,775 × 10⁻⁷) × (1 − 118,1 / 100)]) / [2 × (−5,775 × 10⁻⁷)]

T ≈ 46 °C
✅ Result : the corresponding temperature is approximately 46 °C.


🔹 Practical remarks

• The equation is integrated by default in most industrial temperature controllers and converters.
• For microcontrollers, it can be implemented via a simple polynomial function or replaced by an R/T table.
• The typical error between the equation and the standardized IEC 60751 tables is less than ±0.05 °C.

Thanks to its nominal resistance of 100 Ω, the Pt100 produces a usable signal without extreme amplification, while maintaining very good noise immunity.

It is used with a stable current source or a Wheatstone bridge and a differential amplifier.

Component	Function
RTD Pt100 (3 or 4 wires)	Sensitive platinum element
Current source (0.3 mA)	Feed the probe without overheating
INA333 / AD8426 Amplifier	Amplify the weak signal
16 to 24 bit ADC	Analog-to-digital conversion
Microcontroller (STM32, ESP32, Arduino)	Calculation T = f(R) + compensation
RC filtering / shielding	Reduction of pests and noise

             
	​	​	​+5 V
              │
     Current source (0.3 mA)
              │
           [ Pt100 ]
     (2 power wires + 2 measurement wires)
         │                  │
         │                  │
 Differential amplifier ──→ 24-bit ADC
                          │
                  [ Microcontroller ]
               (Calculating T = f(R) + display)

1️⃣ A constant current flows through the probe.

→ At 0 °C: V = 100 Ω × 0.3 mA = 30 mV

→ At 100 °C: V = 138.5 Ω × 0.3 mA = 41.6 mV

2️⃣ The amplifier raises the signal (gain ≈ 100 → 3 to 4 V).

3️⃣ The ADC digitizes the voltage, then the microcontroller applies the equation to calculate T.

🔹 Best practices

• 🧩 Use a 4-wire setup for precision measurements.
• 💧 Protect the probe from moisture and corrosion.
• ⚙️ Limit the excitation current to < 1 mA to avoid self-heating.
• 🔄 Calibrate regularly at fixed points (0 °C and 100 °C).
• 🧲 Use shielded twisted cables for long distances.