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PT100/PT1000 Resistance vs Temperature

Calculate PT100 or PT1000 RTD resistance at any temperature using the ITS-90 Callendar-Van Dusen equation.

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Formula

R(T) = R₀(1 + AT + BT²) for T ≥ 0°C

Reference: IEC 60751 / ITS-90

R₀— Resistance at 0°C (Ω)
A— 3.9083 × 10⁻³ (/°C)
B— −5.775 × 10⁻⁷ (/°C²)

How It Works

PT100 and PT1000 are platinum resistance temperature detectors (RTDs) that exploit the predictable relationship between temperature and the electrical resistance of platinum. A PT100 sensor has a nominal resistance of 100 Ω at 0 °C; a PT1000 has 1000 Ω at 0 °C. The resistance-temperature relationship is described by the Callendar-Van Dusen (CVD) equation, standardised in IEC 60751 / ITS-90: R(T) = R₀(1 + AT + BT²) for temperatures ≥ 0 °C, with an additional cubic correction term C(T − 100)T³ below 0 °C. The coefficients are A = 3.9083 × 10⁻³ /°C, B = −5.775 × 10⁻⁷ /°C², and C = −4.183 × 10⁻¹² /°C⁴. The approximate sensitivity near 0 °C is 0.385 Ω/°C for PT100 and 3.85 Ω/°C for PT1000. Higher R₀ values give better resolution in low-noise measurement circuits. PT100/1000 sensors cover −200 °C to +850 °C with accuracies as tight as ±0.1 °C for Class AA (IEC 60751).

Worked Example

Problem
Calculate the resistance of a PT1000 sensor at 150 °C.
Solution
1. R₀ = 1000 Ω (PT1000) 2. T = 150 °C (positive, use two-term CVD) 3. A = 3.9083 × 10⁻³, B = −5.775 × 10⁻⁷ 4. R(150) = 1000 × (1 + 3.9083×10⁻³ × 150 + (−5.775×10⁻⁷) × 150²) 5. R(150) = 1000 × (1 + 0.58625 − 0.013) = 1000 × 1.5732 = 1573.2 Ω 6. Sensitivity at 150 °C: dR/dT = 1000 × (A + 2BT) = 1000 × (3.9083×10⁻³ − 2×5.775×10⁻⁷×150) = 3.735 Ω/°C Result: PT1000 reads 1573.2 Ω at 150 °C with sensitivity 3.74 Ω/°C.

Practical Tips

  • ✓Use 4-wire (Kelvin) connection to eliminate lead resistance errors — even 0.1 Ω lead resistance introduces 0.26 °C error in a PT100 system.
  • ✓Choose PT1000 over PT100 when lead resistance is unavoidable (e.g., long cable runs) since lead resistance is proportionally 10× smaller.
  • ✓Limit excitation current to 1 mA or less to keep self-heating below 0.05 °C in typical industrial installations.

Common Mistakes

  • ✗Using only the two-term CVD equation below 0 °C — the cubic term C is significant below −100 °C and omitting it causes errors exceeding 1 °C.
  • ✗Ignoring self-heating error: a 1 mA excitation through a 100 Ω PT100 dissipates 0.1 mW, which can raise sensor temperature by 0.1–0.5 °C depending on mounting.
  • ✗Confusing PT100 and PT1000 R₀ values — plugging 100 Ω calibration data into a PT1000 calculation produces a 10× resistance error.

Frequently Asked Questions

Both use the same platinum resistance-temperature relationship. PT100 has R₀ = 100 Ω and sensitivity ~0.385 Ω/°C; PT1000 has R₀ = 1000 Ω and sensitivity ~3.85 Ω/°C. PT1000 provides 10× better resolution and is preferred when lead resistance is significant or when interfacing directly to microcontroller ADCs.
IEC 60751 defines Class AA (±0.1 °C at 0 °C), Class A (±0.15 °C), Class B (±0.3 °C), and Class C (±0.6 °C). Class B is sufficient for most industrial HVAC and process applications; Class A or AA is used for calibration references and pharmaceutical monitoring.
No. The CVD equation with the IEC 60751 coefficients applies only to pure platinum RTDs. Nickel and copper RTDs use different polynomial fits. For platinum RTDs, always confirm the coefficients match IEC 60751 or the specific national standard used.

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