RTD Callendar-Van Dusen

R(T) = R0 × (1 + A×T + B×T²)

Quick answer

This calculator solves R(T) = R0 × (1 + A×T + B×T²) for R(T). With R0 (at 0°C) 0.47 kΩ, Coefficient A 0.5, Coefficient B 1.1, Temperature 50 °C, the result is 1.305 MΩ.

Calculator

Result
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Formula

R(T) = R0 × (1 + A×T + B×T²)

Description

The Callendar-Van Dusen equation describes the resistance-temperature relationship of RTD (Resistance Temperature Detector) sensors, most commonly Pt100 and Pt1000 platinum elements. For temperatures above 0°C, the second-order polynomial provides accuracy within ±0.01°C. The coefficients A and B are standardized in IEC 60751. Platinum RTDs are the gold standard for precision temperature measurement because of their excellent linearity, stability, and repeatability. The R0 value indicates the resistance at 0°C (100Ω for Pt100, 1000Ω for Pt1000).

Variables

  • R(T) — RTD resistance at temperature T (Ω)
  • R0 — Resistance at 0°C (Ω)
  • A — First coefficient (3.9083 × 10⁻³ °C⁻¹ for IEC 60751)
  • B — Second coefficient (-5.775 × 10⁻⁷ °C⁻² for IEC 60751)
  • T — Temperature (°C)

Practical Notes

IEC 60751 standard coefficients: A = 3.9083e-3, B = -5.775e-7. Below 0°C, a third term C×(T-100)×T³ is added. RTD accuracy classes: Class A ±0.15°C at 0°C, Class B ±0.30°C. Always use 4-wire measurement to eliminate lead resistance errors. Self-heating from the excitation current must be minimized (typically < 1 mA for Pt100).

Symbols and units

Symbol Meaning Default unit Accepted units
R0 R0 (at 0°C) Ω mΩ, Ω, kΩ, MΩ
A Coefficient A — —
B Coefficient B — —
T Temperature °C °C

Step by step

  1. 1. What you know: R0 (at 0°C) 0.47 kΩ, Coefficient A 0.5, Coefficient B 1.1, Temperature 50 °C
  2. 2. The relation: R(T) = R0 × (1 + A×T + B×T²)
  3. 3. Substitute: R0 = 0.47 kΩ, A = 0.5, B = 1.1, T = 50 °C
  4. 4. Result: R(T) = 1.305 MΩ

Worked examples

Minimum range

Given: R0 (at 0°C) 1 Ω, Coefficient A 0.025, Coefficient B 0.055, Temperature 2.5 °C

Result: R(T) = 1.406 Ω

Low range

Given: R0 (at 0°C) 10 Ω, Coefficient A 0.25, Coefficient B 0.55, Temperature 25 °C

Result: R(T) = 3.51 kΩ

Typical

Given: R0 (at 0°C) 0.47 kΩ, Coefficient A 0.5, Coefficient B 1.1, Temperature 50 °C

Result: R(T) = 1.305 MΩ

High range

Given: R0 (at 0°C) 4.7 kΩ, Coefficient A 0.8, Coefficient B 1.76, Temperature 85 °C

Result: R(T) = 60.09 MΩ

Maximum range

Given: R0 (at 0°C) 47 kΩ, Coefficient A 8, Coefficient B 17.6, Temperature 850 °C

Result: R(T) = 598000 MΩ

How R(T) changes with R0 (at 0°C)

R0 (at 0°C) (input) R(T) (result)
47 Ω 130.5 kΩ
117.5 Ω 0.3262 MΩ
0.235 kΩ 0.6524 MΩ
0.3525 kΩ 0.9785 MΩ
0.47 kΩ 1.305 MΩ
0.705 kΩ 1.957 MΩ
0.94 kΩ 2.609 MΩ
1.88 kΩ 5.219 MΩ
3.29 kΩ 9.133 MΩ
4.7 kΩ 13.05 MΩ

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Frequently asked questions

How do you calculate RTD Callendar-Van Dusen?

Use R(T) = R0 × (1 + A×T + B×T²). With R0 (at 0°C) 0.47 kΩ, Coefficient A 0.5, Coefficient B 1.1, Temperature 50 °C, R(T) works out to 1.305 MΩ.

How do you calculate callendar-van dusen (cvd)?

Rearrange for R(T): with R0 (at 0°C) 10 Ω, Coefficient A 0.25, Coefficient B 0.55, Temperature 25 °C, R(T) is 3.51 kΩ.

How are callendar van dusen coefficients?

Rearrange for R(T): with R0 (at 0°C) 0.47 kΩ, Coefficient A 0.5, Coefficient B 1.1, Temperature 50 °C, R(T) is 1.305 MΩ.

What is the formula for RTD Callendar-Van Dusen?

The formula is R(T) = R0 × (1 + A×T + B×T²). The Callendar-Van Dusen equation describes the resistance-temperature relationship of RTD (Resistance Temperature Detector) sensors, most commonly Pt100 and Pt1000 platinum elements.

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