RTD PT100 / PT1000 Calculator
Calculate PT100 and PT1000 RTD resistance, temperature, sensitivity, and self-heating using IEC 60751 Callendar-Van Dusen equations. The calculator keeps RTD CVD math in Celsius and keeps NTC, thermocouple, and ADC workflows out of scope.
Engineering tool
RTD PT100 / PT1000 Calculator
Calculate platinum RTD resistance, temperature, sensitivity, and measurement-current self-heating with IEC 60751 Callendar-Van Dusen equations.
Converted to Celsius before Callendar-Van Dusen evaluation.
Display unit only. CVD equations use °C internally.
Result console
- RTD Resistance
- 138.505Ω
- Temperature
- 100°C
- Resistance
- 138.505Ω
- Sensitivity
- 0.37928Ω/°C
- Normalized Sensitivity
- 0.00379281/°C
- CVD Branch
- positive
- R / R0
- 1.385055
- ΔR from 0°C
- 38.5055Ω
Positive-temperature Callendar-Van Dusen calculation omits the C term by IEC convention.
Formula
Formula reference
IEC 60751 Callendar-Van Dusen model
Do not substitute Kelvin directly into the Callendar-Van Dusen equation.
T>=0°C: R=R0(1+AT+BT²)T<0°C: R=R0(1+AT+BT²+C(T-100)T³)dR/dT positive = R0(A+2BT)dR/dT negative = R0[A+2BT+C(4T³-300T²)]Pself = I²RΔTself ≈ P/DδVariable definitions
- R0
- nominal resistance at 0°C
- T
- Celsius temperature in the CVD convention
- A, B, C
- IEC 60751 coefficients
- Dδ
- dissipation constant
RTD Formula Audit
| PT100 R0 | 100 Ω at 0°C. |
|---|---|
| PT1000 R0 | 1000 Ω at 0°C. |
| IEC A / B / C | A=3.9083e-3, B=-5.775e-7, C=-4.183e-12. |
| Positive CVD | R=R0(1+AT+BT²), T>=0°C. |
| Negative CVD | R=R0(1+AT+BT²+C(T-100)T³), T<0°C. |
| 0°C Convention | 0°C is evaluated on the positive branch; both branches are continuous at R0. |
| Celsius Convention | CVD T is Celsius under the IEC coefficient convention. |
| Positive Inverse | Analytic quadratic candidates with forward residual verification. |
| Negative Inverse | Bounded bisection from -200°C to 0°C. |
| Sensitivity | Positive: R0(A+2BT). Negative includes C(4T³-300T²). |
| Self-Heating | P=I²R and ΔTself≈P/Dδ. |
| Scope | No NTC, thermocouple, ADC, or lead-compensation simulator. |
Worked Examples
| Case | Calculation | Result |
|---|---|---|
| PT100 at 0°C | R0 | 100 Ω |
| PT1000 at 0°C | R0 | 1000 Ω |
| PT100 at 100°C | 100(1+0.0039083×100-5.775e-7×10000) | 138.5055 Ω |
| PT1000 at 100°C | 10×PT100 | 1385.055 Ω |
| PT100 at -100°C | negative branch with C term | 60.25584 Ω |
| PT1000 at -100°C | 10×PT100 | 602.5584 Ω |
| PT100 R=100 Ω | inverse | 0°C |
| PT100 R=138.5055 Ω | positive inverse | 100°C |
| PT100 R=60.25584 Ω | negative bisection | -100°C |
| PT1000 R=1000 Ω | inverse | 0°C |
| 0°C / 32°F / 273.15K | temperature conversion | R=R0 |
| 100°C / 212°F / 373.15K | temperature conversion | same resistance |
| dR/dT at 0°C PT100 | 100×A | 0.39083 Ω/°C |
| 1 mA through 100 Ω | I²R | 0.1 mW |
| 0.1 mW / 2 mW/°C | P/Dδ | 0.05°C |
Engineering Notes
- PT100 is nominally 100 Ω at 0°C; PT1000 is nominally 1000 Ω at 0°C.
- IEC 60751 Callendar-Van Dusen equations use Celsius under the standard coefficient convention.
- This differs from THM-005 NTC Beta equations, which require Kelvin.
- The C term is omitted for T >= 0°C and included for T < 0°C.
- PT100 and PT1000 use the same normalized coefficients with different R0 values.
- 2-wire RTD measurements include lead resistance directly.
- 3-wire compensation depends on matched leads and measurement circuit assumptions.
- 4-wire Kelvin measurement minimizes lead resistance error.
- Measurement current causes I²R self-heating.
- Specific probe temperature limits can be narrower than the mathematical IEC model range.
Common Mistakes
- Thinking PT100 is 100 Ω at 25°C.
- Thinking PT1000 is 1000 Ω at 25°C.
- Putting Kelvin directly into the CVD equation.
- Omitting the C term below 0°C.
- Adding the C term above 0°C.
- Using NTC Beta equations for RTDs.
- Choosing the wrong quadratic root without residual verification.
- Ignoring 2-wire lead resistance and measurement current self-heating.
Support reference
FAQ
What is an RTD?
An RTD is a resistance temperature detector, usually using a metal element whose resistance increases with temperature.
What is a PT100 sensor?
A PT100 is a platinum RTD with nominal resistance of 100 ohms at 0°C.
What is a PT1000 sensor?
A PT1000 is a platinum RTD with nominal resistance of 1000 ohms at 0°C.
What resistance is a PT100 at 0°C?
A standard PT100 is 100 ohms at 0°C.
What resistance is a PT1000 at 0°C?
A standard PT1000 is 1000 ohms at 0°C.
How do I calculate PT100 resistance from temperature?
Use the Callendar-Van Dusen equation with R0 = 100 ohms and the correct positive or negative temperature branch.
How do I calculate PT100 temperature from resistance?
For R greater than or equal to R0, solve the positive quadratic branch. For R below R0, use a bounded numerical solve on the negative branch.
What is the Callendar-Van Dusen equation?
It is the standard RTD resistance-temperature equation using A, B and C coefficients for platinum sensors.
Why does the RTD equation change below 0°C?
The IEC form includes an additional C term below 0°C to fit platinum RTD behavior more accurately.
What are the IEC 60751 A, B and C coefficients?
Common coefficients are A = 3.9083e-3, B = -5.775e-7 and C = -4.183e-12.
Does the Callendar-Van Dusen equation use Celsius or Kelvin?
Under this coefficient convention, the equation uses Celsius temperature. This differs from NTC Beta equations, which use Kelvin.
What is the difference between PT100 and PT1000?
They use the same normalized curve but different nominal resistance: 100 ohms versus 1000 ohms at 0°C.
What is RTD alpha 0.00385?
It is the approximate normalized temperature coefficient for standard platinum RTDs, in ohms per ohm per degree Celsius.
How do I calculate RTD sensitivity?
Differentiate the CVD equation. The positive branch uses dR/dT = R0(A + 2BT).
Why does measurement current heat an RTD?
Measurement current dissipates I²R power in the sensor element, causing self-heating.
How do I estimate RTD self-heating?
Divide measurement power by the dissipation constant: ΔTself ≈ P / Dδ.
What is RTD dissipation constant?
It relates RTD power dissipation to temperature rise and depends on package, probe, medium, flow and mounting.
What is the difference between 2-wire, 3-wire and 4-wire RTDs?
2-wire adds lead resistance directly, 3-wire compensates under matched-lead assumptions, and 4-wire Kelvin measurement minimizes lead-resistance error.
How does lead resistance affect PT100 measurements?
For 2-wire PT100 measurements, lead resistance adds to sensor resistance and creates positive temperature error.
What is the difference between an RTD and an NTC thermistor?
A platinum RTD resistance rises with temperature and uses CVD equations; an NTC resistance falls with temperature and uses Beta or Steinhart-Hart models.
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