Temperature Measurement · RTD · PT100 · PT1000 · IEC 60751
RTD Resistance to Temperature Calculator: PT100, PT1000, Linear and Callendar-Van Dusen Formulas Explained
A complete guide to converting RTD resistance to process temperature: why resistance increases with temperature, the linear approximation formula, the accurate Callendar-Van Dusen equation for wide temperature ranges, PT100 resistance tables, 2-wire and 3-wire lead error correction, and a bidirectional interactive calculator for PT100 and PT1000.
When a PT100 RTD returns a resistance of 138.50 ohms from the field, what is the process temperature? When you are writing a PLC block to convert the AI module's raw resistance reading into a displayed temperature value, which formula do you use? When a calibrator shows 119.40 ohms on a bench test, does the transmitter's output match what you calculate by hand? These are the practical questions that RTD resistance-to-temperature conversion answers every day in process plants and calibration labs.
The RTD (Resistance Temperature Detector) works on one simple physical principle: the electrical resistance of pure metals increases predictably and repeatably as temperature rises. By measuring the resistance precisely, you can calculate the temperature precisely. The relationship is nearly linear over moderate temperature ranges, which is why a simple linear formula works well for many applications. But for calibration work or wide temperature spans, the non-linear Callendar-Van Dusen equation gives a significantly more accurate result.
This guide explains both approaches, gives you the complete PT100 and PT1000 resistance tables, explains how lead wire resistance affects accuracy (and why 3-wire and 4-wire connections exist), and provides a bidirectional calculator that converts both resistance to temperature and temperature to resistance. For context on how RTDs are installed and calibrated in the field, see our guide on how to calibrate a temperature transmitter.
PT100 and PT1000: what the numbers mean and IEC 60751 standard
Alpha (α): the temperature coefficient of resistance and why it is 0.00385 for standard RTDs
Linear formula: T = (Rt - R0) / (α x R0) when to use it and its accuracy limits
Callendar-Van Dusen equation: accurate calculation above 100°C and for calibration
Bidirectional calculator: resistance to temperature AND temperature to resistance
PT100 resistance reference table: selected values from -200°C to +660°C
Lead wire resistance error: how much 2-wire wiring adds to your reading
How 3-wire and 4-wire connections eliminate lead error
Common RTD calculation mistakes in PLC and DCS configurations
How RTD Resistance Changes with Temperature
The resistance of most pure metals increases when temperature rises. This happens because heat causes the metal atoms to vibrate more energetically, which increases the scattering of electrons as they move through the conductor: more scattering means more resistance to electron flow, which means higher electrical resistance.
For platinum (the metal used in PT100 and PT1000 sensors), this relationship is highly predictable, repeatable over thousands of thermal cycles, stable over decades, and well-characterised from -200°C to over 800°C. These properties make platinum the material of choice for precision temperature measurement. The international standard governing platinum RTDs is IEC 60751:2022 (Industrial Platinum Resistance Thermometers), which defines the resistance-temperature relationship, tolerances, and marking requirements for all industrial PT100 and PT1000 sensors.
Figure 1: PT100 resistance-temperature characteristic per IEC 60751. At 0°C the resistance is exactly 100 ohms. At -200°C it falls to 18.52 ohms. At 600°C it rises to 313.7 ohms. The curve is nearly linear in the middle range but shows visible curvature at low and high temperatures.
PT100 vs PT1000: What the Numbers Mean
The number in the RTD name is simply the nominal resistance at 0°C. A PT100 has 100 ohms at 0°C. A PT1000 has 1000 ohms at 0°C. The "PT" stands for platinum. Both follow the same resistance-temperature relationship defined by IEC 60751. They just operate at different absolute resistance levels.
| Parameter | PT100 | PT1000 |
|---|---|---|
| Resistance at 0°C (R0) | 100.00 ohm | 1000.00 ohm |
| Resistance at 100°C | 138.506 ohm | 1385.06 ohm |
| Temperature coefficient (alpha) | 0.003851 /°C | 0.003851 /°C |
| Sensitivity at 0°C | 0.385 ohm/°C | 3.851 ohm/°C |
| Effect of 1 ohm lead resistance | 2.6°C error per ohm | 0.26°C error per ohm |
| Common use | Process plants, temperature transmitters, all industrial applications. The most common RTD type worldwide. | HVAC, building automation, battery management, where lead resistance is harder to control or longer cable runs are used. |
| Preferred wiring | 3-wire or 4-wire to eliminate lead resistance error | 2-wire acceptable for many applications due to 10x lower sensitivity to lead resistance |
The Linear Formula: Quick Conversion for Moderate Temperatures
For temperatures between approximately -50°C and +150°C, the linear (simplified) formula gives results accurate enough for most process control applications. The error compared to the full Callendar-Van Dusen equation is less than 0.5°C in this range.
Where:
T = temperature to find (°C)
Rt = measured resistance at temperature T (ohms)
R0 = nominal resistance at 0°C (100 ohm for PT100, 1000 ohm for PT1000)
alpha = temperature coefficient (0.00385 per °C for IEC 60751 standard)
Reverse formula: Temperature to Resistance Rt = R0 x (1 + alpha x T)
This formula is valid for -50°C to +150°C with less than 0.5°C error. Above 150°C or below -50°C, use the Callendar-Van Dusen equation instead.
Step 1: Subtract nominal resistance Rt - R0 = 119.40 - 100 = 19.40 ohm
Step 2: Calculate denominator alpha x R0 = 0.00385 x 100 = 0.385 ohm per °C
Step 3: Divide to get temperature T = 19.40 / 0.385
T = 50.39°C
CVD result for same resistance: 50.18°C (0.21°C difference, acceptable for most applications)
The Callendar-Van Dusen Equation: Accurate Calculation for Wide Ranges
For accurate work, calibration, and temperatures outside the -50°C to +150°C range, the Callendar-Van Dusen (CVD) equation is used. This polynomial equation is specified in IEC 60751 and accounts for the non-linearity in the resistance-temperature relationship of platinum.
Rt = R0 x [1 + A x T + B x T²]
For T less than 0°C (sub-zero temperatures):
Rt = R0 x [1 + A x T + B x T² + C x (T - 100) x T³]
IEC 60751 Callendar-Van Dusen coefficients:
A = 3.9083 x 10⁻³ per °C
B = -5.775 x 10⁻⁷ per °C²
C = -4.183 x 10⁻¹² per °C⁴ (only used below 0°C)
Note: For sub-zero temperatures the full 4-term polynomial is needed. The coefficient C is only included in the equation when T is below 0°C. For T >= 0°C, the C term drops out and the equation becomes a simple quadratic.
Using the quadratic formula:
T = [-A x R0 + sqrt((A x R0)² - 4 x B x R0 x (R0 - Rt))] / (2 x B x R0)
Worked Example: PT100 at Rt = 175.00 ohm (above 0°C range) R0 = 100, A = 3.9083e-3, B = -5.775e-7
Discriminant = (A x R0)² - 4 x B x R0 x (R0 - Rt)
= (0.39083)² - 4 x (-5.775e-7) x 100 x (100 - 175)
= 0.15275 - 4 x (-5.775e-7) x 100 x (-75)
= 0.15275 - 0.01733
= 0.13542
T = (-0.39083 + sqrt(0.13542)) / (2 x (-5.775e-7) x 100)
= (-0.39083 + 0.36800) / (-0.0001155)
= (-0.02283) / (-0.0001155)
T = 197.7°C Linear formula for same Rt = 175 ohm gives T = (175-100)/0.385 = 194.8°C (2.9°C too low) CVD is 2.9°C more accurate at this temperature. Difference grows larger above 200°C.
RTD Calculator: Bidirectional, PT100 and PT1000
Select PT100 or PT1000, choose which direction to calculate, enter your value, and click Calculate. The calculator uses the Callendar-Van Dusen equation for accurate results above 0°C and the iterative CVD solution below 0°C.
PT100 Resistance Reference Table (IEC 60751)
| Temperature (°C) | PT100 Resistance (ohm) | PT1000 Resistance (ohm) | Practical reference |
|---|---|---|---|
| -200 | 18.52 | 185.2 | Cryogenic applications, LNG |
| -100 | 60.26 | 602.6 | Freezer storage, cold rooms |
| -50 | 80.31 | 803.1 | Cold climate, outdoor winter measurement |
| 0 | 100.00 | 1000.00 | Ice point. Reference for all RTD calibration. |
| 20 | 107.79 | 1077.9 | Typical ambient room temperature |
| 50 | 119.40 | 1194.0 | Warm process streams, HVAC return air |
| 100 | 138.51 | 1385.1 | Boiling water at sea level. Common calibration point. |
| 150 | 157.33 | 1573.3 | Steam, hot process fluids |
| 200 | 175.86 | 1758.6 | High-temp HVAC, industrial ovens |
| 300 | 212.05 | 2120.5 | Chemical reactor jacket temperatures |
| 400 | 247.09 | 2470.9 | Heat treatment furnaces |
| 500 | 280.98 | 2809.8 | High-temperature process heaters |
| 600 | 313.71 | 3137.1 | Upper range of standard PT100 (IEC 60751 Class A limit) |
| 660 | 329.05 | 3290.5 | Maximum usable range for standard industrial PT100 |
Lead Wire Resistance Error: Why 2-Wire RTDs Give Wrong Readings
An RTD measures temperature by measuring resistance. But in a real installation, the transmitter or measurement instrument measures the total resistance of the circuit, which includes the resistance of the wires connecting the RTD to the instrument. These are called lead wires, and their resistance adds directly to the RTD reading, causing the displayed temperature to be higher than the actual process temperature.
Temperature error = Lead resistance total / (alpha x R0)
For PT100 (alpha = 0.00385, R0 = 100):
Temperature error = Lead resistance / 0.385 (degrees per ohm of total lead resistance)
Example: 50 m of copper 2-wire cable, 1.5 mm² conductor Resistance of copper: 0.0119 ohm per metre (at 20°C for 1.5mm² copper)
Total lead resistance (2 conductors x 50 m): 2 x 50 x 0.0119 = 1.19 ohm
Temperature error on PT100: 1.19 / 0.385
Error = +3.1°C (reading too high. Process appears 3.1°C hotter than it is) For PT1000: same 1.19 ohm lead resistance gives 1.19 / 3.851 = 0.31°C error only. This 10x improvement is why PT1000 is preferred where cable runs are long and 3-wire wiring is impractical.
| Connection type | Lead compensation | Accuracy | When to use |
|---|---|---|---|
| 2-wire | None. Both lead resistances add to reading. | Poor for long runs (see example above) | PT1000 only where accuracy is not critical. Never use 2-wire PT100 in a process plant over more than a few metres. |
| 3-wire | Assumes both leads are equal. Measures one lead, subtracts it twice from reading. Error = difference between leads (usually small). | Good. Typical accuracy 0.1-0.3°C for equal-length, equal-gauge leads. | Standard for industrial PT100 installations. Most DCS and PLC AI modules support 3-wire. Specify from the installation start. |
| 4-wire (Kelvin) | Complete. Current supply wires and voltage sensing wires are separate. Sense wires carry no current so their resistance does not affect the measurement. | Excellent. Eliminates lead resistance completely. | Calibration laboratories, precision temperature measurement, reference standards. Required where accuracy better than 0.1°C is needed. |
Common RTD Calculation Mistakes in PLC and DCS Configuration
| Mistake | Effect | Fix |
|---|---|---|
| Using alpha = 0.00392 (American standard) for a European IEC 60751 sensor | About 1.5°C error at 100°C, growing to 5°C at 400°C. | Check the sensor calibration certificate. IEC 60751 sensors (standard in most plants) use alpha = 0.00385. Confirm alpha in transmitter or DCS configuration. |
| Using 2-wire connection for PT100 over a long cable run | Reading permanently high by lead resistance / 0.385 degrees. Impossible to calibrate out unless lead resistance is measured and subtracted manually. | Always install PT100 with 3-wire or 4-wire connection. Rewire if 2-wire was installed incorrectly. For temporary fix, measure lead resistance and apply offset in transmitter. |
| Configuring DCS for PT100 but connecting a PT1000 | Reading completely wrong (PT1000 at 100°C reads 1385 ohm; DCS configured for PT100 would interpret 1385 ohm as a wildly out-of-range or fault condition). | Match the transmitter or AI module configuration exactly to the RTD type installed. Confirm from the transmitter datasheet or wiring diagram. |
| Using the linear formula for temperatures above 200°C | Linear formula gives 2-3°C lower than actual at 200°C, up to 10°C lower at 500°C. | Use the Callendar-Van Dusen equation for any temperature above 150°C or below -50°C. Most modern transmitters implement CVD internally. |
External Resources and References
- IEC 60751:2022 Industrial Platinum Resistance Thermometers. The definitive international standard defining the resistance-temperature relationship, tolerance classes and marking requirements for PT100 and PT1000 sensors. Required reference for all calibration work.
- Omega Engineering: PT100 Resistance-Temperature Table. Comprehensive PT100 resistance values at every degree Celsius from -200°C to +850°C, from a leading temperature measurement manufacturer and reference.
- NIST: Temperature Calibration Reference. US National Institute of Standards and Technology guidance on temperature calibration, thermometer standards and traceability for industrial temperature measurement.
- Emerson: RTD Elements and PT100 Selection Guide. Practical application guidance on RTD element types, tolerance classes, construction and installation from a leading process instrumentation supplier.
- AutomationForum: RTD Resistance to Temperature Calculator. The reference article that inspired this guide, with an embedded calculator tool.
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What we learn today
- PT100 has 100 ohms at 0°C and increases ~0.385 ohm per °C. Linear formula: T = (Rt - R0) / (0.00385 x R0). Use this for -50°C to +150°C. Use the Callendar-Van Dusen equation for wider ranges or calibration work.
- Every 1 ohm of lead wire resistance adds 2.6°C error to a 2-wire PT100 reading. Over 50 m of 1.5 mm² cable the error is typically 3°C. Always use 3-wire or 4-wire connections for PT100 in process plant installations.
- IEC 60751 is the standard for PT100 and PT1000. Standard alpha = 0.00385 per °C (European/IEC standard). Confirm alpha from sensor certificate before entering into DCS or PLC configuration.