Resistance thermometer

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Resistance thermometers, also called resistance temperature detectors (RTDs), are sensors used to measure temperature by correlating the resistance of the RTD element with temperature. Most RTD elements consist of a length of fine coiled wire wrapped around a ceramic or glass core. The element is usually quite fragile, so it is often placed inside a sheathed probe to protect it. The RTD element is made from a pure material, typically platinum, nickel or copper. The material has a predictable change in resistance as the temperature changes and it is this predictable change that is used to determine temperature.

They are slowly replacing the use of thermocouples in many industrial applications below 600 °C, due to higher accuracy and repeatability.[1][2]

R vs T relationship of various metals[edit]

Common RTD sensing elements constructed of platinum, copper or nickel have a repeatable resistance versus temperature relationship (R vs T) and operating temperature range. The R vs T relationship is defined as the amount of resistance change of the sensor per degree of temperature change.[3] The relative change in resistance (temperature coefficient of resistance) varies only slightly over the useful range of the sensor.

Platinum was proposed by Sir William Siemens as an element for resistance temperature detector at the Bakerian lecture in 1871:[4] it is a noble metal and has the most stable resistance-temperature relationship over the largest temperature range. Nickel elements have a limited temperature range because the amount of change in resistance per degree of change in temperature becomes very non-linear at temperatures over 572 °F (300 °C). Copper has a very linear resistance-temperature relationship, however copper oxidizes at moderate temperatures and cannot be used over 302 °F (150 °C).

Platinum is the best metal for RTDs because it follows a very linear resistance-temperature relationship and it follows the R vs T relationship in a highly repeatable manner over a wide temperature range. The unique properties of platinum make it the material of choice for temperature standards over the range of -272.5 °C to 961.78 °C, and is used in the sensors that define the International Temperature Standard, ITS-90. Platinum is chosen also because of its chemical inertness.

The significant characteristic of metals used as resistive elements is the linear approximation of the resistance versus temperature relationship between 0 and 100 °C. This temperature coefficient of resistance is called alpha, α. The equation below defines α; its units are ohm/ohm/°C.

\alpha = \frac{R_{100} - R_0}{100R_0}
 R_0 = the resistance of the sensor at 0°C
 R_{100} = the resistance of the sensor at 100°C

Pure platinum has an alpha of 0.003925 ohm/ohm/°C in the 0 to 100 °C range and is used in the construction of laboratory grade RTDs. Conversely two widely recognized standards for industrial RTDs IEC 60751 and ASTM E-1137 specify an alpha of 0.00385 ohms/ohm/°C. Before these standards were widely adopted several different alpha values were used. It is still possible to find older probes that are made with platinum that have alpha values of 0.003916 ohms/ohm/°C and 0.003902 ohms/ohm/°C.

These different alpha values for platinum are achieved by doping; basically carefully introducing impurities into the platinum. The impurities introduced during doping become embedded in the lattice structure of the platinum and result in a different R vs. T curve and hence alpha value.[5]


To characterize the R vs T relationship of any RTD over a temperature range that represents the planned range of use, calibration must be performed at temperatures other than 0 °C and 100 °C. Two common calibration methods are the fixed point method and the comparison method.[6]

Element types[edit]

There are three main categories of RTD sensors: thin film, wire-wound, and coiled elements. While these types are the ones most widely used in industry there are some places where other more exotic shapes are used, for example carbon resistors are used at ultra low temperatures (-173 °C to -273 °C).[7]

Thin film PRT
Wire Wound PRT
Coil Element PRT

The current international standard which specifies tolerance, and the temperature-to-electrical resistance relationship for platinum resistance thermometers (PRTs) is IEC 60751:2008; ASTM E1137 is also used in the United States. By far the most common devices used in industry have a nominal resistance of 100 ohms at 0 °C, and are called Pt100 sensors ('Pt' is the symbol for platinum, 100 for the resistance in ohm at 0 °C). The sensitivity of a standard 100 ohm sensor is a nominal 0.385 ohm/°C. RTDs with a sensitivity of 0.375 and 0.392 ohm/°C as well as a variety of others are also available.


Resistance thermometers are constructed in a number of forms and offer greater stability, accuracy and repeatability in some cases than thermocouples. While thermocouples use the Seebeck effect to generate a voltage, resistance thermometers use electrical resistance and require a power source to operate. The resistance ideally varies nearly linearly with temperature per the Callendar Van-Dusen equation.

The platinum detecting wire needs to be kept free of contamination to remain stable. A platinum wire or film is supported on a former in such a way that it gets minimal differential expansion or other strains from its former, yet is reasonably resistant to vibration. RTD assemblies made from iron or copper are also used in some applications. Commercial platinum grades are produced which exhibit a temperature coefficient of resistance 0.00385/°C (0.385%/°C) (European Fundamental Interval).[9] The sensor is usually made to have a resistance of 100 Ω at 0 °C. This is defined in BS EN 60751:1996 (taken from IEC 60751:1995). The American Fundamental Interval is 0.00392/°C,[10] based on using a purer grade of platinum than the European standard. The American standard is from the Scientific Apparatus Manufacturers Association (SAMA), who are no longer in this standards field. As a result the "American standard" is hardly the standard even in the US.

Lead wire resistance can also be a factor; adopting three- and four-wire, instead of two-wire, connections can eliminate connection lead resistance effects from measurements (see below); three-wire connection is sufficient for most purposes and almost universal industrial practice. Four-wire connections are used for the most precise applications.

Advantages and limitations[edit]

The advantages of platinum resistance thermometers include:

Limitations: RTDs in industrial applications are rarely used above 660 °C. At temperatures above 660 °C it becomes increasingly difficult to prevent the platinum from becoming contaminated by impurities from the metal sheath of the thermometer. This is why laboratory standard thermometers replace the metal sheath with a glass construction. At very low temperatures, say below -270 °C (or 3 K), because there are very few phonons, the resistance of an RTD is mainly determined by impurities and boundary scattering and thus basically independent of temperature. As a result, the sensitivity of the RTD is essentially zero and therefore not useful.[citation needed]

Compared to thermistors, platinum RTDs are less sensitive to small temperature changes and have a slower response time. However, thermistors have a smaller temperature range and stability.

Sources of error:

The common error sources of a PRT are:

RTDs vs thermocouples[edit]

The two most common ways of measuring industrial temperatures are with resistance temperature detectors (RTDs) and thermocouples. Choice between them is usually determined by four factors.



These elements nearly always require insulated leads attached. At temperatures below about 250 °C PVC, silicone rubber or PTFE insulators are used. Above this, glass fibre or ceramic are used. The measuring point, and usually most of the leads, require a housing or protective sleeve, often made of a metal alloy which is chemically inert to the process being monitored. Selecting and designing protection sheaths can require more care than the actual sensor, as the sheath must withstand chemical or physical attack and provide convenient attachment points.

Wiring configurations[edit]

Two-wire configuration[edit]

Two Wire Resistance Thermometer

The simplest resistance thermometer configuration uses two wires. It is only used when high accuracy is not required, as the resistance of the connecting wires is added to that of the sensor, leading to errors of measurement. This configuration allows use of 100 meters of cable. This applies equally to balanced bridge and fixed bridge system.

Three-wire configuration[edit]

Three Wire Resistance Thermometer

In order to minimize the effects of the lead resistances, a three-wire configuration can be used. Using this method the two leads to the sensor are on adjoining arms. There is a lead resistance in each arm of the bridge so that the resistance is cancelled out, so long as the two lead resistances are accurately the same. This configuration allows up to 600 meters of cable[citation needed].

Four-wire configuration[edit]

Four Wire Resistance Thermometer

The four-wire resistance thermometer configuration increases the accuracy and reliability of the resistance being measured: the resistance error due to lead wire resistance is zero. In the diagram above a standard two-terminal RTD is used with another pair of wires to form an additional loop that cancels out the lead resistance. The above Wheatstone bridge method uses a little more copper wire and is not a perfect solution. Below is a better[disputed ] configuration, four-wire Kelvin connection. It provides full cancellation of spurious effects[disputed ][citation needed]; cable resistance of up to 15 Ω can be handled[citation needed].

A Better Four Wire Resistance Thermometer

Classifications of RTDs[edit]

The highest accuracy of all PRTs is the Standard platinum Resistance Thermometers (SPRTs). This accuracy is achieved at the expense of durability and cost. The SPRTs elements are wound from reference grade platinum wire. Internal lead wires are usually made from platinum while internal supports are made from quartz or fuse silica. The sheaths are usually made from quartz or sometimes Inconel depending on temperature range. Larger diameter platinum wire is used, which drives up the cost and results in a lower resistance for the probe (typically 25.5 ohms). SPRTs have a wide temperature range (-200 °C to 1000 °C) and approximately accurate to ±0.001 °C over the temperature range. SPRTs are only appropriate for laboratory use.

Another classification of laboratory PRTs is Secondary Standard platinum Resistance Thermometers (Secondary SPRTs). They are constructed like the SPRT, but the materials are more cost-effective. SPRTs commonly use reference grade, high purity smaller diameter platinum wire, metal sheaths and ceramic type insulators. Internal lead wires are usually a nickel-based alloy. Secondary SPRTs are limited in temperature range (-200 °C to 500 °C) and are approximately accurate to ±0.03 °C over the temperature range.

Industrial PRTs are designed to withstand industrial environments. They can be almost as durable as a thermocouple. Depending on the application industrial PRTs can use thin film elements or coil wound elements. The internal lead wires can range from PTFE insulated stranded nickel plated copper to silver wire, depending on the sensor size and application. Sheath material is typically stainless steel; higher temperature applications may demand Inconel. Other materials are used for specialized applications.


Sensor assemblies can be categorized into two groups by how they are installed or interface with the process: immersion or surface mounted.

Other applications may require special waterproofing or pressure seals. A heavy-duty underwater temperature sensor is designed for complete submersion under rivers, cooling ponds, or sewers. Steam autoclaves require a sensor that is sealed from intrusion by steam during the vacuum cycle process.

Immersion sensors generally have the best measurement accuracy because they are in direct contact with the process fluid. Surface mounted sensors are measuring the pipe surface as a close approximation of the internal process fluid.


The application of the tendency of electrical conductors to increase their electrical resistance with rising temperature was first described by Sir William Siemens at the Bakerian Lecture of 1871 before the Royal Society of Great Britain. The necessary methods of construction were established by Callendar, Griffiths, Holborn and Wein between 1885 and 1900.

Standard resistance thermometer data[edit]

Temperature sensors are usually supplied with thin-film elements. The resistance elements are rated in accordance with BS EN 60751:2008 as:

Tolerance ClassValid Range
F 0.3-50 to +500 °C
F 0.15-30 to +300 °C
F 0.10 to +150 °C

Resistance thermometer elements can be supplied which function up to 1000 °C. The relation between temperature and resistance is given by the Callendar-Van Dusen equation,

R_T = R_0 \left[ 1 + AT + BT^2 + CT^3 (T-100) \right] \; (-200\;{}^{\circ}\mathrm{C} < T < 0\;{}^{\circ}\mathrm{C}),
R_T = R_0 \left[ 1 + AT + BT^2 \right] \; (0\;{}^{\circ}\mathrm{C} \leq T < 850\;{}^{\circ}\mathrm{C}).

Here, R_T is the resistance at temperature T, R_0 is the resistance at 0 °C, and the constants (for an alpha=0.00385 platinum RTD) are

A =  3.9083 \times 10^{-3} \; {}^{\circ}\mathrm{C}^{-1}
B = -5.775 \times 10^{-7} \; {}^{\circ}\mathrm{C}^{-2}
C = -4.183 \times 10^{-12} \; {}^{\circ}\mathrm{C}^{-4}.

Since the B and C coefficients are relatively small, the resistance changes almost linearly with the temperature.

Values for various popular resistance thermometers[edit]

Values for various popular resistance thermometers
in °C
in Ω
in Ω
in Ω
in Ω
in Ω
in Ω
in Ω
in Ω
Typ: 404Typ: 501Typ: 201Typ: 101Typ: 102Typ: 103Typ: 104Typ: 105
Copied from German version, please don't remove

The function for temperature value acquisition (C++)[edit]

The following code estimates a Pt100 or Pt1000 sensor's temperature in Celcius from its current resistance.

 float GetPt100Temperature(float resistance) {       float const Pt100[] = {80.31, 82.29, 84.27, 86.25, 88.22, 90.19, 92.16, 94.12, 96.09, 98.04,                             100.0, 101.95, 103.9, 105.85, 107.79, 109.73, 111.67, 113.61, 115.54, 117.47,                             119.4, 121.32, 123.24, 125.16, 127.07, 128.98, 130.89, 132.8, 134.7, 136.6,                             138.5, 140.39, 142.29, 157.31, 175.84, 195.84};         int tempC = -50, i = 0, dt = 0;         if (resistance > Pt100[i])          while (250 > tempC)          {                dt = (tempC < 110) ? 5 : (tempC > 110) ? 50 : 40;                  if (resistance < Pt100[++i])                   return tempC + (resistance - Pt100[i-1]) * dt / (Pt100[i] - Pt100[i-1]);                tempC += dt;          }       return tempC; } 

See also[edit]


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