Temperature: RTDs and thermocouples
The two workhorse temperature sensors, how they compare, what their specifications allow, and how each one is calibrated. The calculators below turn the specifications into numbers you can use.
Side by side
| Property | RTD (platinum) | Thermocouple |
|---|---|---|
| How it works | The resistance of a platinum wire or film rises with temperature. | Two different metals joined at the measuring end produce a small voltage that depends on the temperature difference to a reference junction. |
| Typical range | -200 to 850 °C for wire-wound. Thin-film is usually limited to about -50 to 500 °C. | -270 to 1820 °C depending on type. |
| Accuracy | Industrial class A: ±0.15 °C at 0 °C. Standard platinum thermometers (SPRTs) reach the millikelvin level in good labs. | Industrial class 2 type K: ±2.5 °C or 0.75 %. Calibrated noble-metal types can reach a few tenths of a degree near 1000 °C. |
| Stability | Good. Typically a few hundredths of a degree per year. Shock and vibration can shift it. | Fair. Base-metal types drift with time at high temperature, and type K shows hysteresis between about 250 and 600 °C. |
| Signal | Pt100: about 0.39 Ω per °C at 0 °C, and 0.385 Ω per °C on average between 0 and 100 °C. Needs a small, steady current. | About 6 µV per °C (types B, R, S) to about 68 µV per °C (type E). Needs a low-noise voltmeter. |
| Linearity | Smooth and nearly linear, described by the Callendar–Van Dusen equation. | Non-linear. Needs the reference function for its type. |
| Response time | Slower, because the sensing element sits inside a sheath. | Faster, especially fine wire with an exposed junction. |
| Reference junction | None. | Required. Use an ice point or electronic compensation. |
| Wiring | 2, 3 or 4 wire. Four-wire removes lead resistance. | Wire or extension wire of the matching type all the way to the instrument. Mixed metals at connectors add errors. |
| Main error sources | Self-heating, immersion depth, hysteresis, lead resistance. | Inhomogeneous wire, reference junction error, drift, contamination. |
RTD types
| Type | Element | α (Ω/Ω/°C) | R at 0 °C | Typical range | Standard | Notes |
|---|---|---|---|---|---|---|
| Pt100 (385) | Platinum | 0.00385 | 100 Ω | -200 to 850 °C wire-wound, about -50 to 500 °C film | IEC 60751, ASTM E1137 | The most common industrial sensor worldwide. |
| Pt500, Pt1000 (385) | Platinum | 0.00385 | 500 Ω, 1000 Ω | Mostly thin-film, -50 to 500 °C | IEC 60751 | Larger signal and less lead-resistance error. Common in HVAC and electronics. |
| Pt100 (3916, 3902) | Platinum | 0.003916, 0.003902 | 100 Ω | Similar to Pt100 (385) | Legacy JIS and older US curves | Found on older equipment. Use the matching coefficients, not the 385 ones. |
| SPRT | Strain-free high-purity platinum | about 0.003925 | 25.5 Ω (also 0.25 and 2.5 Ω) | -259 to 962 °C across several designs | ITS-90 interpolating instrument | The reference for the best calibrations. Fragile and easily shifted by shock. |
| Ni100, Ni120 | Nickel | 0.00618, 0.00672 | 100 Ω, 120 Ω | About -60 to 180 °C | DIN 43760 and manufacturer curves | High sensitivity and low cost. Limited range and less stable. |
| Cu10 | Copper | 0.00427 | 10 Ω (at 25 °C) | Up to about 260 °C | Manufacturer curves | Linear, used in motor windings. Low resistance, so lead resistance matters a lot. |
IEC 60751 defines tolerance classes for platinum sensors with α = 0.00385 only. Check the current edition of each standard for the full details.
RTD accuracy: without and with coefficients
"Without coefficients" means you read the sensor with the standard curve and rely on its tolerance class, so any sensor of that type can be swapped for another. "With coefficients" means the sensor was calibrated and you use its own constants, so the accuracy is set by the calibration instead of the class.
| Type | Without coefficients (standard curve) | With coefficients (individual calibration) | The coefficients |
|---|---|---|---|
| Pt100 (385) | IEC 60751 tolerance. Class AA: ±(0.10 + 0.0017|t|) °C. Class A: ±(0.15 + 0.002|t|). Class B: ±(0.30 + 0.005|t|). Class C: ±(0.60 + 0.01|t|). At 100 °C: ±0.27, ±0.35, ±0.80, ±1.6 °C | Typically about ±0.02 to ±0.05 °C (k = 2) from a comparison calibration in a bath, plus drift between calibrations. Set by the reference, the bath and the readout. | Callendar–Van Dusen constants R0, A and B, plus C below 0 °C. At least 3 calibration points above 0 °C are needed to solve R0, A and B. |
| Pt500, Pt1000 (385) | The same classes and the same tolerance in °C as Pt100, because IEC 60751 applies to any nominal resistance with α = 0.00385. | Similar to Pt100. Thin-film elements show somewhat more hysteresis, so allow a little more. | The same constants, with R0 near 500 Ω or 1000 Ω. |
| Pt100 (3916, 3902) | Not covered by IEC 60751 classes. Set by the legacy standard or the data sheet. Reading one with the 385 curve gives an error that grows with temperature: about +1.7 °C at 100 °C for a 3916 sensor and about +1.4 °C for a 3902 sensor. | About the same as Pt100 once its own constants are used. This also removes the curve mismatch. | R0, A, B and C solved for that sensor. |
| SPRT | Not applicable. There is no standard curve to rely on, so each SPRT must be used with its own constants. | Typically about ±0.001 to ±0.005 °C (1 to 5 mK) in a good laboratory, and best near the water triple point. | ITS-90 deviation function constants (a, b, and more for wider ranges) from fixed points, plus R at the water triple point. |
| Ni100, Ni120 | Set by DIN 43760 or the manufacturer's data sheet, since IEC 60751 does not cover nickel. Commonly a few tenths of a degree at 0 °C, so check the data sheet. | Limited by stability. Roughly a few hundredths to about a tenth of a degree, and recalibrate more often than platinum. | R0 and the nickel curve constants. For DIN 43760: R = R0(1 + At + Bt² + Dt⁴ + Ft⁶), with A = 5.485e-3, B = 6.65e-6, D = 2.805e-11, F = -2.0e-17. |
| Cu10 | Set by the manufacturer's data sheet. There is no IEC class. | Limited by the small signal and by lead resistance. Calibrated use is the way to get a few hundredths of a degree. | R0 (10 Ω at 25 °C) and α, since the curve is close to linear. Some makers give extra terms. |
These are typical values to show the size of the difference. Use the uncertainty on your own calibration certificate, and the tolerance on your own data sheet.
Try it: solve your own coefficients
Enter calibration points above 0 °C as reference temperature and measured resistance. The calculator solves R0, A and B, then compares reading the sensor with the standard curve against reading it with its own constants. The example is a class A Pt100 that is within tolerance but not perfect.
- R0 (resistance at 0 °C)
- A
- B
- Worst error, no coefficients
- Worst fit residual, own coefficients
- Indicative accuracy with coefficients
| Temperature (°C) | Resistance (Ω) | Error, no coefficients (°C) | Class it meets | Error, own coefficients (°C) |
|---|
Error is the temperature read from the resistance minus the reference temperature. The class is the tightest IEC 60751 class (AA, A, B or C) whose limit at that temperature covers the error. The indicative accuracy combines U and the worst fit residual in quadrature, which is a quick estimate and not a full uncertainty budget. This solver uses the equation for 0 °C and above. Below 0 °C the extra C constant is needed.
Thermocouple types
| Type | Metals (+ / -) | Range (°C) | EMF at 100 °C | IEC class 1 | IEC class 2 | ASTM standard | Notes |
|---|---|---|---|---|---|---|---|
| K | Chromel / Alumel (Ni-Cr / Ni-Al) | -270 to 1372 | 4.096 mV | ±1.5 °C or 0.4 % | ±2.5 °C or 0.75 % | ±2.2 °C or 0.75 % | General purpose in oxidizing air. Alumel is magnetic. Hysteresis around 250 to 600 °C. |
| N | Nicrosil / Nisil | -270 to 1300 | 2.774 mV | ±1.5 °C or 0.4 % | ±2.5 °C or 0.75 % | ±2.2 °C or 0.75 % | More stable than K above about 1000 °C and resists oxidation better. |
| J | Iron / Constantan | -210 to 1200 | 5.269 mV | ±1.5 °C or 0.4 % | ±2.5 °C or 0.75 % | ±2.2 °C or 0.75 % | Usable in reducing atmospheres. The iron rusts, so it is normally limited to about 750 °C. |
| T | Copper / Constantan | -270 to 400 | 4.279 mV | ±0.5 °C or 0.4 % | ±1.0 °C or 0.75 % | ±1.0 °C or 0.75 % | Best base-metal choice below room temperature. Copper oxidizes above about 370 °C. |
| E | Chromel / Constantan | -270 to 1000 | 6.319 mV | ±1.5 °C or 0.4 % | ±2.5 °C or 0.75 % | ±1.7 °C or 0.5 % | Highest output of the standard types. Not magnetic. Good for low temperatures. |
| R | Pt-13 %Rh / Pt | -50 to 1768 | 0.647 mV | ±1.0 °C up to 1100 °C, then ±[1 + 0.003(t - 1100)] °C | ±1.5 °C or 0.25 % | ±1.5 °C or 0.25 % | High temperature in oxidizing air. Easily contaminated by metal vapour or silicon. |
| S | Pt-10 %Rh / Pt | -50 to 1768 | 0.646 mV | Same as R | Same as R | ±1.5 °C or 0.25 % | Similar to R. Widely used as a reference thermocouple in furnace calibration. |
| B | Pt-30 %Rh / Pt-6 %Rh | 0 to 1820 | 0.033 mV | Not defined | ±0.25 % (600 to 1700 °C) | ±0.5 % (870 to 1700 °C) | Tiny output below about 50 °C, so reference junction errors matter little. Best above 1000 °C. |
"Or" means whichever is greater, applied to the reading in °C. Range is the maximum for the wire and is not the same as the range of each class (use the lookup below). EMF is against a 0 °C reference junction. Other types exist, for example tungsten-rhenium (C, D, G) for vacuum or inert atmospheres up to about 2300 °C, and gold-platinum or platinum-palladium for reference work. IEC 60584-1 and ASTM E230 are the usual sources.
Tolerance lookup
Pt100 converter
Callendar–Van Dusen with the IEC 60751 constants: R = R0(1 + At + Bt²) at 0 °C and above, and R = R0[1 + At + Bt² + C(t - 100)t³] below 0 °C. A = 3.9083e-3, B = -5.775e-7, C = -4.183e-12. Edit either box and the other updates.
- Sensitivity
- 1 mΩ of resolution equals
- 0.1 °C equals
How each one is calibrated
RTD, by comparison
- Inspect and check insulation. Look for damage and moisture, and measure insulation resistance at a low test voltage. IEC 60751 sets a minimum, and 100 MΩ at room temperature is the usual figure.
- Choose a reference and points. Use a standard PRT or SPRT with its own traceable calibration. Cover the working range, for example 0, 100 and 200 °C plus both ends.
- Set up a uniform bath. A stirred liquid bath or a dry block with an equalizing block. Put the sensing elements at the same depth. Immerse far enough, and confirm with an immersion profile.
- Measure four-wire. Use a calibrated bridge, or a precision multimeter with a standard resistor. Reverse the current to cancel thermal EMFs.
- Correct self-heating. Measure at two currents (for example 1 mA and 1.4 mA) and extrapolate to zero power.
- Wait, then read. Let the bath settle at each point, then take at least 10 readings, alternating the reference and the unit under test.
- Check R at 0 °C at the start and end. A change shows hysteresis or strain. An ice point or a water triple point cell (0.01 °C) works.
- Calculate. Get the reference temperature from its certificate, then fit the Callendar–Van Dusen constants (R0, A, B, and C below 0 °C) or report the errors at each point.
- Build the uncertainty budget. Reference, bath uniformity and stability, readout, repeatability, self-heating, immersion and hysteresis.
Simulating the sensor with a decade resistance box checks the readout only. It does not calibrate the sensor.
Thermocouple, by comparison or fixed points
- Inspect and note the history. Check the wire, junction and insulation. Calibration applies to the wire as used, and moving it so a different section sits in the gradient changes the result.
- Choose a reference. A type S or R thermocouple in a furnace, or a PRT or SPRT at lower temperatures. For the best uncertainty, use fixed points such as Zn, Al, Ag, Au and Cu.
- Fix the reference junction. Use a proper ice bath at 0 °C, or a calibrated electronic reference, and copper leads to the voltmeter.
- Use a uniform zone. Bind the junctions together in a metal equalizing block, in a tube furnace or a bath.
- Check homogeneity. Move the thermocouple deeper in steps and watch the EMF. A change shows inhomogeneous wire, which is often the biggest error.
- Measure the EMF. Use a nanovoltmeter through a low-thermal scanner. Read the reference and the unit alternately, at heating and cooling if hysteresis matters.
- Convert. Turn the readings into temperatures with the reference function for the type, including the reference junction correction. Work out the deviation (reference minus unit) at each point.
- Fit the deviation. Use a low-order polynomial or a table with interpolation (see the calculator below).
- Build the uncertainty budget. Reference, reference junction, voltmeter, inhomogeneity, furnace uniformity and stability, interpolation and drift.
Base-metal thermocouples change with use, so calibrate before and after a critical job, and do not assume an old certificate still applies.
Reference points used in calibration (ITS-90)
| Fixed point | Temperature (°C) | Typical use |
|---|---|---|
| Water triple point | 0.01 | RTDs and SPRTs. The most important single point. The ice point (0 °C) is the practical version. |
| Gallium melting point | 29.7646 | RTDs |
| Indium freezing point | 156.5985 | RTDs |
| Tin freezing point | 231.928 | RTDs and thermocouples |
| Zinc freezing point | 419.527 | RTDs and thermocouples |
| Aluminium freezing point | 660.323 | High-temperature SPRTs and thermocouples |
| Silver freezing point | 961.78 | High-temperature SPRTs and noble-metal thermocouples |
| Gold freezing point | 1064.18 | Noble-metal thermocouples |
| Copper freezing point | 1084.62 | Noble-metal thermocouples |
Calibration curve: 2nd, 3rd or 4th degree?
A calibration curve is usually a polynomial fitted to your measured points. More terms always fit the points you have more closely, but that does not make it better at the points you did not measure. This calculator fits all three at once and checks each one by leaving every point out in turn and predicting it.
| Degree | Std. error | Max residual | Leave-one-out | Property |
|---|
Residual is measured y minus fitted y. Std. error is the residual scatter after allowing for the number of fitted terms, and it needs more points than terms. Leave-one-out is the typical error when predicting a point that was left out, and it is the fairer comparison. The suggested degree is the simplest one within 5 % of the best leave-one-out error. Where the fits disagree at a point you will use, that spread is a real part of your uncertainty. A rectangular contribution of half the spread is a common way to include it.
Practical rules
- Keep at least two more points than terms. For a 4th degree curve that means 7 points or more, and 9 is better.
- With exactly as many points as terms the curve passes through every point, which proves nothing about the points in between.
- Do not use the equation outside the range of your points. Polynomials diverge quickly there.
- Fit the small deviation from the standard curve rather than the whole curve. Pt100 and thermocouple reference functions already carry the shape, so a 1st or 2nd degree deviation fit is usually enough.
What to expect
- Pt100, resistance to temperature over 0 to 400 °C: 2nd degree leaves about 0.1 °C, 3rd about 0.004 °C and 4th under 0.001 °C. Higher degree matters here.
- Type K, EMF to temperature over 0 to 1000 °C: even 4th degree leaves nearly 1 °C, so use the full reference function instead of a single polynomial.
- Deviation data with scatter: 2nd degree predicts best, and the extra terms in 3rd and 4th degree start fitting noise.