What the PT100 RTD Temperature Converter does
This converter turns platinum RTD resistance into temperature and back for PT100, PT500 and PT1000 sensors, using the Callendar-Van Dusen equation exactly as IEC 60751 defines it. It also shows the class AA to C tolerance limits at your working temperature, the sensor's sensitivity there, and what a 2-wire cable run costs you in degrees.
Two things make RTD arithmetic worth doing properly. Below 0 C the equation gains a cubic term and has no closed-form inverse, so the familiar quadratic formula is wrong - at -100 C it is about 0.2 C out, which matters on a sensor whose whole point is accuracy. And on a 2-wire connection, every ohm of cable is read as temperature: a PT100 changes by only 0.39 ohm per degree, so a 1 ohm loop is 2.6 C of pure error.
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How to use it
- Choose the sensor: PT100, PT500 or PT1000. They are the same curve scaled by the resistance at 0 C.
- Choose the wiring. Three-wire and four-wire cancel the lead resistance; 2-wire does not, and the page will subtract the lead resistance you give it before converting.
- Pick the direction and type the value. Resistance to temperature is the field case; temperature to resistance is what you need to simulate a sensor with a decade box.
- For a 2-wire run, open the lead-resistance section and either type the loop resistance or let the page work it out from the cable length, conductor size and material.
- Read the tolerance table for the class limits at that temperature, and export the resistance table as CSV for a printed reference.
Reading the results
Sensitivity is the number that explains everything else. A PT100 gives 0.391 ohm per degree at 0 C, falling to about 0.33 ohm per degree at 600 C, so the same cable resistance or the same measurement error costs more degrees when the sensor is hot.
The lead-error figure is the direct consequence: loop resistance divided by sensitivity. It is shown even when the wiring cancels it, so the size of the problem you have avoided is visible.
Class limits apply to a new sensor and only within the range for its construction. Wire-wound and thin-film elements of the same class have different ranges - class AA thin film stops at 150 C where the wire-wound version reaches 250 C - so the table shows both.
Below zero the page says it used iteration and tells you what the simple quadratic would have given, so you can see how much the shortcut would have cost.
Worked example: a PT100 reading 138.51 ohm, and the same sensor on 50 m of 2-wire cable
A PT100 element measures 138.51 ohm. Above 0 C the Callendar-Van Dusen equation is R = R0(1 + At + Bt^2), which inverts in closed form to t = (-A + sqrt(A^2 - 4B(1 - R/R0))) / 2B. With A = 3.9083e-3 and B = -5.775e-7 that gives exactly 100.0 C - the value printed in every IEC 60751 table.
Now run the same sensor 50 m away on 2-wire 0.5 mm2 copper. The conductor resistance is rho x L / A with rho = 1.724e-8 ohm-metre, and the current goes out and back, so the length is 100 m: 1.724e-8 x 100 / 0.5e-6 = 3.45 ohm.
The instrument therefore sees 141.96 ohm and reports about 108.9 C. The sensitivity at 100 C is 0.3793 ohm/C, so 3.45 ohm is 9.1 C of error - on a class A sensor whose own permitted error at 100 C is 0.35 C.
The same cable on a PT1000 costs 0.91 C instead, because the sensitivity is ten times higher. That, rather than any accuracy difference in the element, is the practical reason for choosing PT1000 on long runs.
Formulas and scoring rules
- Above 0 C
R(t) = R0 x (1 + A t + B t^2)A = 3.9083e-3, B = -5.775e-7 (IEC 60751, alpha = 0.003851).- Below 0 C
R(t) = R0 x (1 + A t + B t^2 + C (t - 100) t^3)C = -4.183e-12. The cubic term is zero at and above 0 C.- Inverse above R0
t = (-A + sqrt(A^2 - 4B(1 - R/R0))) / (2B)Exact. Below R0 this is only an approximation, and the engine iterates instead.- Sensitivity
dR/dt = R0 x (A + 2B t)0.39083 ohm/C at 0 C for a PT100; the mean 0-100 C slope is 0.3851 ohm/C, which is where alpha comes from.- 2-wire lead error
errorC = loop lead resistance / (dR/dt at t)- Cable loop resistance
R = rho(T) x 2L / AL is the one-way run; the factor of two is the return conductor. Copper rho is 1.724e-8 ohm-metre at 20 C.- Tolerance class limit
AA: +-(0.1 + 0.0017|t|); A: +-(0.15 + 0.002|t|); B: +-(0.3 + 0.005|t|); C: +-(0.6 + 0.01|t|)
Why 3-wire is not as good as it looks
A 3-wire instrument measures the loop through two of the conductors and subtracts one lead's worth from the measurement, assuming the three conductors are identical. In a new, correctly terminated cable they very nearly are, and the residual error is small.
The assumption fails in the ways field cables actually fail: a corroded terminal on one leg, a repair that lengthened one conductor, a junction box where two legs share a crimp. The instrument cannot detect any of that - it simply subtracts the wrong number. Four-wire drives a known current through one pair and senses voltage on the other, so lead resistance cancels regardless of whether the leads match.
The other alpha values
This page speaks only for IEC 60751 sensors, alpha = 0.003851. Sensors made to the Japanese JIS curve (0.003916) and the older American curve (0.003902) exist and look identical. Reading one of them with the IEC equation gives an answer that is right at 0 C and progressively wrong away from it - roughly 1.7 C low at 400 C for a JIS sensor.
If a sensor's data sheet quotes a resistance at 100 C that is not 138.51 ohm for a PT100, it is not an IEC 60751 sensor and none of the numbers here apply to it.
Limitations: what the result does not prove
- It covers IEC 60751 platinum sensors only. JIS and the older US curves use different constants and will give a wrong temperature here.
- It does not model self-heating. A PT100 excited at 1 mA dissipates only 0.1 mW, but in still air with a poorly coupled sheath that can still be worth a few tenths of a degree.
- Three-wire lead cancellation is modelled as perfect. Real three-wire measurements carry whatever mismatch exists between the conductors, which this page cannot know.
- Class limits are for a new sensor within the range for its construction. Drift, contamination and mechanical shock are not covered, and a calibration certificate always takes precedence over a class.
Privacy: where your data goes
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Standards and sources
- IEC 60751 - Industrial platinum resistance thermometers - checked 19 Sep 2026
- NIST Technical Note 1297 - Guidelines for evaluating and expressing measurement uncertainty
- IEC 60228 - Conductors of insulated cables (conductor resistance)
Frequently asked questions
What is 138.51 ohm on a PT100?
Exactly 100 C. It is the anchor value of the IEC 60751 curve: a PT100 reads 100.00 ohm at 0 C and 138.51 ohm at 100 C, which is where the alpha of 0.003851 per degree comes from.
Why does the simple formula not work below 0 C?
Below zero the Callendar-Van Dusen equation includes a C(t - 100)t^3 term, so it is a quartic in t rather than a quadratic and has no practical closed-form inverse. Using the quadratic root anyway gives about -100.2 C for the 60.26 ohm that is really -100 C, and the error grows as it gets colder.
How much error does 2-wire cable add to a PT100?
The loop resistance divided by the sensitivity. At 0 C a PT100 changes 0.391 ohm per degree, so 1 ohm of cable is 2.56 C. Fifty metres of 0.5 mm2 copper is about 3.45 ohm of loop, or 9 C - far more than the sensor's own tolerance.
Should I use PT100 or PT1000?
PT1000 for anything with a cable run, a 2-wire connection or a noisy environment: it produces ten times the resistance change per degree, so lead resistance and input noise matter ten times less. PT100 remains the default where the instrument expects it and the run is short.
What is the difference between class A and class B?
Class A permits +-(0.15 + 0.002|t|) C and class B +-(0.3 + 0.005|t|) C. At 200 C that is 0.55 C against 1.3 C. Class A also has a narrower permitted range, and a thin-film class A sensor is only rated -30 to 300 C where a wire-wound one reaches -100 to 450 C.
Can a PT100 measure below -200 C?
Not to IEC 60751, which defines the curve from -200 C to 850 C. Below that the resistance change per degree collapses and platinum stops being a useful thermometer; cryogenic work uses rhodium-iron or diode sensors with their own calibrations.
My RTD reads open circuit. What resistance is that?
An open element or a broken lead reads very high - megohms - which is far above the 390.5 ohm a PT100 shows at its 850 C limit, so instruments flag it as a sensor break. A short reads near zero, well below the 18.52 ohm of -200 C. This page refuses both rather than converting them into a temperature.
Does the excitation current matter?
Only through self-heating. The resistance is a property of the element, so the measured value should not depend on current, but the power dissipated in it does: doubling the current quadruples the heating. Instruments typically use 0.1 to 1 mA for a PT100 and pulse it to keep the average low.
Last reviewed by the A2Z.Tools team against the sources listed above.
