Electronics & General ElectricalPreliminary engineering
RTD Calculator — PT100 / PT1000 Resistance to Temperature
Convert between platinum RTD resistance and temperature using the Callendar–Van Dusen relation, with the simple linear model shown alongside for comparison.
About this calculator
A platinum resistance thermometer measures temperature through the resistance of a platinum element, which rises in a smooth, highly repeatable, and slightly non-linear way as the element gets hotter. A PT100 is defined by having 100 Ω of resistance at 0 °C and a PT1000 by having 1000 Ω; apart from that scale factor the two sensors follow exactly the same curve.
That curve is described by the Callendar–Van Dusen relation. Above 0 °C it is a quadratic in temperature, using the constants A and B. Below 0 °C the quadratic alone is not good enough, and a third constant C multiplies an additional term that vanishes at and above the ice point — which is why both branches meet exactly at R₀.
This calculator works in both directions. Give it a temperature and it returns the resistance a conforming sensor would show; give it a measured resistance and it returns the temperature that implies. Above 0 °C the inverse is solved in closed form with the quadratic formula. Below 0 °C the relation is a quartic, and rather than carry a second set of published approximation coefficients this tool inverts the curve numerically, so a round trip is exact with respect to the model actually being used.
The simple linear model, R = R₀(1 + α·t), is offered as a separate, clearly-labelled option — and whichever model you choose, the other is evaluated alongside it so you can see the disagreement as a number rather than take it on trust. The two agree at 0 °C and are within about 0.01 °C at 100 °C, by construction of α. They part company quickly after that: about 3 °C apart at 200 °C, about 18 °C at 400 °C, and about 12 °C at −200 °C. The linear model is a useful mental approximation and a poor way to interpret a real sensor.
Design notes & common mistakes
- PT100 and PT1000 follow the same curve; only R₀ differs. A PT1000 gives ten times the resistance change per degree, which makes lead and contact resistance ten times less significant — often the reason to choose one.
- At PT100 sensitivity, roughly 0.39 Ω is one whole degree at 0 °C. On a 2-wire connection the lead resistance is indistinguishable from the element, so a few metres of thin cable is a genuine measurement error rather than a rounding detail.
- Sensitivity is not constant: it falls from about 0.391 Ω/°C at 0 °C to about 0.293 Ω/°C at 850 °C for a PT100. A calibration checked only near ambient does not characterise the top of the range.
- The α = 0.003851 grade is the common industrial one, but it is not the only platinum grade in use. A sensor built to a different α follows a different curve, and reading it with these constants is a systematic error no averaging will remove.
Assumptions
- The sensor conforms to the standard platinum grade with α = 0.003851, the coefficient set this calculator uses.
- The element is at a single uniform temperature, and has settled — no thermal gradient along the sheath and no transient in progress.
- The resistance entered is the element's own: lead-wire resistance has already been excluded by the measurement arrangement.
- Measurement current is low enough that self-heating of the element is negligible.
When to use this calculator
Appropriate for
- Converting a measured RTD resistance into a temperature, or the reverse
- Checking an instrument's or transmitter's RTD linearisation against the standard relation
- Choosing between PT100 and PT1000 by comparing the resistance change a degree buys
- Seeing how far the simple linear approximation departs from the standard curve
- Teaching or learning how resistance thermometry works
Not suitable for
- Designing an over-temperature trip, over-temperature protection, or any safety-instrumented function — this is a measurement conversion, not a protective-function design
- Establishing a calibration or a measurement uncertainty budget, which needs the sensor's tolerance class, the instrument's accuracy and a traceable reference — a full study, not a single conversion
- Interpreting a 2-wire measurement without first accounting for the lead resistance separately
- Working with a non-platinum sensor such as a thermistor or a nickel element, whose curves are entirely different
Engineering use
Boundary of this tool. For measurement analysis and education only. This is not a design tool for a temperature trip, over-temperature protection, or any safety-instrumented function. A temperature measurement very often does feed a protective system, which is exactly why this boundary is stated rather than assumed: designing that protection is a separate engineering activity with its own requirements, redundancy and verification.
Intended use. Measurement analysis and educational calculation for platinum resistance thermometers under the standard Callendar–Van Dusen relation.
Applicable for
- Converting between element resistance and temperature in both directions
- Comparing PT100 and PT1000 behaviour, which differ only in R₀
- Quantifying how far the simple linear approximation departs from the standard relation
- Checking the sensitivity in Ω/°C available at a given temperature
Does not account for
- Lead-wire resistance, which a 2-wire connection adds directly to the reading
- Self-heating from the measurement excitation current
- The sensor's tolerance class — the permitted deviation of a real element from the standard curve
- Long-term drift, mechanical strain, contamination and insulation faults
- Thermal lag and the sheath's response time during a transient
- Instrument accuracy, resolution and cold-end effects in the measuring loop
Verification required
- Confirm the sensor is a standard α = 0.003851 platinum element, not a different platinum grade or a nickel/thermistor sensor
- Confirm the measurement arrangement excludes lead resistance, or account for it separately
- Confirm the sensor's tolerance class and apply its permitted deviation before treating the result as an accuracy figure
- Confirm against an independent traceable reference where the temperature matters
What this calculator does not cover
- Describes an ideal conforming element, not a specific sensor. A real RTD carries a tolerance class (commonly Class A or Class B) whose permitted deviation grows with distance from 0 °C, and that deviation is usually larger than any rounding here.
- Does not model lead-wire resistance. On a 2-wire connection the leads are indistinguishable from the element, and at PT100 sensitivity roughly 0.39 Ω is a whole degree — a few metres of thin cable is a real error.
- Does not model self-heating. The excitation current that measures the resistance also warms the element, and the resulting offset depends on the medium and flow conditions rather than on anything in this calculation.
- Does not account for sensor drift, mechanical strain, contamination or insulation-resistance faults, all of which shift a real element away from the standard curve over its service life.
- The relation is defined between −200 °C and 850 °C; values outside that interval are extrapolation and are flagged as such.
- The linear model option is deliberately a poor description of the sensor away from 0–100 °C, and is offered for comparison rather than for interpreting a measurement.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What temperature is 138.51 Ω on a PT100?
100 °C. A PT100 is 100 Ω at 0 °C and rises to 138.5055 Ω at 100 °C under the standard Callendar–Van Dusen relation. The same resistance on a PT1000 — 1385.06 Ω — is also 100 °C, because the two sensors follow an identical curve and differ only in their 0 °C value.
What is the difference between a PT100 and a PT1000?
Only the resistance at 0 °C: 100 Ω against 1000 Ω. The shape of the resistance–temperature curve is identical, so a PT1000 simply gives ten times the resistance change per degree. That makes lead-wire and contact resistance ten times less significant as a proportion of the reading, which is often the practical reason to pick a PT1000.
Why is the Callendar–Van Dusen relation not a straight line?
Because platinum's resistance genuinely does not rise linearly with temperature. Above 0 °C a quadratic in t, using the constants A and B, describes it well. Below 0 °C a quadratic is no longer adequate, and a third constant C multiplies an extra term that vanishes at and above the ice point — which is why the two branches meet exactly at R₀.
How far off is the simple linear RTD approximation?
It agrees at 0 °C and to about 0.01 °C at 100 °C, because α is defined from those two points. Beyond that it diverges quickly: roughly 3 °C at 200 °C, roughly 18 °C at 400 °C, and roughly 12 °C at −200 °C. This calculator evaluates both models at once so the disagreement is visible as a number rather than taken on trust.
Can I use this to set a high-temperature trip?
No. This is a measurement conversion for analysis and education. Designing an over-temperature trip, over-temperature protection, or any safety-instrumented function is a separate engineering activity with its own requirements for redundancy, response time, failure modes and independent verification, none of which a resistance-to-temperature conversion addresses.
References
- The Callendar–Van Dusen relation and the standard platinum coefficients (α = 0.003851 grade) are specified in IEC 60751, Industrial platinum resistance thermometers and platinum temperature sensors. This calculator implements the relation and generates values from it; no part of the standard's text or tables is reproduced.
- Bela G. Liptak (ed.), Instrument Engineers' Handbook, Volume 1: Process Measurement and Analysis.
- Robert P. Benedict, Fundamentals of Temperature, Pressure, and Flow Measurements.
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