RTD Resistance ↔ Temperature Calculator

A Resistance Temperature Detector (RTD) is a temperature sensor built from a length of pure platinum wire or film whose electrical resistance increases in a well-defined, repeatable way as its temperature rises. Unlike a thermocouple, which generates its own small voltage, an RTD is a passive resistor — you pass a small excitation current through it and measure the voltage drop to determine its resistance, then convert that resistance into a temperature using a standard reference equation. This calculator performs that conversion in both directions: resistance to temperature, and temperature to resistance.

What "PT100" actually means: the number in PT100, PT200, PT500 and PT1000 is the sensor's nominal resistance in ohms at exactly 0°C, called R0. A PT100 reads 100.00Ω at 0°C, a PT1000 reads 1000.00Ω at 0°C, and so on. This is a reference point, not a room-temperature reading — a PT100 at typical room temperature (around 25°C) actually reads close to 109.7Ω, not 100Ω. All four types (PT100/200/500/1000) follow the exact same temperature-resistance curve shape; only the R0 scaling factor differs, since standard platinum RTDs are wound to the same alpha (temperature coefficient) regardless of their base resistance.

RTD Resistance at Room Temperature

"Room temperature" is commonly taken as 20°C or 25°C. Per IEC 60751 (alpha = 0.00385), here's what each standard RTD type reads at both:

Calculated from the IEC 60751 Callendar-Van Dusen equation (the "European curve", alpha = 0.00385) — if your sensor is calibrated to ASTM E1137 instead, use the calculator above for the exact figure. A reading noticeably different from these values at genuine room temperature usually points to a wiring/lead-resistance error, a faulty sensor, or a standard mismatch (IEC vs ASTM) rather than a real temperature difference.

Formula used — the Callendar-Van Dusen equation: the internationally standard model for platinum RTDs is a two-branch polynomial. For temperatures at or above 0°C: R(T) = R0 × (1 + AT + BT²). For temperatures below 0°C, a cubic correction term is added to keep the curve accurate at sub-zero temperatures: R(T) = R0 × (1 + AT + BT² + C(T−100)T³). R0 is the sensor's 0°C resistance (100, 200, 500 or 1000Ω), and A, B, C are constants fixed by the standard the sensor is calibrated to — IEC 60751 or ASTM E1137 — not by the sensor's R0 value.

Going the other way — resistance to temperature: when you already have a measured resistance and need the corresponding temperature, the calculator has to invert the equation above. For the T≥0°C branch, the equation is a simple quadratic in T, so it has a direct closed-form solution using the quadratic formula. For the T<0°C branch, the added cubic term makes the equation a quartic in T with no simple closed-form inverse, so this calculator solves it numerically using Newton-Raphson iteration — starting from a linear estimate and refining the answer step by step until the resistance the equation predicts for that temperature matches your input to within a fraction of a milliohm.

IEC 60751 vs ASTM E1137: both standards describe the same physical phenomenon — platinum's resistance rising with temperature — but fit slightly different polynomial coefficients to slightly different reference platinum wire characteristics. IEC 60751 (the "European curve") uses alpha = 0.00385 Ω/Ω/°C and dominates industrial use worldwide, including in India. ASTM E1137 (the "American curve") uses alpha = 0.00392 Ω/Ω/°C and appears in some older or US-sourced instrumentation. Using the wrong standard's coefficients for a given physical sensor introduces a real, systematic conversion error even though both calculations are internally correct.

Worked example: a PT100 sensor per IEC 60751 reads 138.50Ω. Since this is above R0 = 100Ω, the T≥0°C quadratic branch applies: solving A T + B T² = (R/R0 − 1) with A = 3.9083×10⁻³ and B = −5.775×10⁻⁷ gives T ≈ 100.00°C. Reversing this: a PT100 at exactly 100°C per IEC 60751 gives R(100) = 100 × (1 + 3.9083×10⁻³×100 + (−5.775×10⁻⁷)×100²) ≈ 138.51Ω, confirming the two directions are consistent inverses of the same equation.

The equation is not linear: a common shortcut treats RTD output as strictly linear (resistance = R0 + constant × temperature), and this is a reasonable approximation over a narrow span, but the B coefficient's quadratic term causes real, measurable deviation from linear as the span widens — roughly 0.4°C of error near 100°C span if you ignore B entirely for a PT100, growing larger at higher temperatures. This is exactly why the full Callendar-Van Dusen equation, not a single linear conversion factor, is the correct basis for any measurement expected to hold reasonable accuracy across more than a narrow temperature window.

Lead wire resistance and self-heating: two practical error sources sit entirely outside the Callendar-Van Dusen equation itself. Lead wire resistance adds directly to the sensor's own resistance in a 2-wire hookup, making the sensor appear hotter (or colder, depending on wiring) than it actually is, unless a 3-wire or 4-wire configuration compensates for it. Self-heating occurs because the excitation current used to measure the RTD's resistance dissipates a small amount of power (I²R) inside the sensor itself, raising its temperature slightly above the medium being measured — datasheets specify a dissipation constant (typically in mW/°C) to estimate this effect, and it grows disproportionately if too high an excitation current is used, especially in still air or gas rather than a liquid or solid medium with better heat transfer.

Practical use of this calculator: use it to convert a measured resistance from a multimeter or data logger into a temperature reading when checking sensor health or calibration, to predict expected resistance at a known temperature before wiring a new installation or configuring a PLC/DCS analog input scaling table, to cross-check a printed PT100 resistance table without manual interpolation, or to compare how the same physical resistance reading would be interpreted differently under IEC 60751 versus ASTM E1137 assumptions.

Summary: RTD resistance and temperature are related by the two-branch Callendar-Van Dusen equation, with coefficients set by the calibration standard (IEC 60751 or ASTM E1137) and scaled by the sensor's R0 (100/200/500/1000Ω); the forward direction (temperature to resistance) is a direct polynomial evaluation, while the reverse direction is solved exactly above 0°C and iteratively below 0°C; and lead wire resistance and self-heating are separate, real-world error sources that sit outside this equation and must be managed through correct wiring configuration and appropriate excitation current.

1. Assuming R0 is the room-temperature reading. R0 is the resistance at exactly 0°C, not at typical ambient — a PT100 reads roughly 109.7Ω, not 100Ω, at 25°C. Comparing a measured room-temperature reading directly against the nameplate "100" figure without converting through the equation leads to a false fault diagnosis.

2. Ignoring the B coefficient and using a straight-line approximation. Linear conversion is close enough over a narrow span but drifts increasingly out of true as the measured range widens, since the real curve is quadratic (and cubic below 0°C), not linear.

3. Mixing up IEC 60751 and ASTM E1137 coefficients. Applying the wrong standard's A, B, C constants to a sensor calibrated to the other standard introduces a real, systematic conversion error that looks exactly like a sensor accuracy problem but is actually a calculation mismatch.

4. Using a 2-wire connection without accounting for lead resistance. Every metre of lead wire adds resistance directly in series with the sensor, which the equation cannot distinguish from a genuine temperature change — this is why 3-wire and 4-wire configurations exist for anything beyond short bench-top runs.

5. Applying the T≥0°C quadratic branch below 0°C. Extrapolating the simpler above-zero formula into sub-zero temperatures ignores the cubic correction term and produces a result that looks plausible but is measurably wrong, growing worse the further below 0°C the actual temperature sits.

6. Excessive excitation current causing self-heating error. A higher-than-recommended measurement current dissipates more power inside the sensor itself, raising its own temperature above the medium being measured — this shows up as a small but real positive offset that has nothing to do with the Callendar-Van Dusen equation or wiring configuration.

7. Assuming PT500 or PT1000 behave differently from PT100. All standard platinum RTDs share the same coefficient set for a given standard; only R0 scales. Treating a PT1000 as needing a different formula, rather than the same formula with a different R0, is unnecessary and a common source of spreadsheet errors when building custom scaling tables.