Pt100 resistance ↔ temperature calculator (IEC 60751)
Convert between resistance and temperature for Pt100 / Pt1000 sensors, with class AA, A, B and C tolerances at that temperature.
Standard-curve conversion for an uncalibrated sensor. A calibrated PRT has its own coefficients (Callendar–Van Dusen or ITS-90) on the certificate — use those, not the nominal curve, for measurement.
Result
| Class | Tolerance at 50.0 °C | In ohms |
|---|---|---|
| AA | ±0.185 °C | ±0.0712 Ω |
| A | ±0.250 °C | ±0.0963 Ω |
| B | ±0.550 °C | ±0.2118 Ω |
| C | ±1.100 °C | ±0.4236 Ω |
Classes are defined over limited ranges (e.g. AA -50 to +250 °C (wire-wound); +600 °C for the thin-film variant); values outside are formula extrapolations.
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Pt100 reference points
A worked example
A resistance bridge reads 110.904 Ω on a 100 Ω platinum resistance thermometer. The temperature is wanted, and so is the figure that converts the bridge's ohms uncertainty into degrees.
What you start with
- Measured resistance
- 110.904 Ω
- Nominal resistance R₀
- 100.000 Ω
The arithmetic
- 01
Invert the IEC 60751 reference function for t > 0 °C.
R(t) = R₀(1 + At + Bt²) solved for t at R = 110.904 Ω gives t = 28.016 °C
- 02
Take the sensitivity dR/dt at that temperature.
dR/dt = 0.3876 Ω/°C at 28 °C (0.3908 Ω/°C at 0 °C)
- 03
Convert a resistance uncertainty into a temperature uncertainty.
1 mΩ / 0.3876 Ω/°C = 0.0026 °C
28.016 °C, and 1 mΩ of resistance uncertainty is worth 2.6 mK.
The sensitivity is the join between two budgets. Your bridge's certificate states an uncertainty in ohms; your customer's certificate must state one in degrees; dR/dt is the only honest way across. It is not a constant — it falls from 0.3908 to 0.3876 Ω/°C between 0 °C and 28 °C, and keeps falling — so a budget that uses one figure across a wide range is quietly wrong at both ends.
How the calculation works
- 01t ≥ 0 °C: R(t) = R₀ (1 + A t + B t²); t < 0 °C: R(t) = R₀ (1 + A t + B t² + C (t − 100) t³), with A = 3.9083 × 10⁻³, B = −5.775 × 10⁻⁷, C = −4.183 × 10⁻¹².
- 02Resistance → temperature: closed-form quadratic above 0 °C, Newton iteration below.
- 03Tolerances (IEC 60751:2022): AA ±(0.1 + 0.0017|t|), A ±(0.15 + 0.002|t|), B ±(0.3 + 0.005|t|), C ±(0.6 + 0.01|t|) °C.
Limitations
- Uses the standard curve, not a calibrated sensor's own coefficients; a calibrated PRT should use the coefficients on its certificate.
- Tolerance classes apply over ranges that depend on the element type (wire-wound vs film) — consult the standard for validity limits.
Frequently asked questions
- What resistance does a Pt100 have at 100 °C?
- 138.5055 Ω on the IEC 60751 standard curve (α = 0.003851), usually quoted as 138.51 Ω.
- What is the Class B tolerance of a Pt100 at 0 °C?
- ±0.3 °C, growing to ±0.8 °C at 100 °C: ±(0.3 + 0.005|t|) °C.
- Does the calculator work for Pt1000?
- Yes — set R₀ to 1000 Ω. The temperature coefficient and tolerance classes are the same.
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Pt100 tolerance classes explained (IEC 60751)
Classes AA, A, B and C widen with temperature: Class A is ±0.15 °C at 0 °C but ±0.55 °C at 200 °C. A tolerance class is not a measurement uncertainty.
How to calibrate a Pt100
Calibration by comparison against a reference thermometer, and the factors that decide the uncertainty.
Self-heating in resistance thermometers
The measuring current warms the element above its surroundings: under a millikelvin in a stirred bath, tens in still air. Calibrate in the medium you use.
Readouts and bridges for reference thermometers
A reference PRT is only as good as the instrument reading it. Resolution, linearity, measurement current and calibration of the readout all enter the budget.
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