RTD (Pt100) & Thermistor Calculator

About the RTD (Pt100) & Thermistor Calculator

Convert the resistance of a temperature sensor into its temperature, or a temperature into the resistance to expect, for two kinds of sensor. Platinum RTDs (Pt100, Pt500, Pt1000 or any R0) use the Callendar–Van Dusen equation with the coefficients of IEC 60751, below 0 °C as well as above. NTC thermistors use the Beta model from R25 and β, or the Steinhart–Hart equation, whose three coefficients the calculator can also fit to three points from a datasheet table.

For an RTD you also get its sensitivity, the IEC 60751 tolerance of class AA, A, B or C at that temperature (and whether the class covers it for a wire-wound or film element), and the error that two-wire leads add, worked out from their resistance or from the cable’s length and size. A resistance table over any range, in °C, °F or kelvin, completes the result.

Without a pass, the free preview runs on your own reading: it shows the notes that apply and the temperatures of the table’s first rows, with the temperature or resistance you convert, every other figure and the working hidden; the full result, Copy result and the CSV table come with a Pro pass.

Platinum RTDs: Callendar–Van Dusen (IEC 60751)

• From 0 °C to 850 °C: R = R0·(1 + A·t + B·t²)
• From −200 °C to 0 °C: R = R0·[1 + A·t + B·t² + C·(t − 100 °C)·t³]
• A = 3.9083 × 10⁻³ °C⁻¹, B = −5.775 × 10⁻⁷ °C⁻², C = −4.183 × 10⁻¹² °C⁻⁴, giving a mean temperature coefficient α = 0.00385 /°C from 0 °C to 100 °C

At or above 0 °C the calculator solves the quadratic exactly; below 0 °C it solves the quartic with Newton’s method. A Pt100 is 100 Ω at 0 °C and changes by about 0.39 Ω per °C; a Pt1000 changes ten times as much, which makes lead resistance ten times less important.

Tolerance classes

IEC 60751 limits the deviation of a sensor from the table to ±(a + b·|t|):

• Class AA (W 0.1 / F 0.1): ±(0.1 °C + 0.0017·|t|), wire-wound −50 °C to 250 °C, film 0 °C to 150 °C
• Class A (W 0.15 / F 0.15): ±(0.15 °C + 0.002·|t|), wire-wound −100 °C to 450 °C, film −30 °C to 300 °C
• Class B (W 0.3 / F 0.3): ±(0.3 °C + 0.005·|t|), wire-wound −196 °C to 600 °C, film −50 °C to 500 °C
• Class C (W 0.6 / F 0.6): ±(0.6 °C + 0.01·|t|), wire-wound −196 °C to 600 °C, film −50 °C to 600 °C

Outside its range a class does not apply: the calculator says so and shows the figure in amber.

Two, three or four wires

With two wires the instrument measures the sensor plus both leads, and every ohm of lead looks like about 2.6 °C on a Pt100. Copper’s resistance also changes with its own temperature, so the error moves with the cable. Three wires let the instrument subtract the lead resistance, which cancels when the leads are equal. Four wires measure the voltage at the sensor itself, so leads add no error. The cable helper uses annealed copper at 20 °C (1/58 Ω·mm²/m) and the standard AWG diameters.

NTC thermistors: Beta and Steinhart–Hart

• Beta model: 1/T = 1/T0 + ln(R/R0)/β, with T in kelvin. It is exact at T0 and drifts away from it, because β itself changes with temperature: that is why datasheets name the pair of temperatures β was measured between (B25/50, B25/85).
• Steinhart–Hart: 1/T = A + B·ln R + C·(ln R)³ (Steinhart and Hart, Deep-Sea Research). Three coefficients follow a thermistor’s curve far better over a wide range. The calculator fits them through three points with the closed-form solution of the three equations, and inverts the equation for R as a cubic in ln R (Cardano’s formula, or the trigonometric solution when a fit gives a slightly negative C).
• Temperature coefficient: α = (1/R)·dR/dT, about −4.4 % per °C at 25 °C for β = 3950 K.

Limitations

• Results are for the sensor itself. Self-heating from the measuring current, the instrument’s own accuracy and thermal contact with what you measure all add error.
• RTD conversions follow IEC 60751 platinum (α = 0.00385 /°C). Platinum sensors to older or other curves (α = 0.003916 or 0.003925 /°C) need their own coefficients.
• The lead helper assumes copper at 20 °C. The three-wire case assumes equal leads; the difference between unequal leads adds directly to the reading.
• The Beta model and a three-point fit are only as good as the data behind them; for the best accuracy use points spread over the range you measure.

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