Pt100 RTD resistance and temperature: converting both ways

What a Pt100 sensor actually gives you

A Pt100 is a platinum resistance temperature detector (RTD). Its electrical resistance rises in a repeatable way as temperature rises, and it is defined as 100 Ω at 0 °C. A Pt1000 follows the same curve with ten times the resistance, so 1000 Ω at 0 °C. The instrument or transmitter does not measure temperature directly. It measures resistance, then converts that number to a temperature using a stored equation.

The Pt100 resistance calculator performs the same conversion in either direction. It is useful when checking a decade box or simulator against a transmitter, when comparing a reading taken with a multimeter against a table, or when deciding what resistance a calibrator must be set to for a given test temperature.

The Callendar–Van Dusen equation

The calculator uses the standard platinum curve for a sensor with α = 0.00385. With R₀ equal to 100 Ω (Pt100) or 1000 Ω (Pt1000) and temperature T in °C:

• For T ≥ 0 °C: R = R₀ × (1 + A·T + B·T²)
• For T < 0 °C: R = R₀ × (1 + A·T + B·T² + C·(T − 100)·T³)

The constants are A = 3.9083×10⁻³, B = −5.775×10⁻⁷ and C = −4.183×10⁻¹². The calculator accepts temperatures from −200 °C to 850 °C.

Going the other way, for resistance at or above R₀ the quadratic can be solved directly: T = (−A + √(A² − 4B×(1 − R/R₀))) ÷ (2B). Below R₀ (temperatures under 0 °C) the cubic term makes a closed form awkward, so the calculator searches numerically by repeated halving of the interval between −200 °C and 0 °C until the equation reproduces the entered resistance.

Worked example 1: temperature to resistance

Find the Pt100 resistance at 50 °C.

1. A·T = 3.9083×10⁻³ × 50 = 0.195415
2. B·T² = −5.775×10⁻⁷ × 2500 = −0.001443750
3. R = 100 × (1 + 0.195415 − 0.00144375) = 100 × 1.19397125 = 119.3971 Ω (calculator display, rounded to four decimals)

For a Pt1000 the same temperature gives about 1193.97 Ω. Below zero the extra C term applies. At −50 °C a Pt100 gives 80.3063 Ω. The table lists further points calculated with the same equation.

Between 0 and 100 °C the average sensitivity is about 0.385 Ω per °C for a Pt100, which is why a small resistance error becomes a visible temperature error.

Worked example 2: resistance to temperature and wiring error

A Pt100 element measured directly at its terminals reads 138.51 Ω. Applying the quadratic solution gives 100.0119 °C. The 0.0119 °C difference from a round 100 °C is only because 138.51 is the table value rounded to two decimals; the exact nominal value is 138.5055 Ω.

Now consider a two-wire connection where the two cable conductors together add 0.8 Ω. If the sensor is at 0 °C its true resistance is 100 Ω, but the instrument sees 100.8 Ω and converts that to 2.0475 °C. The error is about 0.8 ÷ 0.39 ≈ 2 °C. The calculator does not model this: it converts the number entered, so enter the resistance at the sensor, not including wiring. Three-wire and four-wire transmitter inputs are designed to compensate or remove lead resistance, subject to the transmitter specification.

The reverse conversion works below zero too. Entering 80.31 Ω returns −49.9906 °C, again because 80.31 is a rounded table value.

From sensor to 4–20 mA signal

Many Pt100 transmitters are configured for a temperature range and send a 4–20 mA signal. Suppose the range is 0 to 200 °C and the sensor, or a simulator, is set to 119.3971 Ω. That corresponds to 50.0075 °C. The expected output is 4 + 16 × (50.0075 − 0) ÷ 200 = 8.0006 mA, which can be checked with the engineering units to 4–20 mA calculator. Reading a measured current back as temperature uses the 4–20 mA to engineering units calculator.

A simulated resistance test is a convenient way to separate sensor problems from transmitter and loop problems, because the simulator replaces the element completely.

Common mistakes

• Using Pt100 values for a Pt1000 sensor or the reverse; check the sensor type before entering a number.
• Assuming the nominal curve includes tolerance class. Class A, class B and similar tolerance limits are separate from this equation.
• Entering a loop resistance that includes long cable on a two-wire circuit.
• Forgetting that a sensor with a different α value uses different constants.
• Measuring resistance with a meter current that is high enough to heat a small element, so that self-heating adds error.
• Rounding a table value and then expecting an exact round temperature.
• Treating the numerical result below 0 °C as exact; it is a converged search result and is accurate to many more digits than the sensor itself.

Checks before you trust the result

• Confirm the sensor is platinum with α = 0.00385 and that its nominal resistance is 100 Ω or 1000 Ω at 0 °C.
• Check that the input is within −200 °C to 850 °C, or the matching resistance limits shown by the tool.
• Verify the result against the sensor or transmitter datasheet table for a few points.
• Confirm the wiring configuration and how the transmitter handles lead resistance.
• Treat the output as an ideal nominal value. It is an estimate and does not replace the manufacturer data or the site calibration procedure.

Frequently asked questions

Why is the Pt100 curve not a straight line?

The B coefficient is negative, so resistance rises slightly less per degree as temperature increases. The deviation from a straight line is small over short spans but not negligible over a wide range.

Can I use this for thermistors or Ni120 sensors?

No. The constants are specific to platinum with α = 0.00385. Other sensor types need their own tables or equations.

Does the calculator include sensor tolerance?

No. It gives the ideal nominal value. Tolerance class, self-heating, lead wires and transmitter accuracy are outside the calculation.

Why does the result differ slightly from my chart?

Published charts are rounded to a limited number of decimals and some use a different reference. Compare the equation with the chart at a known point and decide which one the procedure requires.

Recording the data

For each RTD loop, record the tag, sensor type, R₀, wiring (2, 3 or 4 wire), transmitter range, test temperatures or simulated resistances, the expected and actual outputs, and the equipment used. Keep the as-found and as-left values separately, and note the reference standard identifier. The calibration record template provides columns for range, tolerance, last calibration date, as-found and as-left errors, reference standard and certificate number. Record results as an estimate checked against the approved procedure, not as a certificate.