Pt100 lead wire error calculator: 2-wire, 3-wire and 4-wire

How the calculation works

1. 01A resistance thermometer reports resistance, so any extra resistance in the circuit reads as temperature: error = extra resistance ÷ sensitivity, where sensitivity is dR/dT of the sensor at its temperature.
2. 022-wire: both leads are in the measuring path, so the extra resistance is twice one conductor. 3-wire: the third lead lets the circuit cancel the lead resistance to first order, leaving only the mismatch between the matched leads. 4-wire: separate current and voltage leads, so no lead error to first order.
3. 03Sensitivity comes from the IEC 60751 curve at the sensor temperature: 0.3908 Ω/°C for a Pt100 at 0 °C, falling to 0.3793 Ω/°C at 100 °C. It is not the 0.385 Ω/°C mean-alpha figure often quoted, so the answer changes with temperature as it does in practice.
4. 04Cable resistance is ρ L / A for annealed copper with ρ = 1/58 Ω·mm²/m at 20 °C, corrected by 0.393 % per kelvin to the cable temperature, and the longest 2-wire run follows by solving the error equation for L.

Limitations

• This is the first-order model. The 3-wire result assumes the leads are at the same temperature, so a cable that crosses a hot zone loses some of its compensation.
• It covers lead resistance only. Self-heating, insulation leakage, thermoelectric voltages and the meter's own accuracy are separate errors.
• It describes copper conductors. Nickel-plated or other conductors have a different resistivity, so measure the resistance directly where you can.
• It tells you how big the lead problem is. It does not replace calibrating the sensor together with the leads it is used with.

Frequently asked questions

How much error does a 2-wire Pt100 lead cause?

About 2.6 °C for every ohm of loop resistance at 0 °C, because a Pt100 changes only about 0.39 Ω per °C. Ten metres of 0.5 mm² copper is 0.34 Ω per conductor, so 0.69 Ω in the loop and nearly 1.8 °C of error.

Does a 3-wire connection remove lead wire error?

Mostly. It cancels the lead resistance when the leads are matched, leaving only the mismatch between them. If one lead is 0.1 Ω different from the other, the error is about 0.26 °C. It also assumes the leads sit at the same temperature, which a long cable run does not always satisfy.

Is a Pt1000 better than a Pt100 for long cable runs?

Yes, by a factor of ten for lead resistance. A Pt1000 changes ten times as much per degree, so the same cable resistance produces one tenth of the temperature error. That is why Pt1000 sensors are common where the cable is long and a 2-wire connection is all the transmitter offers.

Why does the error change when the cable gets warm?

Because copper resistance rises by about 0.393 % for every kelvin. A 2-wire error that was right when you checked it on a cool morning drifts as the cable warms, which is why a 2-wire sensor cannot simply be corrected once and left.

When should I use 4-wire?

When the lead error matters and the instrument supports it: laboratory and reference thermometry, and any long run with a tight tolerance. A 4-wire connection measures the sensor voltage with separate leads that carry almost no current, so the lead resistance drops out.