How lead resistance turns into temperature error
An RTD measures temperature through its resistance, so any resistance in the connecting cable looks like extra temperature. The calculator works out the resistance of each conductor from length, cross-section and the resistivity of copper (0.0172 Ω·mm²/m at 20 °C). It then divides the added resistance by the element’s sensitivity from IEC 60751 to express the error in degrees.
How much of the lead resistance reaches the measurement depends on the connection:
- 2-wire: the measuring current flows through both leads, so the instrument sees the element plus twice the lead resistance. ΔR = 2 × R_lead.
- 3-wire: a third lead lets the instrument measure the lead resistance and subtract it, assuming all leads are equal. What remains is the difference between the leads. ΔR ≈ R_lead × mismatch.
- 4-wire: current flows through one pair and voltage is sensed through the other, which carries virtually no current. Lead resistance drops out of the measurement.
Worked example
A PT100 at 100 °C is connected with 10 m of 0.5 mm² copper cable.
- Resistance per conductor: 0.0172 × 10 / 0.5 = 0.344 Ω
- Element sensitivity at 100 °C: 0.3793 Ω/°C
- 2-wire: 2 × 0.344 = 0.688 Ω, so the reading is 1.814 °C high
- 3-wire with 5 % mismatch between the leads: 0.344 × 0.05 = 0.0172 Ω, an error of 0.045 °C
- 4-wire: effectively zero
The 2-wire error alone is more than five times the class A tolerance of the element at that temperature (±0.35 °C). For a ±0.5 °C error budget, the longest 2-wire cable would be 2.76 m.
Choosing the connection
| 2-wire | 3-wire | 4-wire | |
|---|---|---|---|
| Lead error | Full (both leads) | Only the mismatch | Negligible |
| Typical use | Short leads, PT1000, low accuracy | Industrial standard for PT100 | Laboratory, calibration, long runs |
| Instrument support | Universal | Almost all RTD inputs | Most transmitters, fewer PLC cards |
The calculator suggests the fewest wires that keep the error inside your budget; that is also the specification passed to product matching.
Ways to reduce the error
- Use a PT1000. For the same cable, the error in degrees is ten times smaller, because the element’s sensitivity is ten times larger.
- Thicker conductors. Error is inversely proportional to cross-section.
- Mount a transmitter at the sensor. A head-mount transmitter converts the reading to 4–20 mA within centimetres of the element; the long cable then carries a current signal that isn’t affected by its resistance.
- Keep 3-wire leads identical. Use the same cable for all three cores, with no extra terminals or splices in only one lead.
Common mistakes
Assuming 3-wire cancels everything. Compensation is only as good as the lead match. Terminal resistance, corroded connections or a joint in one core all add mismatch.
Forgetting temperature of the cable. Copper resistance rises about 0.39 % per °C. A cable running through a hot area adds more resistance than the 20 °C figure.
Measuring a 2-wire sensor with a multimeter and trusting the reading. The meter includes both leads. Short the leads at the sensor end, measure, and subtract.
Frequently asked questions
Does lead resistance make the reading high or low?
Always high. Extra resistance looks like extra temperature, since platinum resistance rises with temperature.
How do I enter AWG wire?
Select the AWG size in the conductor field; the cross-section in mm² is shown next to it.
Can I use this for nickel or copper RTDs?
No. The sensitivity is calculated from the platinum IEC 60751 curve. For other materials the method is the same, but the sensitivity differs.
Where do I convert resistance to temperature?
Use the PT100 / PT1000 calculator, or the PT100 resistance table for a printed reference.