Strain Gauge Lead Wire Resistance Calculator

What is calculated?

With a full bridge the cable is outside the bridge: the supply leads form a divider with the bridge resistance, reducing sensitivity, and cable temperature changes alter it. With half and quarter bridges the leads are part of the arms: they lower the effective gauge factor, and in two-wire connection every thermal change of lead resistance acts as apparent strain. Keil's example: 3 m, 0.8 mm², 40 K give 0.0216 Ω and 90 µm/m at 120 Ω. Ruge's three-wire connection places the leads in adjacent arms and cancels this effect.

Equations

R_K = ρ·L/q

Vollbrücke: E*/E = R_B/(R_B+2R_K) (Keil Gl. 6.1); ΔE/E = −2ΔR_K/(R_B+2R_K) (Gl. 6.2)

Viertel-/Halbbrücke: ΔR/(R_DMS+R_L) = k*·ε ⇒ k* = k·R/(R+R_L) (Keil Gl. 6.4)

Zweileiter: ε_s = ΔR_L/(k·(R+R_L)) mit R_L = 2R_K

Assumptions and typical mistake

Ohmic effects only; cable capacitance (phase shift, amplitude loss at carrier frequency, Keil sec. 6.3) and six-wire sensing are not modelled.

Entering the doubled cable length (out and back) a second time – the calculator already accounts for the number of leads via the connection type.

What you enter – and where the values come from

Connection

Connection type between strain gauge and instrument: full bridge with all four gauges on the part, half bridge with two gauges, simple two-wire quarter bridge, or temperature-compensated three-wire quarter bridge. Source: measuring-point wiring plan and amplifier terminal diagram. Do not infer it merely from visible conductors because shield and sense wires may be additional.

Cable length (one way) [m]

One-way distance between measuring point and instrument along the cable (not out-and-back – the calculator accounts for the number of leads via the connection type). Source: measure the cable or take it from the cabling plan.

Conductor cross-section [mm²]

Copper cross-section of a single conductor. Thin measuring cables have 0.14 mm², rugged ones 0.5 to 0.8 mm². The smaller the cross-section, the larger the lead resistance and its influence. Source: printed on the cable or in its datasheet.

Resistivity [Ω·mm²/m]

Resistivity of the conductor material in Ω·mm²/m: copper 0.018 (Keil: 1.8·10⁻⁶ Ω·cm), aluminium 0.028. Change only if the cable is not copper.

Gauge / bridge resistance R [Ω]

For quarter and half bridges the nominal resistance of the single gauge (120 or 350 Ω); for the full bridge the input resistance of the whole bridge, which for equal gauges also equals the gauge nominal resistance. Source: gauge package or transducer datasheet (‘input resistance’).

Gauge factor k

The gauge factor is the sensitivity of the strain gauge: it states how much the electrical resistance changes when the gauge is stretched (ΔR/R = k·ε). Without it no strain can be computed from an electrical signal. Source: printed on every gauge package or in the manufacturer datasheet, typically 2.0 to 2.1 for constantan foil gauges; valid at room temperature. The same value must be set in the amplifier.

Cable temperature change ΔT [K]

Temperature change of the cable between balancing and measurement, e.g. when the cable lies in the sun or runs along a warm machine. Source: estimate or measurement at the cable. Enter 0 if only the sensitivity loss is of interest.

Conductor temperature coefficient [10⁻³/K]

Temperature coefficient of the conductor resistance: by how many per mille the lead resistance changes per kelvin. Copper ≈ 4·10⁻³/K (0.4 % per K) – much more temperature sensitive than the gauge's constantan. Source: material table; keep the default for copper.

What this calculator is for

Planning measurement cables for multi-channel setups, judging zero drift of long two-wire connections and correcting the gauge factor for long half-bridge leads.

What comes next

1. Enter connection type, cable length and cross-section.
2. Account for the sensitivity loss when calibrating or correct the instrument gauge factor accordingly.
3. Always use three-wire connection for quarter bridges exposed to temperature change.

How to read the results

• Sensitivity loss is a scale error (all values too small by the same percentage) and is removed by calibrating with the cable connected.
• Apparent strain is a zero error that changes with cable temperature during the measurement and cannot be calibrated away – only three-wire, full-bridge or six-wire connection helps.

What each value means

Resistance per lead R_K [Ω]

Ohmic resistance of a single conductor over the entered length.

Sensitivity factor E*/E or k*/k

Factor by which the sensitivity drops compared with the setup without cable (1 = no influence). For quarter/half bridges this is also the ratio of effective to nominal gauge factor.

Sensitivity loss [%]

Sensitivity loss in percent: the amplifier under-reads the strain by this much unless calibrated with the cable connected. Correction: divide the reading by the factor or reduce the instrument gauge factor accordingly.

Sensitivity change due to ΔT [%]

Full bridge only: percentage change in measurement sensitivity when the cable warms by the entered temperature difference. It acts as a scale error on all readings; for demanding measurements limit it with sense leads or calibration at operating temperature.

Apparent strain due to ΔT [µm/m]

Quarter bridge in two-wire connection only: apparent strain faked by the cable warming – a zero error that looks like real strain. In three-wire connection it becomes zero.

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, secs. 6.2.2–6.2.3 ohmic cable resistance, eqs. (6.1)–(6.4), figs. 6.1–6.3; sec. 6.7.

The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.

Frequently asked questions

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