Calculate the relative and absolute resistance change of a strain gauge from nominal resistance, gauge factor and strain, including the corresponding quarter-bridge signal.
Enter values and run the calculation.
The basic strain-gauge equation links the relative resistance change linearly to strain through the gauge factor. Manufacturers determine k per guideline within ±1000 µm/m on a bending beam with ν₀ = 0.285. For constantan, k combines the geometric term (1+2ν) and the change in resistivity (Keil eq. 2.12).
ΔR/R = k · ε (Keil Gl. 2.2)
ΔR = k · ε · R₀
UM/UB = ΔR/(4R₀) = k·ε/4 (Keil Gl. 4.8)
Entering strain in % instead of µm/m, or not matching the amplifier gauge factor (often fixed at 2.00) to the gauge.
First estimate of the expected signal before installation, choice of nominal resistance and sanity check of amplifier settings. Keil's example: 120 Ω, k = 2, ε = 1000 µm/m give ΔR = 0.24 Ω and 0.5 mV/V.
The gauge factor applies at room temperature in the elastic range; transverse sensitivity, temperature response and creep are excluded. The quarter-bridge signal is the linearised approximation of eq. 4.8.
Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 2.2 sensitivity, eqs. (2.2), (2.12); sec. 4.2, eq. (4.8).
The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.
Per Keil eq. 2.12 geometry alone gives 1+2ν ≈ 1.6; the remainder comes from the resistivity change with volume (Bridgman constant).
For metal grids in the elasto-plastic range ΔR/R = kε remains a good approximation; the bridge circuit itself becomes non-linear (eq. 4.7).
ΔR scales with R₀ while ΔR/R and the bridge signal do not. Higher resistances reduce current and self-heating.