Gauge factor

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Gauge factor (GF) or strain factor of a strain gauge is the ratio of relative change in electrical resistance to the mechanical strain ε, which is the relative change in length.

GF={\frac {{\frac {\Delta R}{R}}}{\varepsilon }}={\frac {{\frac {\Delta \rho }{\rho }}}{\varepsilon }}+1+2\nu

In practice, the resistance is also dependent on temperature. The total effect is

{\frac {\Delta R}{R}}=GF\varepsilon +\alpha \theta


Where

  • ε = strain = \Delta L/Lo
    • \Delta L = absolute change in length
    • Lo = original length
  • ν = Poisson's ratio
  • ρ = Resistivity
  • ΔR = change in strain gauge resistance
  • R = unstrained resistance of strain gauge
  • α = temperature coefficient
  • θ = temperature change

For many materials there is no change in resistivity (\Delta \rho =0), for these materials the gauge factor is simply

GF=1+2\nu


General examples of Gauge Factor values:

Material Gauge Factor
Metal foil strain gauge 2-5
Thin-film metal 2
Single crystal silicon -125 to + 200
Polysilicon ±30
Thick-film resistors 100


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