Strain Gauge Bridge Calculator (Wheatstone Output, Quarter, Half, Full)
The output of a strain gauge Wheatstone bridge for a given strain, gauge factor and excitation, for quarter, half and full bridges, with the resistance change and the non-linearity of the quarter bridge.
Results
The dashed line marks the value you entered.
What this tool does
A strain gauge changes its resistance in proportion to strain: ΔR ÷ R = GF × ε, where the gauge factor GF is about 2 for metal foil. Placed in a Wheatstone bridge, one active gauge (quarter bridge) gives V_out ÷ V_ex = x ÷ (4 + 2x) with x = GF × ε; two gauges in bending (half bridge) give x ÷ 2 and four (full bridge) give x, with no non-linearity and with temperature effects cancelling. At 1000 µε a 350 Ω gauge changes by just 0.74 Ω and a quarter bridge gives about 2.6 mV on 5 V, so an amplifier is nearly always needed.
Formula
ΔR ÷ R = GF × ε · quarter bridge: V_out ÷ V_ex = x ÷ (4 + 2x) · half bridge: x ÷ 2 · full bridge: x (x = GF × ε)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
eps | Strain | µε |
gf | Gauge factor | — |
vex | Bridge excitation voltage | V |
cfg | Bridge arrangement | — |
rg | Gauge resistance | Ω |
VO | Bridge output voltage | mV |
SE | Output per volt of excitation | mV/V |
DR | Change in resistance of an active gauge | Ω |
NL | Deviation from the linear approximation | % |
Worked example
- Strain1000 µε
- Gauge factor2.1
- Bridge excitation voltage5 V
- Bridge arrangement1
- Gauge resistance350 Ω
- Bridge output voltage2.6222 mV
- Output per volt of excitation0.5244 mV/V
- Change in resistance of an active gauge0.7350 Ω
- Deviation from the linear approximation-0.105 %
Limitations
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.