How the strain gauge bridge calculator works
A strain gauge changes its resistance in proportion to the strain of the surface it is bonded to: ΔR / R = GF × ε, where GF is the gauge factor, close to 2 for metal foil gauges. The change is tiny. At 1000 microstrain a 350 Ω gauge changes by 0.7 Ω, which is why gauges are wired into a Wheatstone bridge: the bridge turns a small change of resistance into a voltage that starts from zero.
The calculator covers the three common arrangements with equal arm resistances:
- Quarter bridge. One active gauge and three fixed resistors. Output ratio GF·ε / 4, reduced slightly by the term 1 / (1 + GF·ε / 2).
- Half bridge. Two active gauges with equal and opposite strain, for example on the top and bottom face of a bending beam. Output ratio GF·ε / 2.
- Full bridge. Four active gauges, two in tension and two in compression. Output ratio GF·ε. This is the arrangement inside load cells and torque sensors.
Enter a strain to get the output, or type a measured output to get the strain. The inverse uses the exact equation, including the non-linear term of the quarter bridge.
A worked example
With GF = 2, 1000 µε and 5 V excitation:
| Arrangement | Output ratio | Output at 5 V |
|---|---|---|
| Quarter | 0.4995 mV/V | 2.4975 mV |
| Half | 1 mV/V | 5 mV |
| Full | 2 mV/V | 10 mV |
The full bridge at 1000 µε gives 2 mV/V, the rated output printed on many load cells: a load cell is a full bridge whose spring element reaches roughly that strain at rated load. The load cell output calculator continues from there with capacity, dead load and several cells in parallel.
Why the quarter bridge is not linear
In a quarter bridge only one arm changes, so the current through that arm changes with the strain. The output is 0.1 % low at 1000 µε and 0.5 % low at 5000 µε with a gauge factor of 2, and the error has the opposite sign in compression. Instruments for quarter-bridge work correct this in software. Half and full bridges with equal and opposite strains do not have the effect, because the changes in adjacent arms cancel it.
Excitation, current and self-heating
A higher excitation voltage gives a proportionally larger signal, but every gauge dissipates (Vex / 2)² / R. A 350 Ω bridge at 5 V carries 14.3 mA and each gauge dissipates 17.9 mW; at 10 V the power is four times that. The heat has to leave through the gauge backing into the part. On steel or aluminium that is rarely a problem; on plastics and thin sections it causes drift, and a lower excitation or a 1000 Ω gauge is the usual answer.
From bridge output to a number in a controller
The bridge output is a few millivolts at most, and one microstrain is a few microvolts or less. Whether an input can resolve it depends on its gain and resolution: the ADC resolution calculator converts converter bits and gain into the measured quantity per code.
What the calculation leaves out
- Lead wires. In a quarter bridge the leads are in series with the gauge and reduce the sensitivity; the three-wire connection removes the temperature effect of the leads but not the loss of sensitivity.
- Temperature. Apparent strain from the mismatch between gauge and material, and the change of gauge factor with temperature, are properties of the gauge and its installation.
- Gauge factor tolerance. Typically ±1 %, printed on the gauge package.
- Stress state. The stress shown is E × ε, valid for uniaxial stress. Biaxial stress needs a rosette and Poisson’s ratio.
Frequently asked questions
What is a microstrain?
Strain is a ratio of lengths and has no unit. One microstrain (µε) is a change of one millionth: 1000 µε is 0.1 %, or one millimetre per metre.
Which gauge factor should I enter?
The value on the gauge package. Metal foil gauges are near 2.0 to 2.2; semiconductor gauges are far higher and not linear, and the simple equations here describe them only approximately.
Why does my measured output differ from the calculation?
Check the excitation actually present at the bridge, the lead resistance in a quarter bridge, and whether the strain is really equal and opposite in the active gauges. A bridge that is not balanced at zero load adds an offset that the calculation does not include.