Strain Gauge Calculator
Calculate strain, microstrain, resistance change, gauge factor and ideal bridge output for resistive strain gauge measurements.
SEN-001 focuses on strain-gauge sensing. Load-cell rated-capacity conversion, arbitrary bridge solving and full instrumentation amplifier design are handled by separate calculators.
Engineering tool
Strain Gauge Calculator
Calculate strain gauge resistance change, microstrain, gauge factor and quarter, half or full Wheatstone bridge output using one consistent bridge convention.
Calculation mode
Parameter panel
Negative strain is compression.
Result console
- Resistance Change
- 240 mΩ
- Final Resistance
- 120.24 Ω
- Normalized ΔR/R
- 0.002
- Resistance Change
- 0.2%
- Microstrain
- 1000µε
- Mechanical Status
- Tension
Negative strain is allowed and represents compression in this conventional positive-gauge-factor model.
Strain gauge formula audit
| Strain Definition | ε = ΔL/L, dimensionless. |
|---|---|
| Microstrain Conversion | µε = ε × 10^6; ε = µε × 10^-6. |
| Gauge Factor Definition | GF = (ΔR/R)/ε. |
| Resistance Change | ΔR = GF × ε × R. |
| Compression Convention | Negative strain is compression and produces negative ΔR for positive GF. |
| Adopted Wheatstone Topology | R1/R2 form the left divider, R3/R4 form the right divider. |
| Output Polarity | VOUT = Vright - Vleft = VEX[R4/(R3+R4) - R2/(R1+R2)]. |
| Quarter Mapping | R1 is active: R1 = R + ΔR; R2 = R3 = R4 = R. |
| Half Mapping | R1 = R + ΔR and R3 = R - ΔR for additive tension/compression reference. |
| Full Mapping | R1/R4 = R + ΔR and R2/R3 = R - ΔR for additive full-bridge reference. |
| Small-Signal Approximation | Bridge uses exact Wheatstone output plus a small-signal reference. |
| mV/V Definition | mV/V = (VOUT / VEX) × 1000. |
| Tolerance Model | V1 covers gain/sensitivity terms from GF and excitation tolerance, not complete bridge mismatch. |
| Temperature Boundary | Temperature apparent strain and compensation network design are not solved here. |
| Lead Resistance Boundary | Lead-wire resistance is noted, especially for quarter bridges, but a full 3-wire solver is outside SEN-001. |
Formula reference
Strain Gauge and Bridge Formulas
The calculator uses one fixed Wheatstone bridge convention so exact bridge output, small-signal approximation and polarity remain consistent.
ε = ΔL / Lµε = ε × 10^6GF = (ΔR / R) / εΔR = GF × ε × Rε = ΔR / (GF × R)VOUT = VEX[R4/(R3+R4) - R2/(R1+R2)]Quarter bridge: VOUT/VEX ≈ GFε/4Half bridge: VOUT/VEX ≈ GFε/2Full bridge: VOUT/VEX ≈ GFεmV/V = (VOUT / VEX) × 1000Variable definitions
- ε
- engineering strain, dimensionless
- µε
- microstrain
- GF
- gauge factor
- R
- nominal gauge resistance
- ΔR
- resistance change
- VEX
- bridge excitation voltage
Bridge Formula Audit
| Adopted topology | R1/R2 form the left divider; R3/R4 form the right divider. |
|---|---|
| Excitation polarity | VEX is applied across the top and bottom bridge rails. |
| Output polarity | VOUT = Vright - Vleft. |
| Exact bridge equation | VOUT = VEX[R4/(R3+R4) - R2/(R1+R2)]. |
| Quarter bridge | R1 = R + ΔR; R2 = R3 = R4 = R. |
| Half bridge | R1 = R + ΔR and R3 = R - ΔR; R2 = R4 = R. |
| Full bridge | R1 and R4 increase; R2 and R3 decrease by equal ΔR. |
| Small-signal quarter | VOUT/VEX ≈ GFε/4. |
| Small-signal half | VOUT/VEX ≈ GFε/2. |
| Small-signal full | VOUT/VEX ≈ GFε. |
| Bridge polarity boundary | Sign depends on gauge placement, mechanical orientation and output-node convention. |
| Exact / approximate boundary | Shortcut bridge equations are small-signal approximations, not exact arbitrary-strain formulas. |
Worked Examples
120 Ω, GF 2, 1000 µε
Known: ε = 0.001
ΔR = 0.24 Ω.
Final resistance
Known: R = 120 Ω, ΔR = 0.24 Ω
Rfinal = 120.24 Ω.
Normalized change
Known: GF = 2, ε = 0.001
ΔR/R = 0.002 = 0.2%.
350 Ω gauge
Known: GF = 2, strain = 500 µε
ΔR = 0.35 Ω.
Compression
Known: R = 120 Ω, GF = 2, strain = -1000 µε
ΔR = -0.24 Ω.
Resistance change to strain
Known: ΔR = 0.24 Ω, R = 120 Ω, GF = 2
ε = 0.001 = 1000 µε.
Solve gauge factor
Known: R = 120 Ω, ΔR = 0.24 Ω, strain = 1000 µε
GF = 2.
Quarter bridge approximation
Known: GF = 2, 1000 µε, VEX = 5 V
VOUT/VEX ≈ 0.0005 = 0.5 mV/V; VOUT ≈ 2.5 mV.
Quarter bridge exact
Known: Same values with R1 active
Exact output is close to, but not identical to, 2.5 mV.
Half bridge additive
Known: GF = 2, 1000 µε, VEX = 5 V
Small-signal output ≈ 1.0 mV/V = 5 mV.
Full bridge additive
Known: GF = 2, 1000 µε, VEX = 5 V
Small-signal output ≈ 2.0 mV/V = 10 mV.
Full / quarter ratio
Known: Small-signal comparison
Full bridge sensitivity is 4× quarter bridge.
Half / quarter ratio
Known: Small-signal comparison
Half bridge sensitivity is 2× quarter bridge.
Zero strain
Known: ε = 0
ΔR = 0 and ideal matched bridge output = 0.
Different gauge factor
Known: GF = 2.1, 1000 µε
ΔR/R = 0.0021.
One microstrain
Known: 1 µε
ε = 1e-6.
1000 microstrain
Known: 1000 µε
ε = 0.001 = 0.1%.
Resistance unit check
Known: 120 Ω = 0.12 kΩ
Same ΔR result after unit conversion.
Round trip
Known: Strain → ΔR → strain
Recovered strain matches the original input.
Large artificial strain
Known: Large ΔR/R
Exact bridge output visibly differs from small-signal approximation.
Engineering Notes
| Strain Gauge | A strain gauge changes resistance when mechanically strained. |
|---|---|
| Gauge Factor | Gauge factor should come from the actual sensor datasheet. |
| Microstrain | Microstrain is convenient because real mechanical strain is often very small. |
| Quarter Bridge | Quarter bridges are simple but sensitive to lead resistance and zero offset. |
| Half Bridge | Half bridges can improve sensitivity and compensation when gauges are arranged correctly. |
| Full Bridge | Full bridges can provide higher sensitivity and better compensation in the ideal model. |
| Excitation Voltage | Higher excitation increases output signal but can increase self-heating. |
| mV/V | Bridge sensors often specify sensitivity as millivolts of output per volt of excitation. |
| Temperature Effects | Temperature can create apparent strain, drift and resistance change. |
| Lead Resistance | Lead-wire resistance is especially important in quarter-bridge measurements. |
| Instrumentation Amplifier | Bridge outputs are often small enough to require low-noise differential amplification. |
| SEN-001 Boundary | Load-cell rated capacity conversion is reserved for SEN-002; generic bridge solving is reserved for SEN-003. |
Common Mistakes
- Treating 1000 µε as 1000 strain instead of 0.001 strain.
- Reversing the gauge factor equation.
- Forgetting the nominal resistance term in ΔR = GF × ε × R.
- Rejecting negative strain even though compression is a valid sign convention.
- Calling GFε/4 an exact quarter-bridge equation.
- Using half-bridge or full-bridge shortcut equations without defining gauge placement.
- Forgetting that bridge output polarity depends on node convention.
- Confusing mV/V with mV.
- Ignoring excitation voltage.
- Assuming full bridge is always exactly four times quarter bridge under large nonlinear strain.
- Ignoring lead-wire resistance in quarter bridge measurements.
- Ignoring temperature apparent strain.
- Assuming higher excitation voltage is always better.
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FAQ
What is a strain gauge?
A strain gauge is a resistive sensor that changes resistance when mechanically strained.
What is gauge factor?
Gauge factor relates normalized resistance change to strain: GF = (ΔR/R) / ε.
How do I calculate strain from resistance change?
Use ε = ΔR / (GF × R), where R is nominal gauge resistance and GF is gauge factor.
How do I calculate resistance change from strain?
Use ΔR = GF × ε × R.
What is microstrain?
Microstrain is strain multiplied by one million. One microstrain equals 10^-6 strain.
How many microstrain are in 0.1% strain?
0.1% strain equals 0.001 strain, or 1000 microstrain.
What is a quarter-bridge strain gauge circuit?
In this calculator, a quarter bridge uses one active gauge in R1 and three nominally equal fixed resistors.
What is a half-bridge strain gauge circuit?
This calculator uses two active gauges arranged so tension and compression effects add in the bridge output.
What is a full-bridge strain gauge circuit?
A full bridge uses four active gauges arranged for higher sensitivity and better compensation in the ideal model.
How do I calculate Wheatstone bridge output from strain?
First calculate ΔR from strain and gauge factor, then solve the exact bridge divider voltages and subtract the output nodes.
What does mV/V mean for a bridge sensor?
mV/V is bridge output divided by excitation voltage, multiplied by 1000.
Why is bridge output so small?
Strain-gauge resistance changes are usually tiny, so bridge output is commonly in millivolts and often requires an instrumentation amplifier.
How does temperature affect a strain gauge?
Temperature can change gauge resistance, create apparent strain, cause thermal expansion and shift bridge offset.
How does lead-wire resistance affect measurement?
Lead resistance is especially important in quarter-bridge circuits because it can create zero offset and sensitivity error.
Why can increasing excitation voltage cause self-heating?
Higher excitation increases signal, but it also increases bridge power and can heat the gauge.
What is the difference between a strain gauge and a load cell?
A strain gauge measures strain or resistance change. A load cell is a mechanical sensor assembly that usually uses gauges and is calibrated in force or weight.
Engineering Disclaimer
This calculator provides ideal strain-gauge and bridge arithmetic. Critical strain measurements require mechanical design review, temperature compensation, lead-wire compensation, calibration, appropriate excitation limits, instrumentation amplifier design and measurement validation.