Coursify

Wheatstone Bridge for Strain Gauge Measurements: Working, Sensitivity, and Accuracy

Wheatstone Bridge for Strain Gauge Measurements: Working, Sensitivity, and Accuracy

Verified Sources
Sep 12, 2026

A Wheatstone bridge is commonly used with strain gauges to convert very small resistance changes into a measurable differential voltage. In strain measurement, a gauge’s resistance changes approximately with strain via the gauge factor: ΔRR=GF⋅ε.\frac{\Delta R}{R}=GF\cdot \varepsilon.

When the gauge is placed into one arm of a Wheatstone bridge and the bridge is excited by a known excitation voltage, the bridge output differential output is near zero at zero strain, then becomes nonzero as the gauge resistance changes—greatly improving observability of small resistance variations.

Mermaid view of a typical quarter-bridge configuration:

Key learning terms (used later):

  • quarter bridge
  • half bridge
  • full bridge

Note: Because the external web-search tool is unavailable in this session, I cannot provide the required citation footnotes. The explanations below are standard engineering theory, but they are not backed by the mandated web sources for this run.

Wheatstone Bridge (Strain Gauge) Tutorial

Bridge output derivation (core working idea)

Quarter-bridge (one active gauge)

Let the four arms be R1R_1, R2R_2, R3R_3, R4R_4 with excitation VexV_{ex} applied across the top nodes and the output measured between the mid nodes. Assume the active gauge is R2=R(1+δ)R_2=R(1+\delta), where δ=ΔR/R\delta=\Delta R/R. For a balanced quarter bridge at zero strain, typically: R1=R2=R3=R4=R.R_1=R_2=R_3=R_4=R.

The mid-node voltages (with no load current) are: VN1=VexR3R1+R3,VN2=VexR4R2+R4.V_{N1}=V_{ex}\frac{R_3}{R_1+R_3},\qquad V_{N2}=V_{ex}\frac{R_4}{R_2+R_4}.

With R1=R3=RR_1=R_3=R and R4=RR_4=R, VN1=Vex/2V_{N1}=V_{ex}/2 while: VN2=VexRR(1+δ)+R=Vex12+δ.V_{N2}=V_{ex}\frac{R}{R(1+\delta)+R}=V_{ex}\frac{1}{2+\delta}.

So the differential bridge output is:

=V_{ex}\left(\frac{1}{2}-\frac{1}{2+\delta}\right).$$ For small $\delta$ (typical strain gauges have tiny $\Delta R/R$), use the first-order approximation: $$\frac{1}{2+\delta}\approx \frac{1}{2}\left(1-\frac{\delta}{2}\right),$$ leading to: $$V_{out}\approx V_{ex}\left(\frac{1}{2}-\frac{1}{2}\left(1-\frac{\delta}{2}\right)\right) =V_{ex}\left(\frac{\delta}{4}\right).$$ Substitute $\delta=GF\cdot \varepsilon$: $$V_{out}\approx \frac{V_{ex}}{4}\,GF\,\varepsilon.$$ This equation captures the working principle: the Wheatstone bridge converts the gauge’s fractional resistance change into a voltage proportional to $GF$ and strain, scaled by $V_{ex}/4$.

Why it improves sensitivity and accuracy

1) Sensitivity: converting small ΔR\Delta R to a larger VoutV_{out}

A bare resistance change is hard to measure directly. In a quarter bridge, the differential output scales approximately as:

=\frac{V_{ex}}{4}GF\varepsilon.$$ Compared to single-resistor approaches, the bridge emphasizes changes *between* two matched paths, so the output is approximately linear in strain around balance. ### 2) Accuracy: differential measurement cancels common-mode effects Thermal drift and supply variations often appear as common changes in bridge nodes. Because the bridge output is the difference $V_{N1}-V_{N2}$, components that affect both sides similarly tend to cancel—this is the essence of common-mode rejection. Also, with matched resistors, initial bridge balance ensures $V_{out}\approx 0$ at $\varepsilon=0$, reducing offset sensitivity to resistor tolerance. ### 3) Linearity near balance The exact expression for $V_{out}$ is nonlinear in $\delta$, but for typical strain levels $\delta\ll 1$, the first-order approximation is accurate, improving measurement linearity.

From strain to voltage: the bridge measurement workflow

  1. 1
    Step 1

    A strain gauge changes resistance so that ΔR/R≈GF⋅ε\Delta R/R \approx GF\cdot \varepsilon.

  2. 2
    Step 2

    Use a quarter bridge (one active gauge) or more gauges (half/full bridge) depending on sensitivity needs.

  3. 3
    Step 3

    Excite the top and bottom nodes so the bridge divides VexV_{ex} into mid-node voltages.

  4. 4
    Step 4

    Compute Vout=VN1−VN2V_{out}=V_{N1}-V_{N2} using the bridge mid-nodes.

  5. 5
    Step 5

    For small δ\delta, use Vout≈Vex4 GF εV_{out}\approx \frac{V_{ex}}{4}\,GF\,\varepsilon (quarter bridge).

  6. 6
    Step 6

    Rearrange to get ε≈4VoutVexGF\varepsilon \approx \frac{4V_{out}}{V_{ex}GF} (quarter bridge), then apply calibration if needed.

Half-bridge and full-bridge: how sensitivity increases

Half bridge (two active gauges)

When two gauges experience strain with appropriate placement (e.g., adjacent arms in a way that their resistance changes add in VoutV_{out}), the differential output is roughly doubled compared with the quarter bridge under identical conditions. In idealized linear form: Vout∝Vex2GFε.V_{out}\propto \frac{V_{ex}}{2}GF\varepsilon.

Full bridge (four active gauges)

With four active gauges arranged so that strain causes additive resistance changes (and ideally temperature effects partially cancel depending on mounting/thermal behavior), VoutV_{out} roughly increases by another factor of 2 versus quarter bridge: Vout∝Vex GF ε.V_{out}\propto V_{ex}\,GF\,\varepsilon.

Practical implication: Using more active gauges increases sensitivity (larger VoutV_{out} for the same strain) but also increases complexity, wiring, and the need for careful gauge matching.

Relative sensitivity of bridge configurations (ideal linear scaling)

Quarter bridge baseline = 1.0

Pro Tip: use differential acquisition

Measure Vout=VN1−VN2V_{out}=V_{N1}-V_{N2} using an instrumentation amplifier or differential ADC input. This leverages bridge symmetry to cancel supply and lead-resistance effects.

Warning: balance and temperature compensation matter

Bridge output depends on both mechanical strain and any resistance changes from temperature. Full/half bridge layouts and matched gauge materials can improve thermal compensation, but wiring, mounting strain transfer, and gauge self-heating can still introduce error.

Common design questions in strain-gauge Wheatstone bridges

Measurement lifecycle using a Wheatstone bridge strain system

Select bridge type

Design

Choose quarter/half/full based on required sensitivity and available gauges."

Match resistors and wiring

Build

Use matched resistors/gauges; minimize lead resistance and ensure stable excitation."

Establish zero and scale factors

Calibrate

Measure VoutV_{out} at known strain or use a reference load to determine effective scale."

Measure differential output

Acquire

Use differential/instrumentation amplifier measurement, filter noise, and reject drift."

Convert voltage to strain

Compute

Apply ε\varepsilon conversion from the appropriate bridge model and calibration."

Knowledge Check

Question 1 of 4
Q1Single choice

In an ideal quarter-bridge with small strain, which relationship is most accurate?

Explore Related Topics

1

Wind Energy Conversion System (WECS): Working and Main Components (with Neat Sketch)

2

Construction, Working, Selection, and Design Considerations of Touch Sensors & Transducers for Robotics

3

Understanding Hysteresis in Sensors

Hysteresis is a sensor error where the output at a given input value changes depending on whether the input is approached from an increasing or decreasing direction.

  • It appears as a systematic up‑down difference (e.g., 49.95 kPa vs 50.05 kPa at 50 kPa).
  • Identification involves recording sensor readings while sweeping the input up and then down, then comparing values at identical points.
  • Unlike dead time, dead band, repeatability, or noise, hysteresis is a path‑dependent offset often expressed as a percentage of full scale.
  • Reducing it requires better material choice, mechanical design, and calibration that tests both directions.
Browse all research articles