Wheatstone Bridge
Use this calculator to find the bridge output voltage (Vg) for any four-resistor Wheatstone bridge, check whether the bridge is balanced, and solve for an unknown resistor. Enter the input voltage and the four arm resistances (R1, R2, R3, Rx) below to get instant results.
What Is a Wheatstone Bridge?
A Wheatstone bridge is a circuit used to measure an unknown resistance by comparing it against three known resistances. Samuel Hunter Christie described the circuit in 1833; Charles Wheatstone extended and popularized it in 1843, and the name stuck.
The circuit is built from two voltage dividers wired in parallel across the same supply, with a galvanometer or voltmeter connected between their midpoints. Instead of measuring resistance directly, the bridge measures the voltage difference between the two dividers — a value that hits zero exactly when the resistance ratios on both sides match.
| Component | Role in the Circuit |
|---|---|
| Vin (excitation voltage) | Voltage source driving both divider legs |
| R1, R2 | Left-hand voltage divider (often fixed/reference resistors) |
| R3, Rx | Right-hand voltage divider (Rx is typically the unknown or sensing element) |
| Vg (galvanometer/output) | Measures the voltage difference between the two divider midpoints |
Wheatstone Bridge Formula
The output voltage is the difference between the potentials at the midpoints of the two divider legs:
Vg = Vin × [ (Rx / (R3 + Rx)) − (R2 / (R1 + R2)) ]
| Symbol | Meaning | Unit |
|---|---|---|
| Vin | Excitation (input) voltage | Volts (V) |
| R1 | Known resistor, left arm (top) | Ohms (Ω) |
| R2 | Known resistor, left arm (bottom) | Ohms (Ω) |
| R3 | Known resistor, right arm (top) | Ohms (Ω) |
| Rx | Unknown or variable resistor, right arm (bottom) | Ohms (Ω) |
| Vg | Bridge output (galvanometer) voltage | Volts (V) |
Balanced Condition
A bridge is balanced when Vg = 0 — the two divider legs produce identical output potentials, so no current flows through the galvanometer branch. This happens when the resistance ratios on each side are equal:
R1 / R2 = R3 / Rx → Rx = (R2 / R1) × R3
The balance point doesn't depend on Vin, which is what makes the method so accurate: supply voltage drift or noise doesn't shift the balance condition, only how far the needle swings off it.
| Condition | Vg | What it means |
|---|---|---|
| R1/R2 = R3/Rx | 0 V | Bridge balanced — ratios match on both arms |
| R1/R2 > R3/Rx | Negative | Rx is larger than the balance point requires |
| R1/R2 < R3/Rx | Positive | Rx is smaller than the balance point requires |
How to Use This Calculator
- Enter the excitation voltage (Vin) — the DC voltage feeding the bridge.
- Enter R1 and R2, the known resistors forming the reference arm.
- Enter R3 and the unknown or sensing resistor Rx.
- Read Vg and the balance state directly below the diagram — no manual algebra needed.
- To solve for an unknown resistance instead, adjust Rx until Vg reads 0.0000 V; at that point Rx = (R2/R1) × R3.
Wheatstone Bridge Configurations
Sensor designs rarely use just one variable resistor. How many arms respond to the measured quantity determines sensitivity and how much of the temperature effect cancels out.
| Configuration | Active Arms | Relative Sensitivity | Typical Use |
|---|---|---|---|
| Quarter bridge | 1 (Rx only) | 1× (baseline) | Single strain gauge, general-purpose sensing |
| Half bridge | 2 (opposite or adjacent arms) | 2× | Bending strain measurement, some temperature compensation |
| Full bridge | 4 (all arms active) | 4× | Load cells, precision strain/force sensors, best temperature compensation |
Practical Applications
| Application | How the Bridge Is Used | Typical Resistance Change |
|---|---|---|
| Strain gauges | Gauge resistance shifts as it stretches or compresses with the structure it's bonded to | ~0.1–2% |
| Load cells | Multiple strain gauges in a full-bridge arrangement convert applied force into a proportional voltage | ~0.1–2% |
| Pressure sensors | A diaphragm-mounted bridge converts mechanical deflection into an electrical signal | Varies with diaphragm design |
| RTDs and thermistors | Bridge linearizes and amplifies small resistance changes caused by temperature | ~0.1–0.4% per °C (RTD) |
| Precision resistance measurement | Bridge nulled by adjusting a known resistor until Vg = 0, giving Rx directly from the ratio | N/A (null method) |
Wheatstone Bridge vs. Other Measurement Methods
| Method | Sensitivity to Small ΔR | Immune to Supply Noise? | Typical Accuracy |
|---|---|---|---|
| Wheatstone bridge | High | Yes, at balance | High (0.01–0.1% with matched resistors) |
| Simple voltage divider | Low | No | Moderate |
| Direct ohmmeter reading | Low for small changes | No | Moderate |
| Kelvin (double) bridge | High, for very low resistances | Yes, at balance | Very high, specialized for < 1 Ω |
Sources of Error
| Error Source | Effect | Mitigation |
|---|---|---|
| Resistor tolerance | Offsets the balance point | Use matched, low-tolerance resistors |
| Lead wire resistance | Adds unwanted resistance to the Rx arm | Use 3-wire or 4-wire (Kelvin) connections |
| Self-heating | Resistors drift as current flows through them | Keep excitation current low; use appropriate resistor power rating |
| Temperature drift | All arms shift with ambient temperature | Use half- or full-bridge configurations for compensation |
Video: How the Wheatstone Bridge Works
For a worked walkthrough of solving a bridge circuit in both the balanced and unbalanced case, see How To Solve The Wheatstone Bridge Circuit on YouTube.
FAQ
What is a balanced bridge?
A balanced bridge is the state where the output voltage between the two legs is exactly zero — the resistance ratio on one side matches the ratio on the other. Because this null point doesn't shift with source voltage fluctuations, it's an inherently accurate way to measure resistance.
Why use a bridge instead of a simple voltage divider?
A single voltage divider is sensitive to source noise and carries a non-zero offset. A Wheatstone bridge measures a difference between two dividers, which cancels common-mode noise and lets you detect very small changes (down to a fraction of a percent) around a zero point — sensitivity a plain divider can't match.
How does temperature affect the bridge?
If the arm resistors change value with temperature, the balance point drifts. Sensor designs often turn this into an advantage: placing a matched "dummy" gauge in the adjacent arm cancels out the shared thermal effect, since both resistors drift together.
Can the bridge measure very low resistances?
Standard Wheatstone bridges lose accuracy below about 1 Ω because lead and contact resistance become significant compared to Rx. A Kelvin (double) bridge, which separates current and voltage connections, is the standard choice for low-resistance measurement instead.
What resistor values give the best sensitivity?
Sensitivity is generally highest when all four arms are close to the same value and matched to Rx's expected range. Very unequal ratios (e.g., R1 >> R2) reduce how much Vg moves per unit change in Rx.
Does the bridge work with AC excitation?
Yes — AC-excited bridges (sometimes called impedance bridges when reactive components are involved) are common for measuring capacitance and inductance using the same balance principle, with a detector tuned to the excitation frequency instead of a DC galvanometer.