Wheatstone Bridge Calculator

Calculate unknown resistance and bridge balance conditions using the Wheatstone bridge.

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How a Wheatstone Bridge Converts Resistance Change into Voltage

A Wheatstone bridge compares two voltage-divider ratios rather than measuring one resistance directly. Four resistive arms form two divider branches across the same supply. At balance, the two midpoint voltages are equal, so the detector sees zero output. With the labeling used here, balance requires R1/R2=R3/Rx, giving Rx=R2R3/R1.

The null method is powerful because the unknown is inferred from a ratio at zero detector difference, reducing dependence on detector calibration. In sensor applications the bridge is intentionally allowed to become slightly unbalanced. A small resistance change then produces a small differential voltage that can be amplified with an instrumentation amplifier.

Rx = R2R3/R1,   Vout = Vs[R3/(R1+R3) − R4/(R2+R4)]
SymbolMeaningWhy it appears / units
R1–R4Bridge resistancesΩ; their ratios determine balance and output.
RxUnknown resistanceΩ; found from the balance ratio.
VsExcitation voltageV; sets the scale of the bridge output.
VoutDifferential midpoint voltageV; sign depends on which midpoint is subtracted from which.

For very small fractional changes in a symmetric quarter bridge, the output magnitude is approximately Vs(ΔR/R)/4. That approximation is useful for intuition but is not the exact formula for large resistance changes. Bridge wiring also matters: quarter-, half-, and full-bridge sensor arrangements have different sensitivities and different compensation for temperature and lead resistance.

Worked Examples

Example 1: Balance: R₁=R₂=R₃=1000Ω
R_x=1000×1000/1000
Result: R_x=1000Ω at balance
Null detector shows zero — R_x found
Example 2: Strain gauge: R1=R2=1000Ω, R3=1000Ω, R4=1010Ω (1% resistance change)
V_out = Vs/4 × ΔR/R
Result: 12.5mV at Vs=5V
A mechanical strain value requires the gauge factor through ΔR/R = GF·ε
Example 3: Unknown resistance at balance
R1=120Ω, R2=330Ω, R3=220Ω → Rx=330×220/120
Result: Rx=605Ω
At this resistance, both divider midpoints have the same potential and the ideal bridge output is zero.
Example 4: Small unbalance from a sensor
R1=R2=R3=1000Ω, R4=1005Ω, Vs=5V
Result: Vout≈−6.23 mV
The sign depends on the chosen output polarity. The magnitude is close to the quarter-bridge approximation 5/4×0.005=6.25mV.

Common Mistakes

⚠️
Using the wrong resistor ratio for the chosen labeling

Bridge equations depend on which resistor occupies each arm. Sketch the two divider branches before rearranging the balance relation.

⚠️
Ignoring output-voltage polarity

Swapping the midpoint subtraction changes the sign of Vout but not the physical amount of unbalance. Define the polarity before interpreting a sensor direction.

⚠️
Using the small-change approximation for large ΔR

VsΔR/(4R) is a first-order approximation near balance. Use the exact divider equations when the resistance change is not small.

Frequently Asked Questions

Wheatstone bridge applications?
Strain gauges (load cells, pressure sensors), temperature measurement (RTD in bridge), biosensors, precision resistance measurement. The bridge amplifies small resistance changes to measurable voltages.
Why 4-arm bridge vs simple voltage divider?
Bridge rejects common-mode errors (temperature drift, lead resistance). Both arms of each half-bridge see same temperature — changes cancel. Only differential resistance change (the measurement) produces output.
Why is the output zero when a Wheatstone bridge is balanced?
Each side of the bridge is a voltage divider. At balance, the two divider ratios produce identical midpoint voltages. A detector connected between those midpoints therefore sees no potential difference even though current can still flow through the two divider branches.
Why are Wheatstone bridges useful for strain gauges?
Strain gauges often change resistance by only a small fraction. A bridge converts that small fractional resistance change into a differential voltage centered near zero, which is convenient for precision amplification. Half- and full-bridge arrangements can also increase sensitivity and improve temperature compensation.
Does supply voltage affect the resistance found at balance?
For an ideal bridge made of linear resistors and a perfect null detector, the resistance ratio at balance does not depend on supply voltage. In a real circuit, excessive excitation can cause self-heating, changing resistor or sensor values and introducing measurement error.
What is the difference between a quarter, half, and full bridge?
The names describe how many bridge arms contain active sensing elements. A quarter bridge uses one active element, a half bridge typically uses two, and a full bridge uses four. More active arms can increase sensitivity and provide better cancellation of temperature or unwanted mechanical effects.

Formula Explorer connections

Interpretation: This formula tracks heat, temperature, work, entropy or transport in a thermodynamic system. Assumption: Use absolute temperature where required and consistent energy units. Constant properties, equilibrium, ideal gases or negligible losses may be assumed.

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