Last updated: 2026-07-13

Wheatstone bridge

A Wheatstone bridge measures an unknown resistance by comparison rather than by reading it directly. Four resistive arms are wired as two voltage dividers fed from the same source, and a detector links the midpoints of the two dividers. When the left and right dividers have the same ratio, both midpoints sit at the same potential and the detector reads zero. That balanced state fixes the unknown arm through a ratio, which is far easier to hit precisely than an absolute reading.

This calculator works two ways: give it the three known arms and it returns the unknown resistance $R_x$ that balances the bridge, or switch to the output mode, add the source voltage and the fourth arm, and it returns the detector voltage of an unbalanced bridge.

The balance condition

Label the arms so that $R_1$ and $R_2$ form the left divider and $R_3$ and $R_x$ form the right divider. Each divider's midpoint sits at a voltage set by its own ratio:

The detector reads zero when these are equal. Setting them equal and cancelling the source voltage leaves a pure ratio condition:

Because only ratios matter, the result does not depend on the exact source voltage or on how sensitive the detector is — a defining strength of the method.

Worked example

With $R_1 = 100\ \Omega$, $R_2 = 200\ \Omega$ and $R_3 = 150\ \Omega$:

A $300\ \Omega$ resistor in the fourth arm brings the bridge to balance, so the detector reads zero.

The unbalanced bridge and sensitivity

Away from balance the detector no longer reads zero; it sees the difference between the two divider taps:

For a small change in one arm around the balance point, this output rises almost in proportion to that change. That near-linear response is the reason the bridge is used as a sensor front end: a strain gauge, thermistor, or pressure element sits in one arm, and its tiny resistance change appears as a proportional voltage the rest of the circuit can amplify and read.

The sign of $V_g$ tells you which way the bridge has tipped, and its size tells you how far.

Where the bridge is used

Historically the Wheatstone bridge was the standard laboratory instrument for precise resistance measurement, using a calibrated known arm adjusted until the detector nulled. Today its most common role is signal conditioning for resistive sensors. Load cells built from strain gauges, resistance-thermometer and thermistor probes, and many pressure and force transducers all read out as a small bridge imbalance. Placing two or four active elements in the arms cancels temperature drift and multiplies sensitivity, which keeps the topology in wide use in instrumentation.

Limitations

This is an ideal-resistor model. It assumes the source is ideal, the detector draws no current, and the arms are purely resistive with no lead resistance or contact resistance of their own. Real bridges are affected by finite detector loading, by the resistance of connecting leads (significant for low-value arms, and the reason four-wire methods exist), by resistor tolerance and temperature coefficients, and by thermoelectric voltages at junctions. For demanding work these effects are managed with guarded leads, matched arms, and calibrated components.