Wheatstone Bridge Balance Calculator

A Wheatstone bridge is a circuit of four resistors arranged in a diamond shape, used to precisely measure an unknown resistance or detect small resistance changes by comparing the voltage at two midpoints of the bridge. It was invented to measure unknown resistances with high precision using only a null (zero) detector.

A Wheatstone bridge is balanced, meaning its output voltage Vg is exactly zero, when R1 x R4 = R2 x R3 (equivalently R1/R2 = R3/R4). At this point the bridge output does not depend on the excitation voltage at all, only on the resistor ratios.

With three known resistors R1, R2, R3 and an adjustable or known fourth resistor position Rx, adjust Rx until the bridge output reads zero (balanced), then Rx = R2 x R3 / R1. This calculator's Find Balance Resistor mode computes that value directly.

Vg = Vex x [R2/(R1+R2) - R4/(R3+R4)], where Vex is the excitation voltage applied across the bridge. This measures the voltage difference between the two midpoints of the bridge's two resistor-divider arms.

At balance, R1 x R4 = R2 x R3, which algebraically makes R2/(R1+R2) exactly equal to R4/(R3+R4), so the two divider midpoint voltages are identical and their difference Vg is zero, regardless of the actual excitation voltage used.

In strain gauge, pressure, and temperature sensors, one or more bridge arms use a resistive element whose value changes with the measured quantity. The resulting small unbalance voltage Vg is amplified and calibrated to read out the measured physical quantity directly.

Strain gauge bridges typically produce outputs in the millivolt range (often just a few millivolts per volt of excitation, expressed as mV/V) for typical strain levels, which is why these signals almost always need a precision instrumentation amplifier before further processing.

The sign and magnitude of Vg depend on which arm the varying resistor sits in and the direction of its resistance change, but the balance condition R1R4 = R2R3 and the underlying sensitivity principle apply regardless of which specific arm is the sensing element.

All resistors (R1 through R4 and Rx) are in ohms. The excitation voltage and resulting bridge output voltage Vg are in volts.

A bridge measurement can be far more precise than a typical ohmmeter, especially for detecting very small resistance changes, because it compares the unknown against known references rather than relying on an absolute current-and-voltage measurement, and at balance the result depends only on resistor ratios, not on the excitation source's exact voltage.