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Formulas & Mathematical Logic
Bridge output: Vout = Vin × (Rx / (R3 + Rx) - R2 / (R1 + R2)). This calculates the voltage difference between the two bridge midpoint nodes.
Balanced unknown resistance: Rx = R2 × R3 / R1. This is the Rx value that makes the bridge output approximately zero.
Bridge status: if the absolute output voltage is very close to zero, the calculator marks the bridge as balanced.
Balance error: Error = absolute value of Vout. This shows how far the bridge is from balance in volts.
Step-by-Step Example
Example values: Vin = 5 V, R1 = 1 kΩ, R2 = 2 kΩ, R3 = 1 kΩ, Rx = 2 kΩ.
Left divider ratio: R2 / (R1 + R2) = 2000 / (1000 + 2000) = 0.6667.
Right divider ratio: Rx / (R3 + Rx) = 2000 / (1000 + 2000) = 0.6667.
Vout = 5 × (0.6667 - 0.6667) = 0 V.
Balanced Rx = R2 × R3 / R1 = 2000 × 1000 / 1000 = 2000 Ω.
Practical meaning: when the bridge is balanced, the detector voltage becomes zero and Rx matches the ratio condition.
About This Calculator
Find bridge output voltage and the unknown resistor value for a Wheatstone bridge.
This CalcBoy calculator helps analyze balanced and unbalanced Wheatstone bridge circuits using R1, R2, R3, Rx and input voltage.
A Wheatstone bridge is one of the most useful resistor networks for measuring unknown resistance and detecting very small resistance changes. It uses two voltage divider branches connected across the same supply. The bridge output is measured between the middle nodes of the two dividers. When the ratios are equal, the output voltage becomes zero and the bridge is balanced.
Best UseUnknown resistance measurement, strain gauges, sensor bridges and precision resistor comparison.
Key OutputsBridge output voltage, balanced Rx value, bridge status and balance error.
Design BenefitQuickly compare resistor ratios and predict whether the bridge is balanced.
Practical ReminderReal circuits also depend on resistor tolerance, wiring resistance and detector input impedance.
This calculator is helpful for electronics students, sensor designers, instrumentation circuits and troubleshooting. Wheatstone bridges are commonly used with strain gauges, load cells, pressure sensors, thermistors and resistance transducers. A tiny resistance change can create a small differential output voltage, which is often amplified by an instrumentation amplifier.
Quick tip: use precision resistors and stable excitation voltage when measuring very small bridge output signals.
For practical bridge circuits, also consider temperature drift, self-heating, resistor matching, amplifier offset, input bias current, lead resistance and noise. The calculator gives the ideal bridge output and balance point, then real hardware should be verified with measurement and calibration.