Calculate unknown resistance using Rx = R3(R2/R1). Find bridge voltage, sensitivity, Thevenin equivalent, and explore balance conditions with visual diagram.
The **Wheatstone Bridge Calculator** solves the classic Wheatstone bridge equation Rx = R3(R2/R1) for precision resistance measurement. Invented by Samuel Hunter Christie in 1833 and popularized by Sir Charles Wheatstone, this circuit remains the gold standard for measuring resistance with extraordinary precision — routinely achieving 0.01% accuracy.
The bridge works by comparing an unknown resistance against known standards. When the bridge is balanced (galvanometer reads zero), the unknown resistance is determined solely by the ratios of the known resistors, independent of source voltage. For unbalanced operation, the bridge voltage provides a highly sensitive measure of small resistance changes — the principle behind strain gauges, RTDs, and many other sensors.
This calculator supports solving for any of the four resistors, provides bridge voltage, sensitivity analysis, Thevenin equivalent, a visual bridge diagram, and a comprehensive balance exploration table. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
The Wheatstone bridge is the foundation of precision resistance measurement, strain gauge instrumentation, temperature sensing, and countless industrial measurement systems. Keep these notes focused on your current workflow. Tie the context to real calculations your team runs. Use this clarification to avoid ambiguous interpretation. Align the note with how outputs are reviewed. Apply this only where interpretation varies by use case.
At balance: Rx = R3 × (R2 / R1) Bridge voltage: Vg = Vs × [R3/(R1+R3) − Rx/(R2+Rx)] Thevenin resistance: Rth = R1∥R3 + R2∥Rx Balanced when: R1/R3 = R2/Rx (Kirchhoff)
Result: Rx = 1000 Ω, Vg = 0 mV (balanced)
Rx = 1000 × (1000/1000) = 1000 Ω. With all four resistors equal, the bridge is perfectly balanced: Va = Vb = 2.5V, so Vg = 0. If Rx changes to 1001 Ω (0.1% change), Vg shifts to -1.25 mV — easily measurable, demonstrating the bridge extreme sensitivity.
The Wheatstone bridge was first described by Samuel Hunter Christie in 1833, but Sir Charles Wheatstone popularized it in 1843. The circuit applies Kirchoff's laws: at balance, no current flows through the galvanometer because the voltage divider ratios are equal on both sides. This null-detection method achieves precision limited only by the reference resistors.
The elegant mathematical result Rx = R3(R2/R1) means the measurement depends only on ratios. If R1 and R2 are the same value (ratio = 1), then Rx = R3. A decade resistance box for R3 then directly reads the unknown resistance. Modern bridges use programmable reference resistors with 7+ digits of precision.
**Strain Gauge Instrumentation:** Virtually all electronic scales, load cells, pressure transducers, torque sensors, and accelerometers use Wheatstone bridges with bonded resistance strain gauges. A commercial 350Ω load cell bridge with 5V excitation produces 2 mV/V at full scale (10 mV at 5V). With a 24-bit ADC, this resolves 1 part in 10 million of full scale.
**Temperature Measurement:** Resistance Temperature Detectors (RTDs) — especially Pt100 and Pt1000 platinum elements — are measured with Wheatstone bridges in industrial process control. A Pt100 changes by 0.385 Ω/°C, so a bridge with 0.01Ω resolution achieves ±0.025°C accuracy. Nuclear power plants, pharmaceutical manufacturing, and semiconductor fabs rely on bridge-based RTD measurements.
Beyond the basic four-resistor Wheatstone bridge, specialized variants exist: the Kelvin double bridge for very low resistances (<1Ω), the Wien bridge for frequency measurement, the Maxwell bridge for inductance, and the Schering bridge for capacitance. AC bridges using phase-sensitive detection achieve even better precision and can measure complex impedances at specific frequencies.
An ohmmeter measures V and I, then computes R = V/I — any error in V or I directly affects the result. A balanced Wheatstone bridge depends only on the ratio of known resistors, not on the source voltage or galvanometer sensitivity. Ratio measurements are inherently more precise than absolute measurements.
Sensitivity is the change in bridge voltage per unit change in Rx: dVg/dRx. Maximum sensitivity occurs when all four resistors are equal. Higher source voltage increases sensitivity linearly. Sensitivity is measured in mV per % change in Rx — typical values are 1-25 mV/% for a 5V bridge.
A strain gauge (typically 120Ω or 350Ω) changes resistance by ~0.1% under full-load strain. In a bridge circuit with 5V excitation, this produces ~2.5 mV output. Precision amplifiers and 24-bit ADCs then convert this tiny voltage to a strain measurement with 0.001% resolution.
Quarter bridge: 1 active strain gauge + 3 fixed resistors. Half bridge: 2 active gauges (doubles sensitivity, cancels temperature drift). Full bridge: 4 active gauges (quadruples sensitivity, best temperature compensation). Load cells use full bridges.
Pt100 RTDs (100Ω at 0°C, 138.5Ω at 100°C) are measured in a bridge circuit where the increasing resistance unbalances the bridge. Three-wire and four-wire configurations eliminate lead resistance errors. Modern RTD bridges achieve ±0.01°C accuracy.
Precision of reference resistors (0.01% available commercially), thermoelectric voltages at junctions (use copper-to-copper connections), self-heating of resistors (keep bridge current low), lead resistance (use 4-wire technique), and noise (use shielded cables and lock-in amplifiers).