Wheatstone Bridge Calculator – Measure Unknown Resistance
Calculate unknown resistance using the balanced Wheatstone bridge circuit with high precision.
Enter known resistance values (R1, R2, R3), the bridge output voltage ratio, and supply voltage to solve for the unknown resistance Rx.
Wheatstone Bridge Calculator – Measure Unknown Resistance
Calculate unknown resistance using the balanced Wheatstone bridge circuit with high precision.
Wheatstone Bridge Examples
Click any example to load it into the calculator.
| Circuit Setup | Unknown Rx (Ω) | Notes |
|---|---|---|
| R1=1000Ω, R2=1000Ω, R3=500Ω, Vout=0V, Vs=5V | Rx = 500 Ω | Perfectly balanced bridge. R1/R2 = R3/Rx gives Rx = R2·R3/R1 = 500 Ω. |
| R1=1000Ω, R2=1000Ω, R3=750Ω, Vout=0.25V, Vs=10V | Rx ≈ 830 Ω | Unbalanced bridge. The output voltage indicates a resistance deviation from balance. |
| R1=120Ω, R2=120Ω, R3=120Ω, Vout=0.05V, Vs=5V | Rx ≈ 124.9 Ω | Typical strain gauge setup. A small voltage offset indicates a resistance change of about 4.9 Ω from the nominal 120 Ω. |
| R1=10000Ω, R2=10000Ω, R3=100Ω, Vout=0.01V, Vs=3.3V | Rx ≈ 131 Ω | High-ratio bridge for measuring small resistances. Tiny Vout offset from near-balance shifts Rx from the 100 Ω baseline. |
About the Wheatstone Bridge Calculator
The Wheatstone bridge is one of the most elegant and precise methods for measuring electrical resistance. Invented by Samuel Hunter Christie in 1833 and popularised by Sir Charles Wheatstone in 1843, the bridge circuit remains a cornerstone of electrical measurement and sensor technology more than 180 years later.
The classic Wheatstone bridge consists of four resistors arranged in a diamond (rhombus) configuration, with a voltage source connected across one pair of opposite nodes and a galvanometer (or differential voltmeter) connected across the other pair. When the bridge is balanced — meaning the ratio of resistances in one arm equals the ratio in the other arm — no current flows through the galvanometer. This null condition is exploited to determine an unknown resistance with extraordinary accuracy.
The balance condition is expressed as R1/R2 = R3/Rx, which rearranges to Rx = R2·R3/R1. This formula is exact and requires no calibration; accuracy depends only on how accurately R1, R2, and R3 are known. Precision laboratory bridges can measure resistance to better than one part per million.
When the bridge is not at balance — as is often the case in sensor applications where a small resistance change must be detected — the output voltage Vout is related to the supply voltage Vs by: Vout = Vs·(Rx/(R2+Rx) − R3/(R1+R3)). This calculator uses that formula in reverse: given the measured output voltage, it solves for Rx.
The Wheatstone bridge is indispensable in strain gauge applications. A strain gauge is a resistive element whose resistance changes proportionally to mechanical strain. By bonding strain gauges to a structural member and connecting them in a Wheatstone bridge, engineers can measure forces, pressures, torques, and displacements with sub-microstrain precision. Load cells, pressure transducers, and force sensors in everything from industrial scales to aircraft landing gear typically use Wheatstone bridge configurations.
Temperature sensors based on resistance temperature detectors (RTDs) and thermistors also benefit from bridge circuits. Because resistance changes with temperature, the bridge output voltage varies predictably with temperature, enabling precise temperature measurement. Platinum RTDs (Pt100, Pt1000) are commonly read using bridge circuits in industrial process control.
Modern applications extend to biosensors, chemical sensors, and MEMS devices where tiny resistance changes caused by biological or chemical interactions are detected through bridge imbalances. The fundamental simplicity and noise immunity of the bridge principle — based on a null measurement or a differential voltage — makes it robust against common-mode interference and power supply fluctuations.
How to Use the Wheatstone Bridge Calculator
- Enter the three known resistances R1, R2, and R3 in ohms (Ω). Use the same unit for all three.
- Enter the Supply Voltage (Vs) — the voltage applied across the bridge.
- Enter the Voltage Ratio (bridge output voltage Vout) measured between the two midpoints of the bridge. For a balanced bridge, enter 0.
- Click Calculate. The calculator solves Rx = R2·R3/R1 adjusted for any voltage offset.
- Use the example buttons to load common bridge configurations and verify your setup.
Wheatstone Bridge FAQ
What is a Wheatstone bridge used for?
A Wheatstone bridge is used to measure an unknown electrical resistance with high precision. It works by balancing the bridge circuit so that no current flows through the measuring device, then using the known resistances to calculate the unknown one. It is also widely used in sensor applications (strain gauges, temperature sensors, pressure transducers) where small resistance changes need to be detected accurately.
What is the formula for the Wheatstone bridge?
For a balanced bridge (Vout = 0): Rx = R2 × R3 / R1. For an unbalanced bridge with output voltage Vout and supply voltage Vs: Vout = Vs × (Rx/(R2+Rx) − R3/(R1+R3)). Solving this for Rx gives: Rx = ratio × R2 / (1 − ratio), where ratio = Vout/Vs + R3/(R1+R3).
What does it mean when the bridge is balanced?
A balanced Wheatstone bridge means the output voltage between the two midpoints is exactly zero. This occurs when R1/R2 = R3/Rx. In this condition, no current flows through the galvanometer (or differential voltmeter). The balance condition allows the unknown resistance to be calculated from the three known resistances with no dependence on the supply voltage, which improves accuracy.
Why is the Wheatstone bridge so accurate?
The Wheatstone bridge is accurate because it is a null measurement method — at balance, the result depends only on the ratios of resistances, not on the absolute values of the supply voltage or the sensitivity of the measuring instrument. This eliminates errors from voltage source drift and galvanometer non-linearity. Modern bridge circuits achieve parts-per-million accuracy.
How does a Wheatstone bridge work with strain gauges?
A strain gauge is a resistive element whose resistance changes slightly under mechanical stress. By bonding one or more strain gauges to a structural member and placing them in a Wheatstone bridge, tiny resistance changes (often less than 0.1%) produce measurable output voltages. Four active gauges (full bridge) maximise sensitivity and cancel out temperature effects. This configuration is used in load cells, torque sensors, and pressure transducers.
What are the limitations of the Wheatstone bridge?
The Wheatstone bridge is most accurate near the balance condition. For large resistance deviations, the relationship between Vout and Rx becomes nonlinear, requiring the full formula or correction factors. Lead resistance in long cables can introduce errors unless compensated for. At very high frequencies, capacitance and inductance of the bridge arms affect performance, requiring AC bridge variants (such as Maxwell or Hay bridges) for accurate measurements.