Wheatstone Bridge Calculator
Calculate the unknown resistance in a Wheatstone bridge circuit or check if the bridge is balanced. Enter R1, R2, R3 to solve for R4, or enter all four to verify balance. See also our Ohm's Law Calculator and Resistor Color Code Calculator.
How to Use the Wheatstone Bridge
The Wheatstone bridge is one of the most important and widely used circuits in electrical measurement. Invented by Samuel Hunter Christie in 1833 and popularized by Sir Charles Wheatstone in 1843, this circuit provides an extremely accurate method for measuring unknown resistances. The bridge consists of four resistors arranged in a diamond (or square) configuration with a voltage source across one diagonal and a detector (galvanometer) across the other diagonal.
To use this calculator, enter the values of R1, R2, and R3 to find the value of R4 that would balance the bridge. Alternatively, enter all four resistor values to check whether the bridge is balanced. A balanced bridge means zero voltage (and zero current) across the detector — this null condition is independent of the supply voltage, making the measurement very accurate.
The bridge is balanced when the ratio of resistors in one arm equals the ratio in the other arm: R₂/R₁ = R₄/R₃. This condition means the voltage at both midpoints is equal, so no current flows through the galvanometer. By adjusting one known resistor until the galvanometer reads zero, you can determine the unknown resistance with high precision.
Wheatstone Bridge Formula
Balance Condition:
R₂/R₁ = R₄/R₃
R₄ = R₂ × R₃ / R₁ (solving for unknown)
Bridge Voltage (unbalanced):
V_bridge = V_s × [R₂/(R₁+R₂) - R₄/(R₃+R₄)]
Thevenin Equivalent (from detector terminals):
V_th = V_s × [R₂/(R₁+R₂) - R₄/(R₃+R₄)]
R_th = R₁‖R₂ + R₃‖R₄
Sensitivity:
S = ΔV_bridge / ΔR (volts per ohm change)
Example Calculation
A Wheatstone bridge has R₁ = 100Ω, R₂ = 200Ω, and R₃ = 300Ω. Find R₄ for balance:
Given: R₁ = 100Ω, R₂ = 200Ω, R₃ = 300Ω
Balance condition: R₂/R₁ = R₄/R₃
R₄ = R₂ × R₃ / R₁ = 200 × 300 / 100 = 600 Ω
Verify: R₂/R₁ = 200/100 = 2.0
Verify: R₄/R₃ = 600/300 = 2.0 ✓
If supply = 10V and R₄ = 500Ω (unbalanced):
V_bridge = 10 × [200/(100+200) - 500/(300+500)]
V_bridge = 10 × [0.6667 - 0.6250] = 0.4167 V
Wheatstone Bridge Reference Table
| R₁ (Ω) | R₂ (Ω) | R₃ (Ω) | R₄ balanced (Ω) |
|---|---|---|---|
| 100 Ω | 100 Ω | 100 Ω | 100 Ω |
| 100 Ω | 200 Ω | 300 Ω | 600 Ω |
| 100 Ω | 100 Ω | 470 Ω | 470 Ω |
| 120 Ω | 240 Ω | 180 Ω | 360 Ω |
| 150 Ω | 300 Ω | 200 Ω | 400 Ω |
| 220 Ω | 330 Ω | 470 Ω | 705 Ω |
| 330 Ω | 470 Ω | 680 Ω | 968.48 Ω |
| 470 Ω | 1000 Ω | 470 Ω | 1000 Ω |
| 1000 Ω | 1000 Ω | 1000 Ω | 1000 Ω |
| 1000 Ω | 2200 Ω | 3300 Ω | 7260 Ω |
| 4700 Ω | 10000 Ω | 4700 Ω | 10000 Ω |
| 10000 Ω | 10000 Ω | 10000 Ω | 10000 Ω |
Frequently Asked Questions
What is a Wheatstone bridge?
A Wheatstone bridge is a circuit with four resistors arranged in a diamond shape, used to precisely measure unknown resistances. A voltage source is connected across one diagonal, and a sensitive detector (galvanometer) across the other. When the bridge is balanced (zero detector current), the unknown resistance can be calculated from the three known resistors using R₄ = R₂×R₃/R₁.
Why is the Wheatstone bridge so accurate?
The bridge achieves high accuracy because it uses a null measurement technique — you detect zero current rather than measuring a specific value. This eliminates errors from the detector's calibration, supply voltage variations, and lead resistance. The accuracy depends only on the precision of the three known resistors, which can be made to very tight tolerances (0.01% or better).
What are common applications of the Wheatstone bridge?
Wheatstone bridges are used in strain gauge measurements (structural engineering), temperature sensing (RTD bridges), pressure transducers, load cells (weighing scales), gas sensors, and precision resistance measurement. Modern instrumentation amplifiers often interface directly with bridge circuits to measure tiny resistance changes representing physical quantities.
What happens when the bridge is unbalanced?
When unbalanced, a voltage appears across the detector terminals proportional to the resistance imbalance. This voltage is V_bridge = V_s × [R₂/(R₁+R₂) - R₄/(R₃+R₄)]. In sensor applications, this unbalance voltage is amplified and measured to determine the physical quantity (strain, temperature, pressure) causing the resistance change.
How do strain gauges use the Wheatstone bridge?
Strain gauges change resistance slightly when deformed (typically 0.1-0.5% for full-scale strain). By placing one or more strain gauges in a Wheatstone bridge, the tiny resistance change produces a measurable voltage output. Quarter-bridge uses one active gauge, half-bridge uses two, and full-bridge uses four gauges for maximum sensitivity and temperature compensation.
Can I use the Wheatstone bridge for AC measurements?
Yes, AC bridges (like the Wien bridge, Maxwell bridge, and Schering bridge) extend the Wheatstone principle to measure capacitance, inductance, and impedance. The balance condition becomes Z₂×Z₃ = Z₁×Z₄ using complex impedances. AC bridges require both magnitude and phase balance, giving two independent equations to solve for two unknowns (e.g., capacitance and dissipation factor).
Bridge Circuit Variations
Several variations of the basic Wheatstone bridge exist for specialized measurements. The Kelvin double bridge adds extra arms to eliminate lead resistance errors when measuring very low resistances (below 1Ω). The Wien bridge uses capacitors and resistors to measure frequency or capacitance. The Maxwell bridge measures inductance by balancing it against a known capacitance. The Schering bridge is optimized for measuring capacitance and dielectric loss in high-voltage insulation testing.
Practical Considerations
When building a Wheatstone bridge, use precision resistors with low temperature coefficients for the reference arms. The supply voltage should be stable but its exact value does not affect the balance point. For maximum sensitivity, all four resistors should be of similar magnitude. Lead resistance can introduce errors — use four-wire connections for the unknown resistor when measuring low values. Self-heating from the measurement current can change resistance values, so use the minimum current necessary for adequate detector sensitivity.