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Wheatstone Bridge Calculator

Calculate Unknown Resistance with Balanced Bridge

Mode
R1 (Ω)
R2 (Ω)
R3 (Ω)
Rx (Ω) (unknown)

Wheatstone Bridge Formulas

Balance condition: R1/R2 = R3/Rx
Unknown: Rx = R2 × R3 / R1
Output: Vout = Vin × (R3/(R3+Rx) - R1/(R1+R2))
At balance: Vout = 0, Rx = R2×R3/R1

A Wheatstone bridge precisely measures unknown resistance by comparing it against known values. When balanced, no current flows through the center galvanometer. The bridge is the foundation of many sensor measurement circuits.

⚠ The bridge is most sensitive near balance. For precise measurement, use a high-resolution adjustable R3 and sensitive null detector. Temperature affects all resistor values.

What is a Wheatstone Bridge?

The Wheatstone bridge, invented by Samuel Hunter Christie in 1833 and popularized by Sir Charles Wheatstone, is a circuit for measuring unknown electrical resistance. It consists of four resistors in a diamond configuration with a voltage source across one diagonal and a galvanometer across the other. When balanced, the ratio of two adjacent resistors equals the ratio of the other two.

Balance Condition

R1/R2 = R3/Rx. When balanced, Vout = 0 and no current flows through the center. Solve for any unknown resistor.

Sensitivity

Maximum sensitivity when all resistors are equal. Use high-resolution adjustable R3 (decade box) for precise null detection.

Unbalanced Output

Vout = Vin × (R3/(R3+Rx) - R1/(R1+R2)). Near balance, Vout ≈ Vin × ΔR/(4R) for small changes. Used in strain gauges.

Temperature Effects

Resistors change value with temperature. Use precision resistors with low temperature coefficient (ppm/°C) for accurate measurements.

Teaching Example: R1=100Ω, R2=200Ω, R3=150Ω. Find Rx.
Balance: 100/200 = 150/Rx → Rx = 200×150/100 = 300Ω.
Verify: 100/200 = 0.5 and 150/300 = 0.5. Balanced! Vout = 0V.

Applications

Strain Gauges RTD Sensors Pressure Sensors LDR Circuits Precision Metrology

Frequently Asked Questions

How does a Wheatstone bridge work?▼
Four resistors form a diamond. When R1/R2 = R3/Rx, the bridge is balanced (Vout=0). This allows accurate measurement of unknown Rx.
How to find unknown resistance?▼
Adjust R3 until Vout=0 (null). Then Rx = R2 × R3 / R1. The ratio method eliminates errors from voltage source variations.
What is bridge sensitivity?▼
Maximum sensitivity when all 4 resistors are equal. Near balance, Vout ≈ Vin × ΔR/(4R). Strain gauges use this linear region.
Wheatstone vs Kelvin bridge?▼
Wheatstone (medium R, 1Ω-1MΩ). Kelvin (low R, below 1Ω, 4-wire). Megger (high R, above 1MΩ). Each optimized for different ranges.

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