How does a Wheatstone bridge work?

A Wheatstone bridge consists of four resistors arranged in a diamond shape with a voltage source across two opposite corners. When the bridge is balanced (R1/R2 = R3/R4), the voltage difference between the two middle nodes is zero. Any imbalance produces a measurable voltage proportional to the resistance change.

What is the Wheatstone bridge balance condition?

The bridge is balanced when R1/R2 = R3/R4. At balance, Vout = 0 regardless of the supply voltage. To find the unknown resistor R4 for balance: R4 = R2 × R3 / R1.

How do you calculate Wheatstone bridge output voltage?

Vout = Vin × (R4/(R3+R4) − R2/(R1+R2)). When the bridge is balanced, Vout = 0. When unbalanced, Vout can be positive or negative depending on which arm has the excess resistance.

What are common applications of Wheatstone bridges?

Wheatstone bridges are used in strain gauge measurements, temperature sensing with RTDs (PT100), load cells and weight scales, and precision resistance measurement. They convert small resistance changes into measurable voltage signals.

Wheatstone Bridge Calculator

Calculate bridge balance resistor and output voltage for Wheatstone bridge circuits.

Component Values

Results

R4 for Balance1.000 kΩ

Balance ConditionR1/R2 = R3/R4

Wheatstone Bridge: From Load Cells to Strain Gauges

Use this calculator when you're interfacing a load cell, strain gauge, pressure sensor, or RTD (PT100/PT1000) to a microcontroller or data acquisition system. These sensors work by changing their resistance slightly — often by just a fraction of a percent — when stressed. A plain voltage divider can't resolve such tiny changes. The Wheatstone bridge can, because it measures the difference between two dividers, cancelling out the common-mode voltage and leaving only the small sensor signal.

Example: a 350Ω strain gauge changes resistance by ±0.1Ω under full load (a 0.03% change). With R1=R2=R3=350Ω and R4=gauge, at 5V excitation, the bridge output is about 5V×(0.1/700)≈0.7mV. That's the signal you're amplifying. An INA128 or HX711 instrumentation amplifier with a gain of 128 gives you about 90mV — enough to measure with a 10-bit ADC. The calculator's 'Vout' result is exactly this differential voltage.

The 'Find R4 for Balance' mode tells you which fixed resistor makes the bridge output exactly zero at a known reference condition (e.g., no load). Starting from balance is important because it lets you set your amplifier gain high without saturating the output. For temperature sensors: use the 'Calculate Vout' mode, enter your RTD's resistance at the measured temperature, and compute the bridge output voltage you'd see with your fixed resistors.

Balance Condition

R1/R2 = R3/R4

Vout

Vout = Vin × (R4/(R3+R4) − R2/(R1+R2))

Key Points

Balance: R1/R2 = R3/R4 → Vout = 0
Very sensitive to small resistance changes (used in sensors)
Output polarity indicates which arm has excess resistance
Best sensitivity when all four resistors are similar in value

Applications

Strain gauge and load cell measurement
Temperature sensing with RTD (PT100, PT1000)
Pressure sensor signal conditioning
Precision resistance measurement

Practical Examples

350 Ω strain gauge at 1000 µε

A 350 Ω strain gauge (GF = 2) in a quarter-bridge, 10 V excitation. At 1000 microstrain: ΔR = 0.7 Ω.

Vout = (ΔR / 4R) × Vin = (0.7 / 1400) × 10 = 5 mV differential

RTD temperature measurement

PT100 RTD (100 Ω at 0°C, α = 0.385 Ω/°C) in a Wheatstone bridge to measure temperature with high precision.

At 100°C: R = 138.5 Ω · Bridge imbalance ≈ 87 mV with 5 V excitation and 100 Ω arms

Formula Reference

Wheatstone bridge

Balanced condition: R1/R2 = R3/R4  →  Vout = 0

Unbalanced output:
Vout = Vex × (R4/(R3+R4) – R2/(R1+R2))

For small ΔR (sensor change):
Vout ≈ Vex × (ΔR/R) / 4  (one active arm)
Vout ≈ Vex × (ΔR/R) / 2  (two active arms — half bridge)
Vout ≈ Vex × (ΔR/R)      (four active arms — full bridge)

Gauge factor (strain gauges): GF = (ΔR/R) / ε

More Examples

Load cell signal (full bridge, 350Ω, 10V excitation)

Typical output: 2 mV/V × 10V = 20mV at full load. Use instrumentation amp (INA128, G=100): Vout = 20mV×100 = 2V full scale. Resolution with 12-bit ADC (3.3V ref): 0.8mV/bit → 2000mV/0.8 = 2500 counts.

Full-scale output: 2V · ADC counts at full load: 2500

NTC temperature bridge (R0=10kΩ at 25°C)

R1=R2=R3=10kΩ, R4=NTC. At 25°C: bridge balanced, Vout=0. At 50°C: R_NTC≈3.6kΩ → Vout = 5×(3.6/13.6 – 0.5) = –1.18V. Amplify ×10 → –11.8V/100°C sensitivity.

Sensitivity: –11.8V/100°C (amplified ×10)

Design tip

Match resistors to < 0.1% tolerance for best bridge balance.
Use instrumentation amplifier (INA128, AD8221) — never a simple op-amp — for bridge readout.
Cable resistance matters: use 6-wire Kelvin connection for precision load cells.
Self-heating error: limit excitation voltage to keep power < 50mW per resistor.

Did you know? The Wheatstone bridge was invented by Samuel Hunter Christie in 1833 but popularised by Charles Wheatstone in 1843 — yet it bears only Wheatstone's name. It remains the basis of precision resistance measurements used in strain gauges and platinum RTD sensor circuits today.