When is the bridge balanced?

The bridge is balanced when R1×R4 = R2×R3. At balance, no current flows through the bridge (galvanometer reads zero). This condition is independent of the source voltage.

What is the bridge used for?

Precision resistance measurement, strain gauge circuits (load cells, pressure sensors), temperature measurement (RTD bridges), and general sensor circuits where small resistance changes need to be detected as voltage changes.

Can I solve for any missing resistor?

Yes. Enter any three of the four resistors and leave the fourth blank. The calculator solves for the missing value that would balance the bridge.

Wheatstone Bridge Calculator

R₁×R₄ = R₂×R₃

V_b = V_s(R₃/(R₁+R₃) − R₄/(R₂+R₄))

Wheatstone Bridge — Enter 3 or 4 Resistors

R₁ Resistor 1

R₂ Resistor 2

R₃ Resistor 3

R₄ Resistor 4 (or unknown)

Leave blank to find R₄ for balance

V Source Voltage (optional)

For bridge voltage calculation

Enter at least 3 resistors

Wheatstone Bridge Results

Balance Condition

—

Bridge Voltage V_b

—

R₄ (for balance)
—
Ω

V_bridge

—

R₁×R₄ vs R₂×R₃

—

R₁

—

R₂

—

R₃

—

Figure 1: The Wheatstone Bridge has four resistors in a diamond. When R₁×R₄ = R₂×R₃, the bridge is balanced and the voltage between nodes A and B is zero. Any imbalance produces a measurable bridge voltage.

Table of Contents

Fundamentals

What Is a Wheatstone Bridge?
The Balance Condition

Worked Examples

Finding an Unknown Resistor
Strain Gauge Bridge
Temperature Sensor Bridge

Deep Dive

Bridge Sensitivity
Applications

Reference

Frequently Asked Questions
Related Circuit Analysis Calculators

What Is a Wheatstone Bridge?

A Wheatstone Bridge is a circuit of four resistors arranged in a diamond (or bridge) configuration. It was invented by Samuel Hunter Christie in 1833 and popularised by Sir Charles Wheatstone. The circuit is used to precisely measure an unknown resistance by comparing it against known resistors, and it forms the basis of most modern sensor circuits including strain gauges, load cells, and RTD temperature sensors.

The bridge has two voltage divider arms connected in parallel across a supply voltage. A galvanometer or voltmeter measures the voltage difference between the midpoints of the two arms. When the bridge is balanced, this voltage is zero. The Parallel Circuit Calculator analyses the simpler case of two parallel branches without the cross-connection.

The Balance Condition

Balance: R₁ × R₄ = R₂ × R₃
When balanced, V_bridge = 0 regardless of supply voltage.
Unknown: R_x = R₂ × R₃ / R₁ (solve for any missing arm).

The beauty of the balance condition is that it depends only on the ratios of resistances, not on the absolute supply voltage. This makes the measurement independent of supply fluctuations — a major advantage for precision work.

Worked Example — Finding an Unknown Resistor

Given: R₁ = 1 kΩ, R₂ = 2.2 kΩ, R₃ = 3.3 kΩ. Find R₄ for balance.

R₄ = R₂ × R₃ / R₁ = 2200 × 3300 / 1000 = 7260 Ω (7.26 kΩ)

If you measure the unknown resistor and it differs from 7.26 kΩ, the bridge will be unbalanced and show a voltage. The Circuit Current Calculator can find the galvanometer current for a given imbalance.

Worked Example — Strain Gauge Bridge

Given: All arms 350 Ω (unstrained), V_s = 5 V. Strain gauge changes to 350.7 Ω.

V_bridge = 5 × (350/(350+350) − 350.7/(350+350.7)) = 5 × (0.5 − 0.4999) = 2.5 mV

A 0.2% change in resistance produces only 2.5 mV — this is why strain gauge amplifiers have gains of 100–1000. The Voltage Drop Calculator helps account for cable resistance between the bridge and amplifier.

Worked Example — Temperature Sensor Bridge

Given: Pt100 RTD at 0°C = 100 Ω, R₁ = R₂ = R₃ = 100 Ω, V_s = 5 V

At 0°C: bridge balanced, V_b = 0 V.

At 100°C: RTD = 138.5 Ω. V_b = 5 × (100/200 − 138.5/238.5) = 0.404 V

The bridge converts the RTD resistance change to a voltage that can be measured by an ADC or analogue meter.

Bridge Sensitivity

Bridge sensitivity is the voltage change per unit resistance change at balance. For a bridge with equal arms R and supply V_s, sensitivity is approximately V_s/(4R) volts per ohm. Higher supply voltage and lower nominal resistance increase sensitivity. However, increasing V_s also increases self-heating in the sensor, which limits practical excitation voltage.

Applications

Wheatstone bridges are used in load cells (weight measurement), pressure transducers, accelerometers, strain gauge rosettes for stress analysis, RTD temperature measurement, and precision resistance measurement. The Thevenin Equivalent Calculator can simplify a loaded bridge into a single source and impedance for amplifier input analysis.

Frequently Asked Questions

Does the supply voltage matter for balance?

No. The balance condition R₁×R₄ = R₂×R₃ depends only on resistance ratios. However, the supply voltage determines the sensitivity — how much voltage you get per unit resistance change when the bridge is near balance.

What is a quarter bridge, half bridge, and full bridge?

In a quarter bridge, one arm is the sensor and three are fixed resistors. In a half bridge, two opposite arms are sensors (doubles sensitivity). In a full bridge, all four arms are sensors (quadruples sensitivity and cancels temperature drift). Load cells typically use full bridges.

Can I use AC with a Wheatstone Bridge?

Yes. AC bridges are used to measure capacitance and inductance by replacing some arms with reactive components. The balance condition becomes a complex equation involving both magnitude and phase. The Maxwell bridge, Wien bridge, and Schering bridge are common AC variants.

How accurate is a Wheatstone Bridge?

Very accurate. With precision reference resistors (0.01% tolerance) and a sensitive null detector, a Wheatstone Bridge can measure resistance to 0.01% accuracy. This makes it superior to simple ohmmeter measurements.

What happens when the bridge is loaded?

If a finite-impedance load (like an amplifier input) is connected across the bridge output, it draws current and affects the bridge voltage. For high-impedance loads (FET-input amplifiers) this effect is negligible. For low-impedance loads, use Thevenin analysis to find the actual output voltage.

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Last updated: March 2026