Wheatstone Bridge

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

Quick answer

This calculator solves Vout = Vin × (R3/(R3+R4) - R2/(R1+R2)) for Vout. With Supply Voltage 12 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, R4 4.7 kΩ, the result is 2.659 V.

Calculator

Result
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Formula

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

Description

The Wheatstone bridge is a measurement circuit consisting of four resistors in a diamond configuration, powered by a voltage source, with the output measured across the middle of the two voltage divider branches. When the bridge is balanced (R1 × R3 = R2 × R4, equivalently R1/R2 = R4/R3), the output voltage is zero. Any imbalance produces an output voltage proportional to the difference. This makes it extremely sensitive to small resistance changes, which is why it is universally used with strain gauges, load cells, RTDs, and other resistive sensors. An instrumentation amplifier is typically used to amplify the small bridge output.

Variables

  • Vout — Bridge output voltage (V)
  • Vin — Bridge excitation voltage (V)
  • R1 — Resistor in the first divider arm (Ω)
  • R2 — Resistor in the first divider arm (Ω)
  • R3 — Resistor in the second divider arm (Ω)
  • R4 — Resistor in the second divider arm (Ω)

Practical Notes

For maximum sensitivity, all four resistors should be similar in value. A quarter-bridge uses one active sensor and three fixed resistors. A half-bridge uses two active sensors (opposite arms) for 2x sensitivity and temperature compensation. A full-bridge uses four active sensors for 4x sensitivity and excellent temperature rejection. Bridge excitation can be AC for improved noise immunity.

Symbols and units

Symbol Meaning Default unit Accepted units
Vin Supply Voltage V pV, nV, µV, mV, V, kV
R1 R1 kΩ mΩ, Ω, kΩ, MΩ
R2 R2 kΩ mΩ, Ω, kΩ, MΩ
R3 R3 kΩ mΩ, Ω, kΩ, MΩ
R4 R4 kΩ mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Supply Voltage 12 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, R4 4.7 kΩ
  2. 2. The relation: Vout = Vin × (R3/(R3+R4) - R2/(R1+R2))
  3. 3. Substitute: Vin = 12 V, R1 = 10 kΩ, R2 = 22 kΩ, R3 = 47 kΩ, R4 = 4.7 kΩ
  4. 4. Result: Vout = 2.659 V

Related quantities from the same inputs

  • P = V² / R = 14.4 mW
  • I = V / R = 1.2 mA

Worked examples

Minimum range

Given: Supply Voltage 0.33 V, R1 100 Ω, R2 0.22 kΩ, R3 0.47 kΩ, R4 47 Ω

Result: Vout = 73.13 mV

Low range

Given: Supply Voltage 3.3 V, R1 1 kΩ, R2 2.2 kΩ, R3 4.7 kΩ, R4 0.47 kΩ

Result: Vout = 0.7312 V

Typical

Given: Supply Voltage 12 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, R4 4.7 kΩ

Result: Vout = 2.659 V

High range

Given: Supply Voltage 0.23 kV, R1 100 kΩ, R2 0.22 MΩ, R3 0.47 MΩ, R4 47 kΩ

Result: Vout = 50.97 V

Maximum range

Given: Supply Voltage 2.3 kV, R1 1 MΩ, R2 2.2 MΩ, R3 4.7 MΩ, R4 0.47 MΩ

Result: Vout = 0.5097 kV

How Vout changes with Supply Voltage

Supply Voltage (input) Vout (result)
1.2 V 0.2659 V
3 V 0.6648 V
6 V 1.33 V
9 V 1.994 V
12 V 2.659 V
18 V 3.989 V
24 V 5.318 V
48 V 10.64 V
84 V 18.61 V
120 V 26.59 V

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Frequently asked questions

How do you calculate Wheatstone Bridge?

Use Vout = Vin × (R3/(R3+R4) - R2/(R1+R2)). With Supply Voltage 12 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, R4 4.7 kΩ, Vout works out to 2.659 V.

What is the formula for Wheatstone Bridge?

The formula is Vout = Vin × (R3/(R3+R4) - R2/(R1+R2)). The Wheatstone bridge is a measurement circuit consisting of four resistors in a diamond configuration, powered by a voltage source, with the output measured across the middle of the two voltage divider branches.

Related Concepts

All Sensors & ADC formulas →
ADC Resolution (LSB) ADC Theoretical SNR Steinhart-Hart Temperature Wheatstone Bridge Linear Sensor Transfer Function Oversampling SNR Improvement RTD Callendar-Van Dusen Strain Gauge Resistance Change

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