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Wheatstone Bridge Resistor & Strain Gauge Calculator

Popularized by Sir Charles Wheatstone in 1843, the Wheatstone bridge circuit enables precision measurement of minuscule resistance shifts by evaluating differential voltage.

Bridge excitation power supply voltage in Volts.

Top-left arm resistor in Ohms.

Top-right arm resistor in Ohms.

Bottom-left arm reference resistor in Ohms.

Bottom-right unknown resistor or strained gauge resistance in Ohms.

Calculated Result
49.50 mV

Bridge Output Voltage

Differential Output Voltage (V_out)

49.50 mV (0.0495 V)

Balanced Rx Value

1000 Ω

Bridge State

Deflected (Unbalanced)

Bridge Sensitivity

2.5 mV/Ω

Calculation Breakdown

  1. 1. Balanced Resistance ConditionR_x(null) = (R₂ · R₃) / R₁ = (1000 · 1000) / 1000 = 1000 Ω
  2. 2. Node Voltages CalculationV_nodeA = V_in · [R₂ / (R₁ + R₂)] = 10 · [1000 / 2000] = 5.0000 V; V_nodeB = V_in · [R_x / (R₃ + R_x)] = 5.0495 V
  3. 3. Differential Output VoltageV_out = V_nodeB - V_nodeA = 49.50 mV

Bridge Output Voltage vs Strain Resistance (10V Excitation)

Interactive visualization based on your current inputs

V_out (mV)
-25.1-0.4244974990 Ω1000 Ω (Null)1010 Ω1020 Ω1030 ΩRx (Ω)V_out (mV)

What Is the Wheatstone Bridge Resistor & Strain Gauge Calculator?

The Wheatstone bridge is an electrical network of four resistor arms used to detect minute variations in electrical resistance.

How Does the Wheatstone Bridge Resistor & Strain Gauge Calculator Work?

When the ratios of the arms are equal (R1/R2 = R3/Rx), the potential difference between the center midpoints is exactly zero volts.

Wheatstone Bridge Resistor & Strain Gauge Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

R_x(null) = \frac{R_2 \cdot R_3}{R_1}, \quad V_{out} = V_{in} \left( \frac{R_x}{R_3 + R_x} - \frac{R_2}{R_1 + R_2} \right)

Balanced Rx equals R2 times R3 over R1. Output voltage is excitation times difference of voltage divider fractions.

How to Use the Wheatstone Bridge Resistor & Strain Gauge Calculator

  1. Enter the bridge excitation supply voltage (e.g. 5V, 10V, or 12V).
  2. Input the known bridge arm resistances R₁, R₂, and R₃.
  3. Enter the sensor gauge resistance Rx.

Step-by-Step Example Calculation

1,000 Ω Quarter-Bridge with 20 Ω Gauge Deflection

Input Values:

vInVolts:10
r1Ohms:1000
r2Ohms:1000
r3Ohms:1000
rxOhms:1020
Worked Steps: With 10V excitation and a 20 Ω strain increase (Rx = 1020 Ω), the differential bridge produces 49.50 mV.

Understanding Your Result

Differential Output (V_out): Millivolt reading across center terminals.

Balanced Null Rx: Resistor value required to achieve zero output voltage.

Bridge Sensitivity: Millivolts of output change per Ohm of resistance change.

Factors That Affect the Result

  • Excitation voltage (directly scales Vout), initial bridge arm matching, and gauge lead wire resistance.

When Should You Use This Calculator?

  • Load cell weighing scales, structural strain monitoring, aerospace wing testing, and RTD temperature transmitters.

Assumptions & Limitations

  • Assumes high input impedance instrumentation amplifier reading Vout (negligible output load current).

Frequently Asked Questions

Calculation Accuracy & Reference Note

Exact nodal analysis solution of balanced/unbalanced resistive bridge networks.

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