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Wheatstone Bridge Calculator

Calculate the unknown resistance in a balanced Wheatstone bridge from the three known resistor values

Frequently Asked Questions

How does a Wheatstone bridge measure resistance?

Four resistors form a diamond with a detector across the middle. When the bridge is balanced and no current flows through the detector, the unknown resistance is found from the ratio of the three known resistors.

What is the balanced-bridge condition?

At balance the ratio R1 to R2 equals the ratio R3 to the unknown resistor Rx. Because it depends only on resistor ratios, the measurement is insensitive to the exact supply voltage.

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How This Calculator Works

A Wheatstone bridge is a classic circuit for measuring an unknown resistance with high precision. It arranges four resistors in a diamond shape with a detector across the middle. By adjusting the known resistors until the detector reads zero, the bridge is balanced and the unknown value can be found from a simple ratio.

The Balanced-Bridge Condition

When the bridge is balanced, no current flows through the detector and the ratio R1 to R2 equals the ratio R3 to the unknown resistor Rx. Rearranging this relationship gives Rx equal to R3 times R2 divided by R1. Because the result depends only on resistor ratios, the measurement is insensitive to the exact supply voltage.

How To Use It

Enter the three known resistances R1, R2, and R3 in ohms. The calculator returns the unknown resistance Rx that balances the bridge. Strain gauges, thermistors, and load cells all rely on small changes in one bridge arm to produce a measurable output.

Tips

The result is a ratio, so supply voltage does not affect it.
Use precise known resistors for an accurate Rx.
Small bridge imbalances are the basis of sensor measurements.

Bridge Balance and Null Detection

A balanced Wheatstone bridge produces zero output voltage across the detector regardless of the supply voltage. This null condition occurs when R1/R2 = R3/R4, and at that ratio the bridge is a pure ratio device: doubling the supply voltage does not change the balance condition or the null reading. This makes the bridge extremely insensitive to supply voltage fluctuations, which is one reason it dominated precision resistance measurement for over 150 years.

The sensitivity of the null detector determines the overall measurement resolution. A galvanometer (analog current meter) can detect current changes of 1-10 nA, allowing bridge imbalances of micro-ohms to be detected when the bridge resistance values are appropriate. In modern electronic bridges, a precision instrumentation amplifier replaces the galvanometer, and analog-to-digital conversion allows direct digital readout of the imbalance.

Historical Measurement

The Wheatstone bridge was popularized (though not originally invented) by Sir Charles Wheatstone in 1843, and it became the standard technique for precision resistance measurement in physics and engineering laboratories throughout the 19th and early 20th centuries. Laboratory-grade Wheatstone bridges used decade resistance boxes as the adjustable R3 arm, allowing the operator to dial in the balance point and read the unknown resistance from the decade switch settings. The Kelvin double bridge extends the Wheatstone principle to 4-wire resistance measurement, eliminating lead and contact resistance errors that become significant when measuring resistances below about 1 Ω. Precision wire resistance measurement, grounding electrode resistance testing, and contact resistance verification all use Kelvin bridge techniques.

Strain Gauges and Load Cells

The most widespread industrial application of the Wheatstone bridge is strain measurement. A metallic foil strain gauge consists of a thin conductor bonded to a backing film. When the backing is bonded to a structure under stress, the gauge stretches or compresses with the structure, changing its electrical resistance. The resistance change follows ΔR/R = GF x ε, where GF is the gauge factor (approximately 2 for metal foil gauges) and ε is the mechanical strain. For a 120 Ω gauge at 1000 microstrain, the resistance change is only 0.24 Ω, or 0.2%. Measuring such a small resistance change directly is impractical, but a Wheatstone bridge converts this tiny ratio change into a proportional voltage output.

In a quarter-bridge configuration, one arm of the bridge is the active strain gauge and the other three arms are fixed resistors. In a half-bridge, two adjacent arms are active gauges arranged to respond to the same load (doubling the output) or to cancel temperature effects (one gauge in tension, one in compression). In a full bridge (most sensitive), all four arms are active gauges. A full bridge with two gauges in tension and two in compression produces an output four times larger than a quarter bridge for the same applied strain.

Load Cell Configuration

A load cell is a mechanical structure (typically machined aluminum or steel) with four strain gauges bonded to it in a full Wheatstone bridge configuration. When the structure flexes under an applied force, two gauges stretch and two compress, producing a differential output voltage proportional to the applied force. Excitation voltage is typically 5-10 V DC or AC, and the full-scale output is 1-3 mV per volt of excitation. This means a load cell excited at 5 V produces a full-scale output of only 5-15 mV, which requires amplification by a precision instrumentation amplifier before analog-to-digital conversion. Load cells appear in virtually every weighing application: platform scales, crane scales, vehicle weighing, force testing machines, and medical weighing equipment.

Temperature Compensation

One of the most important practical advantages of the Wheatstone bridge configuration in sensor applications is inherent temperature compensation. If all four gauge resistors change by the same percentage when temperature changes (because they are the same material and at nearly the same temperature), the bridge balance condition R1/R2 = R3/R4 remains satisfied and the output stays at zero for zero applied stimulus. In practice, temperature compensation requires that the gauges be made from the same batch of alloy, bonded to the same substrate, and located close together. For highest accuracy, self-temperature-compensating gauge alloys are available whose resistance-temperature coefficient is matched to a specific substrate material, further reducing thermal output.

Other Bridge Sensor Applications

The Wheatstone bridge topology is not limited to strain measurement. Any sensor whose output is a resistance change can be placed in a bridge arm to convert the resistance change into a proportional voltage.

RTD Temperature Measurement

Platinum resistance temperature detectors (PT100 with 100 Ω at 0°C, PT1000 with 1000 Ω at 0°C) have a highly predictable, stable resistance-temperature relationship. When placed in a Wheatstone bridge with precision reference resistors, the bridge output voltage indicates temperature with uncertainties as low as ±0.1°C over a wide range. The higher resistance of PT1000 sensors reduces the effect of lead resistance on the measurement, which is important in installations with long cable runs. For the highest accuracy, 4-wire (Kelvin) connections eliminate lead resistance errors entirely.

Capacitance Bridge (AC)

When an AC supply is used instead of DC, the bridge arms can contain capacitors, inductors, or impedances of any kind in addition to resistors. AC bridges are the standard technique for measuring capacitance and inductance with high accuracy. The Maxwell bridge, Wien bridge, Schering bridge, and Hay bridge are all variants optimized for different impedance types and frequency ranges. Impedance bridges in calibration laboratories measure capacitance to parts per million accuracy, serving as traceability standards for all lower-tier capacitance measurements.

Gas Sensors

Catalytic bead (Pellistor) gas sensors for detecting combustible gases use two matched ceramic beads in a Wheatstone bridge. The active bead contains a platinum catalyst; when combustible gas contacts it, the gas oxidizes and releases heat, raising the bead temperature and increasing its resistance. The reference bead is identical but contains no catalyst, so it responds only to ambient temperature changes and not to the target gas. The bridge output is proportional only to the gas concentration because the reference bead cancels ambient temperature fluctuations. This is a direct application of the bridge temperature compensation principle described above.

Pressure Sensors

MEMS (micro-electromechanical systems) piezoresistive pressure sensors integrate four silicon piezoresistors into a thin silicon diaphragm. When pressure deflects the diaphragm, two resistors in tension and two in compression produce a full Wheatstone bridge output. The sensor is fabricated by bulk micromachining of a silicon wafer, with the diaphragm formed by anisotropic etching. These sensors appear in automotive MAP (manifold absolute pressure) sensors, tire pressure monitoring systems, barometric pressure sensors in weather stations, and medical invasive blood pressure monitoring catheters.

Frequently Asked Questions

How sensitive is a Wheatstone bridge?

Bridge sensitivity depends on the sensor element and the detection electronics. A full Wheatstone bridge with a 350 Ω strain gauge bridge excited at 10 V produces approximately 10-30 mV at full scale, representing resistance changes of about 0.1-0.3%. With a 24-bit ADC and a precision instrumentation amplifier, resistance changes of less than 0.001% can be resolved, corresponding to microstrains or millikelvin temperature changes. In laboratory Wheatstone bridge instruments with galvanometer detection, the null point can be set with milliohm precision when using decade resistance boxes as the adjustable arm.

Can I measure DC or AC resistance with a bridge?

DC excitation is simpler and standard for most resistive sensor applications including strain gauges, RTDs, and thermistors. AC excitation is required for bridges that include capacitors or inductors, such as impedance bridges for component measurement. AC excitation at 50-100 Hz also avoids galvanic effects at electrode-electrolyte interfaces in electrochemical sensing applications, where DC current would cause electrolysis and change the electrode properties. Some precision resistance bridges use AC excitation even for purely resistive elements to take advantage of lock-in amplifier detection techniques that reject noise outside a narrow bandwidth around the excitation frequency, greatly improving sensitivity.