Wheatstone Bridge Calculator

Precision resistance measurement

What is a Wheatstone bridge?

A Wheatstone bridge is a four-resistor electrical network used to compare resistance values with high sensitivity. The resistors are arranged as two voltage dividers connected across the same supply. A detector, meter, or measurement circuit compares the voltage at the midpoint of one divider with the midpoint of the other.

When both midpoint voltages are equal, the bridge output is zero and the circuit is described as balanced. At balance, the resistor ratios are equal, allowing an unknown resistance to be calculated from three known resistances.

Wheatstone bridges are widely used in laboratory measurements, resistance calibration, strain-gauge systems, pressure sensors, load cells, temperature sensors, and other circuits where a small resistance change must be converted into a measurable voltage.

Four-resistor network

Wheatstone bridge resistor arrangement

This calculator models R1 and R2 as the upper and lower resistors of the left voltage-divider arm. R3 and Rx form the corresponding upper and lower resistors of the right arm.

• R1 is the upper-left bridge resistance.
• R2 is the lower-left bridge resistance.
• R3 is the upper-right bridge resistance.
• Rx is the lower-right resistance, which may be unknown.
• Vs is the voltage supplied across the complete bridge.
• Vout is the difference between the left and right midpoint voltages.

Different textbooks may label or rotate the bridge arms differently. The balance equation must always match the physical resistor arrangement being used. The labels on this page correspond directly to the calculator inputs and formulas shown below.

Null-balance condition

Wheatstone bridge balance equation

The bridge is balanced when the ratio of the two resistors in the left arm equals the ratio of the two resistors in the right arm.

At this condition, both midpoint voltages are equal. An ideal voltmeter connected between the midpoints reads zero volts, and no current flows through an ideal detector branch.

Solve the missing resistance

Unknown resistance formula

Rearranging the balance equation gives the unknown lower-right resistance:

Because this calculation depends on a resistance ratio, R1, R2, and R3 may be entered in ohms, kilo-ohms, or mega-ohms, provided all three values use the same unit. The calculated Rx value will use the same resistance unit.

Worked balance example

Calculate an unknown bridge resistance

Suppose a balanced Wheatstone bridge has R1 = 100 Ω, R2 = 200 Ω, and R3 = 300 Ω. Calculate Rx.

1. Write the equation: Rx = R2 × R3 ÷ R1.
2. Substitute the known values: Rx = 200 × 300 ÷ 100.
3. Multiply R2 by R3: 200 × 300 = 60,000.
4. Divide by R1: Rx = 60,000 ÷ 100 = 600 Ω.

The unknown resistance is therefore 600 Ω. The two ratios are 100 ÷ 200 = 0.5 and 300 ÷ 600 = 0.5, so the bridge is balanced.

Differential bridge signal

Wheatstone bridge output-voltage formula

A Wheatstone bridge can also be analyzed as two voltage dividers connected to the same supply. The left midpoint voltage depends on R1 and R2, while the right midpoint voltage depends on R3 and Rx.

Combining the divider equations gives:

A positive result means the left midpoint voltage is higher than the right midpoint voltage. A negative result means the right midpoint is higher. A result of zero volts indicates an ideal balanced bridge.

Worked voltage example

Calculate an unbalanced bridge output

Consider a bridge supplied by 12 V with R1 = 100 Ω, R2 = 300 Ω, R3 = 200 Ω, and Rx = 300 Ω.

1. Calculate the left midpoint voltage: Vleft = 12 × 300 ÷ (100 + 300) = 9 V.
2. Calculate the right midpoint voltage: Vright = 12 × 300 ÷ (200 + 300) = 7.2 V.
3. Subtract the right voltage from the left: Vout = 9 − 7.2 = 1.8 V.

The bridge output is +1.8 V. Because the two midpoint voltages are different, the bridge is unbalanced.

Balanced voltage condition

Why does a balanced bridge produce zero output?

When the resistance ratios are equal, both divider arms produce the same fraction of the supply voltage at their midpoint. Subtracting two equal voltages gives zero.

This zero-output condition is also called a null condition. Null measurements can be highly sensitive because the detector only needs to identify whether a small difference remains rather than measure the complete resistance directly.

Detecting small resistance changes

Wheatstone bridge sensitivity

A bridge initially adjusted to balance can produce a measurable voltage when one resistor changes by a very small amount. This makes the circuit useful with resistive sensors whose resistance varies with force, pressure, strain, temperature, light, or another physical quantity.

Sensitivity depends on the supply voltage, nominal resistor values, bridge geometry, sensor position, and the input impedance and gain of the measurement circuit. A larger supply voltage generally produces a larger output for the same fractional resistance change, but it can also increase sensor self-heating and power dissipation.

Practical instruments often feed the small differential output into an instrumentation amplifier. This amplifier provides high input impedance, good common-mode rejection, and sufficient gain for data acquisition or control systems.

Sensor bridge arrangements

Quarter-, half-, and full-bridge circuits

Measurement bridges are often classified by the number of active sensing elements in the four bridge arms.

• A quarter bridge uses one active sensor and three fixed or completion resistors.
• A half bridge uses two active elements, often arranged to improve sensitivity or temperature compensation.
• A full bridge uses four active sensing elements and can provide the largest output and strongest compensation when arranged correctly.

The basic calculator on this page treats all four values as ideal resistances. It does not automatically model strain-gauge orientation, gauge factor, mechanical strain, or temperature compensation.

Laboratory and engineering uses

Where Wheatstone bridges are used

• Measuring an unknown electrical resistance by comparison.
• Strain-gauge load cells and force sensors.
• Pressure transducers and diaphragm sensors.
• Resistance-temperature detectors and thermistor circuits.
• Precision calibration and resistance standards.
• Structural testing and material-strain measurement.
• Electronic scales and weighing systems.
• Educational laboratory experiments on resistance ratios and null measurement.

Input consistency

Resistance and voltage units

Enter every resistance using one consistent unit. For example, all four values may be entered in ohms or all four may be entered in kilo-ohms. Mixing 100 ohms with a value entered as 2 but intended to mean 2 kilo-ohms will produce an incorrect ratio.

• Ohm inputs produce an unknown resistance in ohms.
• Kilo-ohm inputs produce an unknown resistance in kilo-ohms.
• Supply voltage should be entered in volts.
• Output voltage is reported in volts and may be positive, negative, or zero.

Resistance ratios are dimensionless, so the balance condition is unaffected by the chosen resistance scale as long as the values are consistent.

Real component behavior

Resistor tolerance and bridge error

Real resistors do not normally equal their marked values exactly. A resistor with a one-percent tolerance may differ from its nominal resistance by as much as one percent under specified conditions.

Small deviations in any bridge arm can create a nonzero output even when the nominal resistor values appear balanced. Precision bridge circuits therefore use accurate matched resistors, trimming components, calibration procedures, or software correction.

Temperature also changes resistance. Matched components with similar temperature coefficients can reduce drift, while physical placement and thermal symmetry can improve measurement stability.

Practical measurement factors

Meter loading, lead resistance, and noise

An ideal bridge detector draws no current. A real voltmeter or amplifier has finite input impedance and can slightly load the bridge. High-input-impedance measurement equipment minimizes this effect.

Lead and contact resistance can become important when measuring very low resistances. Kelvin or four-wire connections are commonly used in precision low-resistance measurements to separate current-carrying leads from voltage-sensing leads.

Electrical noise, supply ripple, electromagnetic interference, and thermoelectric voltages can also affect small bridge signals. Shielding, filtering, stable excitation, differential amplification, and careful grounding help preserve measurement accuracy.

Practical laboratory method

How to use a Wheatstone bridge

1. Connect the four resistors in the bridge arrangement represented by R1, R2, R3, and Rx.
2. Apply a stable supply voltage across the top and bottom bridge nodes.
3. Connect a sensitive voltmeter or null detector between the two midpoint nodes.
4. Adjust a known resistance, when the physical bridge includes an adjustable element, until the detector approaches zero.
5. Record the three known resistance values at balance.
6. Calculate the unknown value using Rx = R2 × R3 ÷ R1.
7. Repeat the measurement when necessary and estimate uncertainty from component tolerances, instrument resolution, and repeatability.

Before applying power, verify the resistor ratings and expected current. High supply voltage or low resistance can cause excessive power dissipation and component heating.

Component safety

Resistance, current, and power dissipation

Each bridge arm forms a series branch across the supply. The current in the left arm and right arm can be estimated independently.

A resistor's calculated power should remain comfortably below its rated power. Temperature rise can change resistance and create additional measurement error even when the component is not immediately damaged.

Understanding the result

How to interpret bridge output

• Vout = 0 V: the ideal bridge is balanced.
• Vout > 0 V: the left midpoint voltage is higher than the right midpoint voltage.
• Vout < 0 V: the right midpoint voltage is higher than the left midpoint voltage.
• A small nonzero result may represent a real sensor change, component mismatch, measurement offset, temperature drift, or electrical noise.

The sign of output depends on which midpoint is defined as positive. Reversing the meter leads reverses the sign but does not change the magnitude of imbalance.

Model assumptions

Assumptions and limitations

This calculator models an ideal resistive Wheatstone bridge supplied by a steady direct voltage. Every resistance must be positive and finite.

It does not automatically include resistor tolerance, temperature coefficient, self-heating, detector loading, source resistance, lead resistance, contact resistance, noise, amplifier offset, or calibration uncertainty.

Reactive AC bridge circuits containing capacitors or inductors require complex impedance calculations. Those circuits cannot be analyzed correctly by replacing impedance with resistance alone.

Common questions

Wheatstone bridge calculator FAQ