0
V
0
Ω²
2.5
V
2.5
V
1,000
Ω
0
V
0
Ω²
2.5
V
2.5
V
1,000
Ω
The Wheatstone bridge is a precision electrical measurement circuit invented by Samuel Hunter Christie in 1833 and popularized by Sir Charles Wheatstone. It consists of four resistors arranged in a diamond (rhombus) topology: R1 and R3 form one voltage divider (left arm), R2 and R4 form a second voltage divider (right arm), both supplied from the same source voltage. The output voltage is measured across the midpoints of the two dividers.
The bridge is balanced (Vout = 0) when the ratio R1/R3 = R2/R4, or equivalently, R1 × R4 = R2 × R3. At balance, both midpoints are at exactly the same potential, and no current flows through a galvanometer or differential amplifier connected across the output. This null condition is detected with great precision, making the Wheatstone bridge one of the most accurate resistance measurement methods available.
The classic application is precision resistance measurement: R1, R2, and R3 are known precision resistors, and R4 is the unknown. Adjust a variable reference resistor until the bridge balances (Vout = 0), then R4 = R2 × R3 / R1. This null-detection method is far more accurate than direct Ohm's Law measurement because it is independent of the supply voltage stability and relies only on the precision of the known resistors.
Modern applications use the unbalanced Wheatstone bridge for sensor measurement. When a strain gauge, thermistor, or pressure sensor changes resistance slightly from its nominal value, the bridge becomes unbalanced and produces a small output voltage proportional to the resistance change. Amplified by an instrumentation amplifier, this voltage provides a precise measurement of temperature, strain, pressure, or other physical quantities.
The sensitivity of the bridge at near-balance is: ΔVout ≈ (Vs/4) × ΔR/R for a quarter-bridge (one active element), Vs/2 × ΔR/R for half-bridge, and Vs × ΔR/R for full bridge (all four elements active). Using more active bridge elements improves sensitivity and common-mode noise rejection — a full bridge (all four gauges active, alternating in tension/compression) provides four times the sensitivity of a single gauge.
In industrial process control, Wheatstone bridge circuits form the core of RTD (resistance temperature detector) transmitters, load cell signal conditioners, and pressure transducer electronics. Precision analog-to-digital converters used in weigh scales and industrial measurements use bridge circuits with sub-microvolt resolution instrumentation amplifiers and 24-bit ADCs to achieve measurement resolutions of 1 part in 10 million.
This calculator finds the bridge output voltage, balance condition (R1×R4 − R2×R3 = 0 at balance), individual node voltages at the midpoints, and the value of R4 that would bring the bridge to exact balance — immediately useful for sensor range design and calibration.
Node A voltage: V_A = Vs × R3/(R1+R3). Node B voltage: V_B = Vs × R4/(R2+R4). Bridge output: Vout = V_A − V_B. Balance condition: R1×R4 − R2×R3 = 0 (zero means balanced). Balanced R4: Rx = R2×R3/R1 (solve balance equation for R4). Positive Vout means left arm node A is higher; negative means right arm node B is higher.
Vout = 0: bridge is balanced — R1/R3 = R2/R4. Vout > 0: V_A > V_B, left arm voltage divider provides higher midpoint. Vout < 0: V_B > V_A. Small Vout (millivolts) indicates near-balance typical of sensor measurements. Balance condition = 0 confirms exact balance. The Rx_balanced value shows the R4 needed for null.
Inputs
Results
Perfectly balanced bridge: all 1 kΩ, 5 V supply. Both midpoints at 2.5 V, Vout = 0. Any change in R4 (sensor) from 1 kΩ produces a proportional output voltage.
Inputs
Results
A 350 Ω strain gauge changing by 0.35 Ω (0.1% resistance change, typical for 1000 µε strain) with 10 V excitation produces Vout ≈ −2.5 mV — typical quarter-bridge sensitivity of 2.5 mV per milliohm change at this excitation.
A Wheatstone bridge is balanced when R1/R3 = R2/R4, or equivalently R1 × R4 = R2 × R3. At balance, Vout = 0 regardless of supply voltage. This null condition makes the measurement independent of supply voltage drift — only the precision of the known resistors R1, R2, R3 limits accuracy.
Quarter bridge: one active sensor element (R4), other three are fixed. Half bridge: two active elements (e.g., R3 and R4 in tension and compression). Full bridge: all four elements are active sensors. Full bridge offers highest sensitivity (4× quarter bridge), best temperature compensation, and best rejection of common-mode disturbances like temperature changes.
A strain gauge changes resistance proportionally to mechanical strain: ΔR/R = GF × ε, where GF is the gauge factor (~2 for metal foil gauges) and ε is strain in µε. The bridge converts this tiny ΔR into a measurable voltage. For 1000 µε and GF = 2: ΔR/R = 0.002. With V_supply = 10 V, Vout ≈ V_supply × GF × ε / 4 = 10 × 0.002 / 4 = 5 mV. An instrumentation amplifier amplifies this to a usable signal level.
An instrumentation amplifier (in-amp) is a differential amplifier with very high common-mode rejection ratio (CMRR), high input impedance, and precise, adjustable gain. Bridge outputs are differential small signals on a large common-mode voltage (Vs/2). The in-amp amplifies only the differential Vout while rejecting the common-mode offset. INA125, AD620, and similar devices are standard bridge amplifiers with 60–120 dB CMRR.
The Kelvin (Thomson) bridge is a modified Wheatstone bridge for measuring very low resistances (milliohms and microohms), where contact and lead resistances would introduce significant error in a standard Wheatstone bridge. It uses two extra resistors to compensate for the resistance of the current-carrying links, enabling accurate measurement of wire, contact, and bond wire resistances critical in quality control for electronics manufacturing.
Bridge excitation is the supply voltage Vs applied to the bridge. If the same supply voltage powers both the bridge and the ADC reference, the measurement is ratiometric — output voltage Vout = k × Vs, and since ADC full scale also = Vs, the ratio Vout/Vs = k cancels the supply voltage, making the digital reading independent of supply voltage variations. This technique eliminates a major source of measurement error in sensor systems.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Parallel Resistance Calculator
Circuit Analysis Calculators
Series Resistance Calculator
Circuit Analysis Calculators
Parallel Capacitance Calculator
Circuit Analysis Calculators
Series Capacitance Calculator
Circuit Analysis Calculators
Parallel Inductance Calculator
Circuit Analysis Calculators
Series Inductance Calculator
Circuit Analysis Calculators
