Wheatstone Bridge Calculator
Trace a DC resistive bridge from arm ratios to midpoint voltages. Solve the resistance required for balance, quantify the entered mismatch, and see how a finite voltmeter input resistance loads the null signal.
Set the four bridge arms
R1 and R2 form the left divider. R3 and Rx form the right divider. The source is connected across the top and bottom nodes; the detector spans the two midpoints.
The entered Rx is 1.000% above its 1,000.000 Ω balance target. Its midpoint sits higher by 12.438 mV before loading and about 12.437 mV across the 10.000 MΩ detector.
Bridge equations and sign convention
With the detector treated as an open circuit, each side is an independent voltage divider. The left midpoint voltage is excitation multiplied by R2 divided by R1 plus R2. The right midpoint is excitation multiplied by Rx divided by R3 plus Rx. This calculator reports right midpoint minus left midpoint: a positive sign means the right node is at higher electrical potential.
Vright = Vs × Rx ÷ (R3 + Rx)
Vbridge = Vright − Vleft
Balance: R1 ÷ R2 = R3 ÷ Rx, so Rx = R2 × R3 ÷ R1
Balance is a ratio condition, not a requirement that all four resistors be equal. A 1 kΩ over 10 kΩ left side balances a 100 Ω over 1 kΩ right side because both upper-to-lower ratios are the same. The source voltage changes signal magnitude and bridge heating but does not change the ideal balance resistance.
What the null result means
At exact balance, both divider midpoints have the same voltage and an ideal detector draws no current. This null method can compare an unknown against stable ratio arms without requiring the detector to measure the full resistance directly. Historical and precision bridges exploit that comparison, but real metrology adds calibrated standards, reversal, lead compensation, thermal control, guarding, and uncertainty analysis.
The percentage mismatch shown here compares entered Rx with the calculated balance target. It is not the same as bridge output as a percentage of excitation because divider sensitivity is nonlinear and depends on arm values. Near a symmetric bridge, a small fractional resistance change produces roughly one quarter as much fractional output relative to excitation, but use the full equation for reporting.
If Rx is a strain gauge, RTD, thermistor, or other sensor, translate resistance into the physical quantity using that sensor’s calibrated relationship. This calculator stops at resistance and voltage.
Detector loading through Thevenin resistance
A real voltmeter or amplifier has finite input resistance. Looking back into the midpoint pair with an ideal voltage source shorted, the bridge Thevenin resistance equals R1 parallel R2 plus R3 parallel Rx. The open-circuit bridge voltage then drives that resistance in series with the detector input.
The loaded reading equals open bridge voltage multiplied by detector resistance divided by detector resistance plus bridge Thevenin resistance. A 10 MΩ meter barely loads a 1 kΩ bridge, but it can substantially load megohm arms. Input bias current, capacitance, common-mode range, offset voltage, noise, and isolation can matter even when resistance loading looks negligible.
The displayed branch currents and source power assume the detector branch is open. A low-resistance detector couples the dividers, so exact supply current requires a full loaded network solution. This separation keeps the loading claim explicit.
Worked 1% off-balance example
Set R1, R2, and R3 to 1,000 Ω, Rx to 1,010 Ω, and excitation to 5 V. The left divider is symmetric, so its midpoint is exactly 2.500000 V. The right divider midpoint is approximately 2.512438 V. Right minus left is therefore +12.438 mV with no detector connected.
The balance target from R2 × R3 ÷ R1 is 1,000 Ω, making entered Rx 1.000% high. With the source shorted for the Thevenin calculation, the left parallel pair is 500 Ω and the right parallel pair is about 502.49 Ω. Together they present about 1,002.49 Ω to the detector.
A 10 MΩ detector receives approximately +12.437 mV and carries only +1.244 nA in this ideal resistance model. Loading reduces the open signal by about 0.0100%. The left branch carries 2.5000 mA and the right branch carries 2.4876 mA with the detector open. Their combined source power is about 24.938 mW. Individual resistor heating should be checked when excitation or resistance changes.
Build a credible bridge measurement
| Source of error | Effect | Control or test |
|---|---|---|
| Reference tolerance and drift | Moves the ratio and therefore the inferred balance resistance. | Use characterized standards and include calibration uncertainty and temperature coefficients. |
| Lead and contact resistance | Adds to bridge arms, especially damaging low-resistance measurements. | Use appropriate Kelvin or four-terminal connections and clean, stable contacts. |
| Self-heating | Changes temperature-sensitive resistors while the bridge is energized. | Limit excitation, calculate arm power, observe settling, and test at multiple excitation levels. |
| Thermal EMF | Adds a small DC voltage that can imitate imbalance. | Use low-thermal connections and source reversal where the method permits. |
| Detector common mode | A small differential rides on midpoint voltage and may exceed amplifier limits. | Check common-mode input range, isolation, input bias, offset, and protection. |
| Leakage and humidity | Creates unintended parallel resistance for high-value bridges. | Clean insulation, guard sensitive nodes, control humidity, and verify open-circuit behavior. |
Power and safety boundary
This calculator treats every resistor as a linear, positive, time-invariant component and the excitation as ideal DC. It does not model resistor power ratings, voltage coefficients, breakdown, source resistance, transients, inductance, capacitance, or hazardous-energy limits. Even a low-voltage bridge can overheat a small sensor when resistance is low or excitation is excessive.
Do not connect an unisolated bridge, oscilloscope, data-acquisition unit, or meter to mains, high-energy batteries, industrial equipment, or a grounded system without a qualified design and correctly rated protection. Verify category, voltage, current, isolation, fusing, clearances, and procedures. De-energize and confirm absence of hazardous voltage where applicable.
Choosing arm values and excitation
Equal nominal arms maximize symmetry and make small-change interpretation convenient, but they are not mandatory. Select values that keep sensor current and self-heating acceptable while producing a signal large enough for the detector’s noise and offset performance. Very low resistance raises current and lead-error concerns; very high resistance raises leakage, bias-current, noise, and settling concerns.
For a sensor bridge, calculate each arm’s worst-case power over the entire resistance and supply range. Account for supply tolerance, ambient temperature, sensor thermal resistance, duty cycle, and fault conditions. Ratiometric conversion can reduce sensitivity to excitation drift when the analog-to-digital reference follows the same source, but it does not remove bridge heating or reference-resistor drift.
A quarter bridge, half bridge, and full bridge describe how many active sensing elements occupy the arms. Their temperature compensation and sensitivity differ. This generic four-resistor tool lets each arm be entered, but it does not automatically apply strain-gauge gauge factors, completion resistors, three-wire compensation, or mechanical strain relationships.
Measurement record for repeatable results
Record the as-built arm values, excitation measured at the bridge, detector identity, warm-up time, ambient temperature, polarity, and whether the reported voltage was open-circuit or loaded. Repeat a zero check before and after the test. That short record helps distinguish a real sensor change from source drift, connector movement, temperature shift, or a detector that did not remain on the intended range.
Wheatstone bridge FAQs
Must all four resistors match for balance?
No. Balance requires equal arm ratios: R1/R2 equals R3/Rx under this labeling. Many different absolute resistance combinations satisfy that condition.
Why does the bridge output have a sign?
The calculator defines output as right midpoint minus left midpoint. Positive means the right node is higher. Swapping detector leads reverses the observed sign without changing mismatch magnitude.
Does increasing excitation improve accuracy?
It increases the ideal signal, but also raises resistor power as voltage squared and can cause sensor self-heating. Source noise, detector range, component ratings, and thermal error set practical limits.
Why include meter input resistance?
A finite detector completes a path between midpoints and reduces the open-circuit signal. The Thevenin calculation estimates that loading for a purely resistive detector.
Can this measure a strain gauge or RTD directly?
It calculates the bridge’s electrical response. Converting resistance to strain or temperature requires the sensor calibration, wiring configuration, excitation limits, compensation method, and uncertainty budget.
When are four-wire connections needed?
They are valuable when lead and contact resistance is material compared with the unknown or accuracy requirement. The appropriate Kelvin bridge or instrument method must be designed around separate current and potential terminals.
References
These U.S. government metrology and electrical sources support the bridge balance, resistance, and measurement-practice discussion.
- National Bureau of Standards Monograph 39 — Calibration Procedures for Direct-Current Resistance Apparatus
- National Bureau of Standards — A Wheatstone Bridge for Resistance Thermometry
- National Bureau of Standards — Wheatstone Bridges and Accessories for Resistance Thermometry
- U.S. Department of Energy — Electrical Science, Volume 2