Calculators
Wheatstone Bridge Calculator
Analyze an ideal Wheatstone bridge and solve the balance condition.
Analyze an ideal unloaded Wheatstone bridge. Enter all resistance values in the same unit; the calculated balance relationship is independent of whether you use Ω, kΩ, or MΩ.
Convention: R1 over R2 is the left divider, R3 over R4 is the right divider, and Vout = Vleft − Vright.
Bridge output voltage
0 V
Balanced bridge
Left midpoint2.5 V
Right midpoint2.5 V
R1 / R21
R3 / R41
R4 required for balance2200 (same resistance unit as inputs)
This is an ideal DC divider model. A real measuring instrument, sensor, resistor tolerance, self-heating, lead resistance, and source resistance can change the observed output.
About This Tool
A Wheatstone bridge compares two resistor-divider ratios. It is widely used to detect small resistance changes and to measure an unknown resistance relative to known values. This calculator models an ideal four-resistor bridge supplied by a DC voltage. It shows the two divider midpoint voltages, their signed difference, whether the bridge is balanced, and the R4 value that would satisfy the balance equation for the entered R1, R2, and R3 values.
How To Use It
- Enter the DC supply voltage across the top and bottom nodes of the bridge.
- Enter R1 and R2 for the upper and lower resistors of the left divider, then R3 and R4 for the right divider. Use one consistent resistance unit for all four values.
- Read Vleft, Vright, and Vout. This calculator defines Vout as Vleft minus Vright, so swapping measurement leads reverses the sign.
- For a null-balance measurement, compare the entered R4 with the calculated R4 required for balance.
Examples
Balanced bridge with unequal resistor values
With R1 = R2 = 1 kΩ and R3 = R4 = 2.2 kΩ, both ratios are 1. A 5 V supply puts each midpoint at 2.5 V, so the ideal differential output is 0 V.
Unbalanced bridge
For a 5 V supply, R1 = 1 kΩ, R2 = 2 kΩ, R3 = 1 kΩ, and R4 = 1 kΩ, the left midpoint is about 3.333 V and the right midpoint is 2.5 V. With the stated polarity, Vout is about +0.833 V.
Solve an unknown resistance at balance
If R1 = 120 Ω, R2 = 330 Ω, and R3 = 470 Ω, balance requires R4 = R2 × R3 / R1 = 1292.5 Ω. At ideal balance, the detector between the midpoint nodes sees zero differential voltage.
Useful Notes
Wheatstone bridge output formula
Each side is an unloaded voltage divider. Vleft = Vs × R2/(R1 + R2) and Vright = Vs × R4/(R3 + R4). Using this page's polarity convention, Vout = Vleft − Vright. A negative result simply means the right midpoint is at a higher potential than the left midpoint.
Balance condition
The bridge is balanced when its midpoint voltages are equal. For positive resistor values this reduces to R1/R2 = R3/R4, or equivalently R1 × R4 = R2 × R3. Solving for R4 gives R4 = R2 × R3 / R1.
Why resistance units can be shared
The divider equations depend on resistance ratios. If every resistor is entered in the same unit, that common scale cancels. Four values entered in kΩ therefore produce the same bridge voltages as the corresponding values entered in Ω.
Loaded versus unloaded bridges
The simple formulas assume the midpoint measurement does not draw meaningful current. A real voltmeter, amplifier, ADC input, or detector has finite input impedance. If that impedance is not very large compared with the bridge resistances, it loads the network and changes the midpoint voltages.
Sensors and small resistance changes
Strain gauges, RTDs, pressure sensors, and other resistive elements are often arranged in bridge circuits because a small resistance change can create a measurable differential voltage around a balanced operating point. Accurate sensor conversion requires the sensor's transfer behavior, excitation limits, temperature effects, wiring, and amplifier characteristics in addition to the ideal bridge equations.
Practical error sources
Resistor tolerance, temperature coefficient, self-heating, contact and lead resistance, supply variation, and measurement offset can all affect a physical bridge. Precision measurements commonly use calibrated components, stable excitation, suitable instrumentation amplifiers, and error analysis rather than relying on nominal resistor values alone.
FAQ
What does a zero output voltage mean?
In the ideal unloaded model, zero differential output means the two divider midpoint voltages are equal and the bridge ratios satisfy the balance condition. It does not prove that real components have their exact nominal values.
Can I enter resistor values in kΩ?
Yes. Enter all four resistors in the same resistance unit. The voltage result depends on ratios, and the calculated R4-for-balance result is expressed in that same input unit.
Why can the bridge output be negative?
The sign depends on which midpoint is treated as positive. This calculator uses left midpoint minus right midpoint. Reversing meter or amplifier inputs reverses the sign without changing the magnitude.
Does supply voltage affect the balance resistance?
Not in the ideal ratio model. Supply voltage scales the midpoint and differential voltages, while the resistor ratio required for balance remains the same.
Can this calculate strain directly from a strain gauge bridge?
No. Converting bridge voltage into strain requires gauge factor, bridge configuration, excitation, temperature compensation, and other sensor-specific assumptions. This tool intentionally stays with the general ideal resistor bridge.
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