Free · Electrical networks

Wheatstone Bridge: Voltage and Resistance Ratios

Calculate ideal unloaded bridge midpoint voltage or the resistance ratio needed for a balanced four-resistor bridge.

Formula & worked example
Private in your browser
No signup

Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With 12 V excitation, left resistors 100/100 ohms and right resistors 100/300 ohms, midpoint voltages are 6 V and 9 V. Right-minus-left output is 3 V.

Vbridge=Vin[Rx/(R3+Rx)−R2/(R1+R2)]; balanced Rx=R2 R3/R1

Worked example

Enter these known values and leave the other values blank.

I want to calculate the...: Voltage across the bridge VG
Excitation: top relative to bottom: 12 V
R==1==: 100 Ω
R==2==: 100 Ω
R==3==: 100 Ω
R==x==: 300 Ω

Bridge output: right midpoint minus left: 3 V

Assumptions and limitations

Ideal positive resistances and an unloaded midpoint measurement. Meter input current, wire/contact resistances, component tolerances, self-heating and frequency dependence are excluded.
R1 is upper left, R2 lower left, R3 upper right and Rx lower right. Excitation is top-node voltage relative to the common bottom node; bridge output is right midpoint minus left midpoint.
Balanced mode calculates the resistor ratio for a nonzero excitation and zero differential midpoint voltage. It does not infer a resistance from a zero-voltage unexcited circuit.
Resistance inverse solutions require sufficient independent known values and a nonzero excitation. A bridge voltage outside the two positive-divider limits cannot imply a positive unknown resistance.

Common questions

What does a negative bridge voltage mean?

The right midpoint is below the left midpoint under the declared right-minus-left sign convention. It does not mean a negative resistance.

Which resistors make the bridge balanced?

The two divider ratios must match: R2/(R1+R2)=Rx/(R3+Rx), giving Rx=R2 R3/R1 for positive resistances.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

Explore electrical networks or browse all physics calculators.