Bridge circuit inputs
Choose a mode, enter the arm values, and compute output or solve an unknown arm at balance.
Example data table
| Case | R1 (Ω) | R2 (Ω) | R3 (Ω) | R4 (Ω) | Vs (V) | Expected Vout (V) | Note |
|---|---|---|---|---|---|---|---|
| Balanced | 1000 | 1000 | 1000 | 1000 | 5 | 0 | Equal ratios on both legs. |
| Slight unbalance | 1000 | 1000 | 1000 | 1010 | 5 | ≈ -0.0124 | Right divider shifts lower node voltage. |
| Solve unknown | 1000 | 500 | 2000 | ? | 5 | 0 | At balance, R4 = R3·R2/R1 = 1000. |
Use the table as a quick check for your inputs and expected behavior.
Formula used
Node voltages
Left midpoint: Vleft = Vs · R2 / (R1 + R2)
Right midpoint: Vright = Vs · R4 / (R3 + R4)
Right midpoint: Vright = Vs · R4 / (R3 + R4)
Bridge output
Open-circuit output (left minus right): Vout = Vleft − Vright
Normalized output: Vout/Vs helps compare different supplies.
Normalized output: Vout/Vs helps compare different supplies.
Balance condition
A resistive bridge is balanced when R1/R2 = R3/R4, producing Vout ≈ 0.
Solving an unknown arm at balance
If R4 is unknown: R4 = (R3 · R2) / R1.
Similar rearrangements apply for unknown R1, R2, or R3.
Similar rearrangements apply for unknown R1, R2, or R3.
Output loading via Thevenin
Divider equivalents: Rleft = R1 || R2, Rright = R3 || R4.
Output resistance: Rout = Rleft + Rright.
With load RL: Vout_loaded = Vout · RL / (RL + Rout).
Output resistance: Rout = Rleft + Rright.
With load RL: Vout_loaded = Vout · RL / (RL + Rout).
How to use this calculator
- Select Analyze to compute output, balance ratios, and loading effects.
- Pick a resistance unit, then enter R1–R4 and supply voltage Vs.
- Optionally add RL to model measurement or amplifier input loading.
- Add tolerance to estimate a worst-case output magnitude from component variation.
- Use temperature and coefficient fields to see drift relative to 25°C.
- Use Solve when one arm is unknown and the bridge is balanced.
FAQs
1) What is a bridge circuit used for?
A bridge compares two voltage dividers to detect tiny resistance changes. It is common in sensors, calibration tasks, and precision measurement where small unbalance produces a measurable output.
2) When is a Wheatstone bridge balanced?
The bridge is balanced when the divider ratios match: R1/R2 equals R3/R4. At balance, the midpoint voltages are equal and the output between midpoints is ideally zero.
3) Why does my output change when I add RL?
RL draws current from the bridge output and forms a divider with the bridge’s output resistance. If RL is not much larger than Rout, the measured voltage is reduced and may shift your reading.
4) How can I estimate error from resistor tolerance?
Enter a tolerance percentage to see a worst-case output estimate using corner combinations. This is a simple design check that highlights sensitivity when ratios are close but not perfectly matched.
5) Which arm should be the unknown for best results?
Choose the arm that is practical to adjust or measure. In many labs, the unknown is placed in one arm and a precision decade resistor is used in another arm to re-balance reliably.
6) What does “Normalized Vout/Vs” mean?
It is the output voltage divided by the supply voltage. This ratio makes it easy to compare bridge behavior under different supplies and helps with amplifier gain planning.
7) How should I model temperature effects?
Provide an ambient temperature and a temperature coefficient in ppm/°C. The calculator applies the same coefficient to all arms as a quick drift estimate relative to 25°C.
8) Can this handle AC impedance bridges?
This tool focuses on resistive bridges. For AC impedance bridges, complex impedances and phase must be modeled. You can still approximate using equivalent resistances when reactance is negligible.