Formula used
A Wheatstone bridge has four resistive arms. With a supply applied across the top and bottom nodes, the detector measures the voltage between the two middle nodes. The bridge is balanced when those middle-node voltages are equal:
- R1 / R2 = R3 / R4
- Equivalent balance forms: R1·R4 = R2·R3 and R4 = (R2·R3)/R1 (solve any arm similarly).
For unbalanced analysis, the middle-node voltages (open circuit) are computed using divider relations:
- Vleft = Vs · R2 / (R1 + R2)
- Vright = Vs · R4 / (R3 + R4)
- Vout(open) = Vleft − Vright
When a detector with resistance Rg is connected between the middle nodes, the current is estimated using a Thevenin model:
- Rth = (R1 || R2) + (R3 || R4)
- Ig = Vout(open) / (Rth + Rg)
How to use this calculator
- Select which arm you want to solve for balance.
- Enter the three known arm resistances in ohms.
- Leave the selected unknown arm blank (recommended).
- Optionally enter Vs and Rg to evaluate output and meter current.
- Set a tolerance percentage to estimate a practical trim range.
- Press Calculate to view results above the form.
- Use Download CSV to save inputs and computed values.
- Use Download PDF to print or save the report.
Example data table
| Case | R1 (Ω) | R2 (Ω) | R3 (Ω) | Balanced R4 (Ω) | Vs (V) | Rg (Ω) | Vout(open) (mV) | Ig (µA) |
|---|---|---|---|---|---|---|---|---|
| 1 | 1000 | 500 | 2000 | 1000 | 5 | 1000 | 0 | 0 |
| 2 | 1200 | 800 | 1500 | 1000 | 3.3 | 2000 | 0 | 0 |
| 3 | 1000 | 1000 | 1000 | 900 | 5 | 500 | 131.579 | 120.5 |
Practical guide to Wheatstone bridge balancing
1) Why balance matters
A balanced bridge drives the detector voltage toward zero, allowing small resistance changes to stand out from the baseline. In metrology and sensing, a near-zero output reduces offset drift and simplifies amplification. In an ideal balance, the ratio condition R1/R2 = R3/R4 holds exactly.
2) Typical resistance ranges
Many lab demonstrations use arms from 100 Ω to 10 kΩ. Strain-gauge bridges commonly use 120 Ω, 350 Ω, or 1000 Ω gauges. Precision resistor decades often provide 0.01% to 0.1% accuracy, while general parts are 1% to 5%.
3) Sensitivity near balance
Around balance, the output changes approximately linearly with a small change in one arm. For equal arms (R1=R2=R3=R4=R), a small increase ΔR in R4 produces an open-circuit output of about Vout ≈ Vs·(ΔR)/(4R). This explains why higher supply voltage increases signal, while larger base resistance reduces it.
4) Using the computed unknown
This calculator solves the selected unknown arm so the bridge balances. For example, if R4 is unknown, it uses R4 = (R2·R3)/R1. The tolerance range estimates worst-case limits when the known resistors vary by the chosen percent. A trim potentiometer can be sized to cover this range.
5) Detector current and protection
Real detectors have finite resistance. The meter current depends on the Thevenin resistance seen between mid nodes: Rth = (R1||R2) + (R3||R4). High imbalance with a low Rg can create excess current. Use the displayed current and power to decide whether a series resistor or higher Rg is needed.
6) Best practices in measurements
Keep lead lengths short, use stable connections, and allow resistors to reach thermal equilibrium. For low-ohm bridges, contact resistance becomes significant; for high-ohm bridges, input leakage matters. Choose a supply that avoids self-heating, especially for strain gauges and temperature sensors.
7) Common applications
Wheatstone bridges are used for resistance metrology, strain-gauge load cells, pressure transducers, and RTD temperature sensing. In quarter-, half-, and full-bridge sensor layouts, balance improves linearity and allows differential amplification with good noise rejection.
8) Interpreting imbalance percentage
The imbalance percentage compares the left and right ratios. Values near 0% indicate near balance, while larger magnitudes suggest a wiring mistake, swapped arms, or a resistor that is far from nominal. Use the open-circuit output and ratio check together for troubleshooting.
FAQs
1) What does “balanced” mean in a Wheatstone bridge?
A bridge is balanced when the two middle-node voltages are equal, so the detector sees nearly zero voltage and negligible current.
2) Which arm should I choose as the unknown?
Choose the arm you can adjust or replace in practice. Many setups use a variable resistor for one arm, so solving that arm provides a direct target value.
3) Why does my output voltage stay nonzero even near balance?
Lead resistance, contact resistance, resistor tolerance, and detector loading can shift the balance point. Small wiring asymmetries also create residual output.
4) How does supply voltage affect sensitivity?
Higher supply voltage increases the output voltage change for the same resistance change. However, too much voltage can cause self-heating and drift in sensors.
5) What is the role of galvanometer resistance Rg?
Rg loads the bridge. A larger Rg draws less current and reduces loading effects. A smaller Rg increases current and can exaggerate imbalance or risk meter damage.
6) How should I use the tolerance range?
Use it to pick a trim range for a potentiometer or resistor decade. The range approximates worst-case balance limits when the known resistors vary by the stated percent.
7) Can this calculator be used for sensor bridges?
Yes. For strain gauges or RTDs, enter nominal resistances and solve the balancing arm. Then evaluate output voltage and detector current for expected resistance changes.