Wheatstone Bridge Balance Calculator
What a balanced Wheatstone bridge tells you
A Wheatstone bridge measures an unknown resistance by comparing two resistor ratios. At balance, the detector or galvanometer between the middle nodes reads zero because both sides of the bridge sit at the same potential. That null condition is powerful: it lets you compute the unknown resistance from three known resistors without needing to measure current through the unknown directly.
Balance formula
For the arrangement used by this calculator, the balance condition is
Solving for the unknown arm gives
All resistance values must use the same unit. If you enter R1, R2, and R3 in ohms, the result is ohms. If you enter them all in kiloohms, the result is kiloohms.
Worked example
If R1 = 120 Ω, R2 = 100 Ω, and R3 = 150 Ω, then Rx = (100 / 120) × 150 = 125 Ω. The bridge is balanced when the unknown arm is 125 Ω, because the two divider ratios match and the detector branch has no voltage difference.
Comparison table
| R1 | R2 | R3 | Computed Rx | Note |
|---|---|---|---|---|
| 120 Ω | 100 Ω | 150 Ω | 125 Ω | Default teaching example |
| 1 kΩ | 1 kΩ | 470 Ω | 470 Ω | Equal ratio arms copy R3 |
| 10 kΩ | 2 kΩ | 5 kΩ | 1 kΩ | Smaller R2/R1 ratio lowers Rx |
Practical notes
Real bridge measurements depend on resistor tolerance, temperature coefficient, lead resistance, detector sensitivity, and noise. Precision bridges often use stable reference resistors and a variable arm that can be adjusted until the detector reads null. For sensors such as strain gauges or thermistors, a bridge may be intentionally unbalanced so the detector voltage reveals a small resistance change. This calculator covers the balanced case only.
Measurement workflow
Use resistors with tolerance appropriate to the unknown you are trying to infer. If R1 and R2 are only 5% parts, the computed Rx should not be treated as a precision measurement. A bridge is most useful when the ratio arms are stable and the unknown sits in a range where the detector can resolve a small imbalance.
Keep all values in the same unit before entering them. Mixing ohms and kiloohms is the most common input error because the ratio may still look plausible. If the computed result seems far outside the expected range, rescale the inputs, check whether R1 and R2 were swapped, and verify that the physical circuit matches the arrangement assumed by the calculator.
Assumptions and limitations
The equation assumes an ideal null measurement with no detector current at balance. It does not include thermoelectric offsets, contact resistance, self-heating, AC bridge effects, or sensor nonlinearity. Use the result to understand the balance ratio, then apply instrument uncertainty and component tolerance for lab or field measurements.
For teaching, change one resistor at a time and watch how the required unknown moves. Increasing R2 relative to R1 raises Rx, while increasing R1 relative to R2 lowers it. That ratio behavior is the central idea behind bridge measurements and is easier to remember than the formula alone.
If you are matching a real unknown resistor, choose ratio arms that keep the computed Rx near the expected value. Extremely unbalanced ratios can produce mathematically valid answers that are awkward to realize with available resistor decades or trim ranges.
Bridge Null Hunter Mini-Game
Temperature swings, contact resistance, and sensor drift nudge the Wheatstone bridge off its perfect ratio. Tune the variable arm fast enough to hold the galvanometer near zero and bank calibration points before the null escapes.
Null offset: awaiting launch.