What this calculator does
A Wheatstone bridge measures resistance by comparison rather than by measuring current and voltage directly. Four resistors are arranged in two branches, and the bridge is balanced when no current flows through the detector between them.
The reason it is so accurate is that balance depends only on the ratios of the resistances, not on the supply voltage or on the sensitivity of the detector. A null reading is far easier to identify precisely than a small deflection.
The formula
At balance, R1 divided by R2 equals R3 divided by the unknown, so the unknown equals R2 times R3 divided by R1. The ratio rows confirm the balance condition holds.
| Term | Meaning |
|---|---|
| Balance condition | The state where no current flows through the detector, which occurs when the two branch ratios are equal. |
| Null measurement | Measuring by adjusting until a reading is zero, which avoids depending on the accuracy of the meter. |
| Bridge arm | Each of the four resistances in the arrangement. |
The inputs explained
| Field | What to enter |
|---|---|
| R1 (Ω) | The first known resistance, in ohms. |
| R2 (Ω) | The second known resistance, in ohms. |
| R3 (variable arm at balance) (Ω) | The variable arm adjusted to achieve balance, in ohms. |
When to use it
Measuring an unknown resistance precisely
Comparing against known resistors avoids depending on the accuracy of a voltmeter or ammeter.
Reading a strain gauge
Strain gauges change resistance by a tiny fraction, and a bridge turns that change into a measurable voltage.
Understanding sensor circuits
Many resistive sensors, including thermistors and load cells, are read through a bridge for exactly this reason.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the unknown resistance follow the variable arm?
The same fixed arms with the variable arm adjusted across a range.
| R3 (variable arm) | Unknown resistance Rx | Ratio R1/R2 |
|---|---|---|
| 100 Ω | 150.000 Ω | 0.6667 |
| 150 Ω | 225.000 Ω | 0.6667 |
| 220 Ω | 330.000 Ω | 0.6667 |
Questions
Why is a null measurement more accurate?
Because identifying exactly zero is far easier than reading a precise non-zero value. The detector only needs to be sensitive, not calibrated, and the supply voltage drops out of the calculation entirely.
Does the supply voltage affect the result?
Not at balance. Higher voltage makes the detector more sensitive to being off balance, but the balance point itself depends purely on the resistance ratios.
Why are bridges used for strain gauges?
Because a strain gauge changes resistance by perhaps a tenth of a per cent. Measuring that directly is hard; measuring the resulting bridge imbalance against a reference is straightforward.
What if the bridge cannot be balanced?
Usually the unknown lies outside the range the variable arm can reach, which is fixed by changing the ratio arms. Bridges typically offer several ratio settings to cover different decades of resistance.
For combining resistances directly, see the resistors in series and parallel calculator. For the voltage division underlying each branch, see the voltage divider calculator.