This calculator finds the unknown resistance in a balanced Wheatstone bridge from the three known resistors, the classic method for measuring resistance precisely. The Wheatstone bridge is one of the most elegant circuits in electronics: four resistors arranged in a diamond, with a sensitive detector across the middle. When the bridge is balanced, no current flows through the detector, and at that point the ratios of the resistances on each side are equal. This lets you determine an unknown resistance with great accuracy by adjusting a known variable resistor until balance is reached, then reading off the value, rather than measuring current or voltage directly, which is far less precise. The principle underlies precision resistance measurement, strain gauges, and many sensor circuits where tiny changes in resistance must be detected. This calculator does the balance calculation. You enter the three known resistances, and the calculator returns the unknown resistance that would balance the bridge, the bridge ratio, and the known values for reference. The results update as you type. Use it for electronics and physics study, for designing bridge circuits, or for sensor work. At balance, the unknown resistance equals the third resistor multiplied by the ratio of the second to the first, following from the equal-ratio condition that defines a balanced bridge. The beauty of the method is that it depends only on the ratios of resistances, not on the supply voltage or the sensitivity of the detector, as long as the detector can tell when the current is zero. This makes it inherently accurate, since a null reading is easy to judge precisely. Wheatstone bridges remain widely used today in instrumentation, particularly with strain gauges in load cells and pressure sensors, where the bridge converts a tiny resistance change into a measurable voltage. The arrangement here takes the unknown as the fourth arm balanced against the other three.
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300 Ω
unknown resistance (Rx) at balance
Bridge ratio (R2/R1)2
R1100 Ω
R3150 Ω
At balance: R1/R2 = R3/Rx, so Rx = R3 x R2 / R1. Depends only on resistance ratios, not the supply voltage, which is why the bridge is so accurate.
How it works
A Wheatstone bridge is balanced when the ratio of the first pair of resistors equals the ratio of the second pair, so no current flows through the detector. Rearranging that condition, the unknown resistance equals the third resistor multiplied by the ratio of the second resistor to the first.
Worked example
With R1 = 100 ohms, R2 = 200 ohms and R3 = 150 ohms, the unknown resistance that balances the bridge is R3 times R2 divided by R1, which is 150 times 200 divided by 100, equalling 300 ohms. At that value the detector reads zero current and the bridge is balanced.
