Wheatstone Bridge Calculator — Unknown Resistance from Balanced Bridge
A Wheatstone bridge is a precision circuit for measuring unknown electrical resistance. Enter the three known resistors (R1, R2, R3) and the calculator solves for the unknown resistance Rx using the balanced-bridge condition, then shows the ratio arms and optional sensitivity.
Ω
Ω
Ω
V
Rx = R2 × R3 ÷ R1 (balanced bridge condition)
- 1
Ratio arm R1 ÷ R2
100 ÷ 200 = 0.5 - 2
Numerator R2 × R3
200 × 150 = 30,000 - 3
Unknown resistance Rx = R2 × R3 ÷ R1
30,000 ÷ 100 = 300At bridge balance R1/R2 = R3/Rx, rearranged to solve for Rx.
How does this calculator work?
Solve for unknown resistance with Rx = R2 × R3 ÷ R1. The Wheatstone bridge balances when R1/R2 = R3/Rx — at that point the galvanometer reads zero and Rx is determined precisely. Enter R1, R2, and the standard resistance R3; adjust the ratio arm (R1/R2) to set your measurement range.
Formula
How this is calculated
A Wheatstone bridge consists of four resistors arranged in a diamond: R1 and R2 form one voltage-divider arm (the ratio arm); R3 and the unknown Rx form the other (the measurement arm). A battery is connected across one diagonal and a galvanometer across the other. The bridge is balanced — galvanometer current is zero — when the two divider ratios are equal: R1/R2 = R3/Rx. Rearranging gives Rx = R2 × R3 ÷ R1.
In practice, R3 is a calibrated variable resistor that is adjusted until the galvanometer reads zero, at which point the unknown Rx can be read from R3. The ratio arm (R1/R2) sets the measurement range: a 1:1 ratio gives Rx ≈ R3; a 10:1 ratio multiplies R3 by 10, allowing very large or very small resistances to be measured by scaling R1/R2.
The sensitivity field (V/Ω) tells you how much the output voltage changes per ohm deviation near balance — higher sensitivity means the galvanometer deflects more visibly for a small Rx change, giving a more precise null detection. Sensitivity = Vs × R3 / (R3 + Rx)² at balance. This calculator assumes ideal components: no contact resistance, no thermoelectric EMFs, and a galvanometer with infinite input resistance.
Frequently asked questions
Balanced means the galvanometer reads zero — no current flows through it. This happens when R1/R2 = R3/Rx, so the two voltage dividers produce identical mid-point voltages. At balance, the unknown Rx can be calculated precisely from the three known values.
A Wheatstone bridge nulls the measurement — you detect zero current rather than measuring a small one. This eliminates errors from contact resistance, lead resistance, and meter accuracy. The null method can achieve parts-per-million precision that ohmmeters cannot match.
The ratio arm scales the measurement range. With R1 = R2 (ratio 1:1) Rx ≈ R3, suitable for mid-range resistances. Setting R1 = 10 × R2 gives Rx = R3/10 (useful for small Rx); R1 = R2/10 gives Rx = 10 × R3 (for large Rx). Most precision bridges offer switchable ratio arms of 1, 10, 100, and 1 000.
Also known as
TG we-Calculate Editorial Team. (2026). Wheatstone Bridge Calculator — Unknown Resistance from Balanced Bridge [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/wheatstone-bridge-calculator
TG we-Calculate Editorial Team. "Wheatstone Bridge Calculator — Unknown Resistance from Balanced Bridge." TG we-Calculate. 2026. https://we-calculate.com/calculator/wheatstone-bridge-calculator.
TG we-Calculate Editorial Team, "Wheatstone Bridge Calculator — Unknown Resistance from Balanced Bridge," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/wheatstone-bridge-calculator
@misc{wecalculate_wheatstone_bridge_calculator, title = {Wheatstone Bridge Calculator — Unknown Resistance from Balanced Bridge}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/wheatstone-bridge-calculator}}, year = {2026}, note = {TG we-Calculate} }
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