numvana

Wheatstone Bridge Calculator

Find the unknown resistance that balances a Wheatstone bridge (Rx = R2 × R3 ÷ R1) and the bridge's output voltage for a given actual Rx.

Rx that balances the bridge
100 Ω
Bridge output voltage (at entered Rx)
0 mV
Bridge balanced?
Yes

How it works

A Wheatstone bridge wires four resistors in a diamond — R1 and Rx in one branch, R2 and R3 in the other — with a meter across the two midpoints. The bridge reads zero volts (is 'balanced') exactly when the two branches' resistance ratios match: R1/Rx = R2/R3. Rearranged for the unknown, that gives Rx = (R2 × R3) ÷ R1 — the standard way to measure an unknown resistor against three known, precise ones without needing an absolute voltage or current reading.

Away from balance, this calculator also reports the bridge's actual output voltage for whatever Rx you enter, using the general bridge-output formula Vout = Vex × [R3/(R1+R3) − Rx/(R2+Rx)] — useful for seeing how far off balance (and in which direction) a real measured Rx is from the value that would zero the bridge.

FAQ

Which arm is R1 versus R2/R3?

R1 sits in the same branch as Rx (the resistor being measured), while R2 and R3 form the other, known branch. The balance condition R1×R3 = R2×Rx (equivalently Rx = R2×R3/R1) only holds with the resistors wired in that arrangement — swapping which known resistor sits opposite which changes the ratio.

Why use a bridge instead of just measuring resistance directly?

A balanced bridge depends only on resistance ratios, not on the exact excitation voltage or a meter's absolute accuracy — you're detecting a null (zero) reading, which is far more precise than reading an absolute voltage or current value off a real-world instrument. That's why bridge circuits remain the standard for precision resistance measurement, and the same balanced-ratio principle underlies strain gauge and load cell circuits.

Related calculators