Wheatstone Bridge Calculator
Find the unknown resistance of a balanced Wheatstone bridge (Rx = R2·R3/R1) or the output voltage of an unbalanced bridge, with both midpoint voltages and the supply current.
How it works
Balance: R1 / R2 = R3 / Rx → Rx = R2 × R3 ÷ R1 · unbalanced output: Vout = Vs × [Rx ÷ (R3 + Rx) − R2 ÷ (R1 + R2)] (open-circuit, measured right midpoint minus left midpoint)
A Wheatstone bridge is two voltage dividers fed from the same supply: R1 over R2 on the left, R3 over Rx on the right. When the ratios match, both midpoints sit at the same voltage and a galvanometer between them reads zero — so an unknown resistance can be measured very precisely from three known ones, independent of the supply voltage. Slightly unbalanced bridges are how strain gauges, RTDs and load cells turn a tiny resistance change into a measurable voltage.
Worked example
With R1 = 100 Ω, R2 = 200 Ω and R3 = 150 Ω, the bridge balances when Rx = 200 × 150 ÷ 100 = 300 Ω; both midpoints are then at 6.667 V from a 10 V supply. If Rx is actually 330 Ω the right midpoint rises to 6.875 V and the bridge outputs 208.3 mV.
Sources: Wheatstone bridge — Wikipedia · HyperPhysics — Wheatstone bridge
Frequently asked questions
What is the balance condition of a Wheatstone bridge?
R1/R2 = R3/Rx, or equivalently R1 × Rx = R2 × R3: the products of opposite arms are equal. Then no current flows through the detector and Rx = R2 × R3 ÷ R1.
Why is the bridge method so accurate?
At balance the detector only has to sense zero, which a sensitive galvanometer can do far more precisely than it can measure an absolute value. The result depends only on the ratio of the known resistors, not on the supply voltage or the meter calibration.
How are Wheatstone bridges used with strain gauges?
The strain gauge is one (quarter bridge), two or all four arms. Stretching it changes its resistance by a fraction of a percent, which unbalances the bridge and produces a millivolt output proportional to strain — the principle of every load cell and electronic scale.
Does the formula include the detector resistance?
The output voltage shown is the open-circuit (Thevenin) voltage, i.e. measured with a high-impedance voltmeter. A low-resistance galvanometer loads the bridge; to find its current, use the delta-wye conversion or Thevenin’s theorem with the bridge resistance.
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This calculator is for educational purposes. Double-check important results before acting on them.