Free Wheatstone Bridge calculator
Find the resistance that balances a Wheatstone bridge — Rx = R3 × (R2/R1) — and the output voltage when the bridge is off balance, updated live, as you type.
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Idealized model — real bridges deviate with resistor tolerance, supply sag, and loading.
Results are estimates. Consult a professional.
How the Wheatstone bridge calculator works
A Wheatstone bridge is four resistors wired as two voltage dividers across one supply. The calculator works the two questions the bridge answers. First, given three known arms it finds the unknown resistance that balances the bridge — the value at which the output reads zero. Second, for any value of that fourth arm it finds the output voltage the bridge produces when it is off balance. Enter R1, R2, R3 and the supply voltage, set the unknown arm Rx, and both results update live, as you type.
The labeling is fixed so every number lines up: R1 is the top-left arm and R2 the bottom-left arm, forming the left divider; R3 is the top-right arm and Rx the bottom-right arm, forming the right divider. The output is the voltage between the two divider mid-points.
The balance condition and the unknown-resistance formula
The bridge is balanced when the two dividers split the supply in the same ratio, so no voltage appears across the middle. In symbols that is R2/(R1+R2) = Rx/(R3+Rx), which simplifies to the classic ratio R1/R2 = R3/Rx.
Rearranging for the unknown gives Rx = R3 × (R2 / R1). The ratio R2/R1 is the only thing that matters — doubling both leaves Rx unchanged — which is why the bridge is a ratio instrument and far more precise than reading a single resistance off a meter.
Why balance beats a direct reading
A multimeter compares the unknown against its own internal reference, so its accuracy is capped by that reference and by lead resistance. A balanced bridge instead compares the unknown against three other resistors and looks only for zero. Detecting zero is easy and precise; you never have to trust the absolute value of the supply or the detector, only that the output has reached null.
How a Wheatstone bridge measures an unknown resistance
In the original instrument, one arm is a calibrated variable resistor and a sensitive galvanometer sits across the middle. You adjust the variable arm until the galvanometer reads zero — the null point. At null the bridge is balanced, so the unknown follows directly from the arm values.
- Wire the unknown into one arm — here the bottom-right arm, Rx.
- Adjust a known arm until the detector across the middle reads zero current.
- Read the null condition — the bridge is now balanced.
- Compute Rx from Rx = R3 × (R2 / R1) using the three known arms.
Because the method hunts for zero rather than measuring a level, it is immune to drift in the supply voltage and to the exact sensitivity of the detector. That is the enduring appeal of the bridge for precision resistance work.
A worked example: finding Rx and the bridge output voltage
Priya is checking a sensor arm against a bridge built from R1 = 100 Ω, R2 = 200 Ω and R3 = 150 Ω, run from a 5 V supply. She wants the resistance that balances the bridge, then the output voltage when the real part measures slightly high.
Step 1 — Find the balancing resistance
Rx = R3 × (R2 / R1) = 150 × (200 / 100) = 150 × 2 = 300 Ω. If the sensor reads exactly 300 Ω, the bridge nulls and the output is 0 V.
Step 2 — Compute the output when the part is off balance
Suppose the real part measures Rx = 330 Ω, about 2% high. The left divider gives R2/(R1+R2) = 200/300 = 0.6667; the right divider gives Rx/(R3+Rx) = 330/480 = 0.6875.
Vout = 5 × (0.6667 − 0.6875) = 5 × (−0.020833) = −0.10417 V, or about −104.17 mV.
Output voltage of an unbalanced bridge
Most real bridges are never perfectly balanced — they are deliberately run off balance so the output voltage reports how far off they are. The output is the difference between the two divider voltages: Vout = Vin × ( R2/(R1+R2) − Rx/(R3+Rx) ).
Reading the sign
Vout is zero at balance, swings one way as Rx rises above the balance value, and the other way as it falls below. The polarity therefore tells you the direction of the change — tension versus compression on a strain gauge, for example — while the magnitude tells you how large it is. Treat the sign as information, never as a fault.
Why the signal is small
A 1–2% arm change typically yields only tens of millivolts from a few-volt supply, because both dividers start near the same fraction. That is why bridge outputs are almost always fed into an instrumentation amplifier before they reach an analog-to-digital converter. The bridge supplies a clean differential signal; the amplifier makes it big enough to use.
Quick reference: balance ratios and output voltage
These rows use R3 = 150 Ω and Vin = 5 V throughout, with the unknown arm Rx held at 330 Ω so you can see how the balance value and the output move as the R2/R1 ratio changes.
| R1 (Ω) | R2 (Ω) | Balance Rx = R3×(R2/R1) | Vout at Rx = 330 Ω |
|---|---|---|---|
| 100 | 100 | 150 Ω | −937.5 mV |
| 100 | 150 | 225 Ω | −437.5 mV |
| 100 | 200 | 300 Ω | −104.17 mV |
| 100 | 220 | 330 Ω | 0 mV (balanced) |
| 100 | 250 | 375 Ω | +133.93 mV |
| 100 | 300 | 450 Ω | +312.5 mV |
Output is V(node A) − V(node B); it crosses zero exactly where the balance value reaches 330 Ω (R1 = 100 Ω, R2 = 220 Ω). Figures from this calculator's own engine.
Where Wheatstone bridges are used: strain gauges and sensors
The bridge's real job today is not lab resistance measurement but turning a tiny resistance change into a usable voltage. Most strain gauges, load cells and pressure sensors are wired as one or more arms of a Wheatstone bridge.
- Strain gauges and load cells — a gauge bonded to a part changes resistance under strain; the bridge converts that into millivolts proportional to force or weight.
- Pressure and torque sensors — the same gauge-on-a-bridge idea applied to a flexing diaphragm or shaft.
- Temperature sensing (RTDs and thermistors) — a resistance that tracks temperature sits in one arm; the output reads the deviation.
- Precision resistance measurement — the classic null method, still used where a multimeter is not accurate enough.
Sensor bridges also cancel error. Putting matched gauges in opposite arms makes shared effects — chiefly temperature drift — affect both dividers equally, so they drop out of the difference and only the strain you care about remains.
Wheatstone bridge terms defined
How accurate is this Wheatstone bridge calculator?
The math is exact. The balance value Rx = R3 × (R2/R1) and the output Vout = Vin × (R2/(R1+R2) − Rx/(R3+Rx)) are computed directly from your inputs with full floating-point precision, so if your resistor and voltage values are right, the results are right to the displayed decimals.
What the model leaves out is real-world hardware. It assumes ideal resistors, a stiff supply, and a detector that draws no current. Real bridges deviate slightly because resistors carry tolerances (often ±1% to ±5%), the supply sags under load, lead and contact resistance add into the arms, and self-heating shifts values over time. For a loaded output — a detector or amplifier that draws current from the middle — the simple two-divider formula is an approximation; account for the load impedance when it is comparable to the arm resistances. Treat the calculator as the exact ideal answer, then allow margin for component tolerance and loading in a physical build.
Frequently asked questions about the free Wheatstone Bridge calculator
About this Wheatstone Bridge calculator
This calculator runs entirely in your browser. Nothing you enter is sent to a server — the balance resistance and the bridge output voltage are computed locally and update the moment you change an arm value or the supply.
It is one of our electronics calculators. Browse the full set on the all calculators page.