Wheatstone Bridge Calculator

The bridge measures an unknown resistance by balancing it against three known ones — at balance, no current crosses the detector, and the unknown falls out of a ratio. Enter the three known arms (in the layout described below), and this calculator returns the unknown resistance at balance.

Measurement by Nothing Happening

Most meters deflect; the bridge nulls. Four resistors form a diamond — two voltage dividers side by side — and a sensitive detector spans the middle. When the dividers' ratios match (R1 ÷ R2 = R3 ÷ Rx), the midpoints sit at equal potential, the detector reads exactly zero, and the unknown is computed as Rx = R2 × R3 ÷ R1 from the known arms alone. The supply voltage cancels, the detector's calibration cancels (it need only find zero, the easiest point to locate precisely), and the accuracy is inherited entirely from the standard resistors — which is why bridges measured resistance to parts per million for a century and why their descendants (the strain-gauge bridge in every load cell and pressure sensor) still run industry. The calculator evaluates the balance equation for the stated layout; the layout paragraph in its note is not decoration, since a bridge's formula is its topology, and the reader wiring a real bridge must match arms to labels.

Worked Example: A 300 Ω Unknown

The defaults: R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω. Rx = 200 × 150 ÷ 100 = 300 Ω. In the laboratory the procedure runs the other way: Rx is the mystery, R3 is a calibrated decade box, and the experimenter dials R3 until the galvanometer's needle settles on nothing — then reads the answer off the dials, the calculator run in reverse by hand. The ratio arms R1 and R2 are often picked as a decade pair (10:100, 1:1, 100:10) to slide the measurement range, and the bridge's sensitivity peaks when all four arms are comparable — choose ratios that bring R3's dial near the unknown's size, the calculator's inputs showing the arithmetic of that choice. Three knowns, one null, one unknown: metrology's most elegant transaction. Its elegance is also its longevity insurance: in an age when every other instrument on the bench has been digitised into a black box, the bridge survives openly — in sensor front-ends, in the calibration laboratory's decade boxes, in the first circuits course's rite of passage — because its principle can be stated in one line, audited in one diagram, and trusted in one null. The calculator is that line, computed.

The Bridge's Second Career: Sensing

Deliberately unbalance the bridge and it becomes a sensor amplifier: make Rx a strain gauge, a thermistor or a photoresistor, and the detector's output becomes a small voltage proportional (nearly) to the resistance's change — tiny changes, which a direct ohmmeter could never resolve, read out against the bridge's stable zero. Quarter-bridge (one active arm), half and full bridges (two and four, doubling and quadrupling sensitivity while cancelling temperature drift) instrument everything from jet-engine test rigs to bathroom scales — every electronic scale you have stood on was a Wheatstone bridge confessing your weight through four strain gauges. The calculator computes the balance point the sensor bridges are trimmed to; their working offsets are measured from it.

The Post Office Box

Generations of students met the bridge as furniture: the "post office box," a mahogany case of plug-switched ratio arms and standard coils named for the telegraph engineers who used its portable ancestors to locate faults in buried cables — a bridge reading at the near end, by ratio arithmetic, betrayed the distance to a break or a short, computed from the resistance per mile of the line. The same null method, in Murray and Varley loop tests, still finds faults in power cables today. The calculator's decade inputs honour the furniture: R3's plug-and-dial decades are the reason bridges are specified in ratios at all, and the post office box is the bridge's folk name in the countries that wired an empire with it.

The Bridge Inside Every Sensor Module

A modern pressure-sensor chip is this page micromachined: four piezoresistors diffused into a silicon diaphragm, wired as a full bridge, so the diaphragm's flexure unbalances the ratios in proportion to pressure — and the chip's datasheet quotes the imbalance in millivolts per volt of excitation, the bridge's output normalised exactly as the balance equation would predict. Barometers in phones, manifold-pressure sensors in engines, and the load pins in aircraft landing gear all report through Wheatstone's diamond. The calculator's three-resistor arithmetic is the calibration skeleton inside each: trim R3 (or its laser-trimmed on-chip equivalent) until the unloaded bridge nulls, and every subsequent millivolt is data.

Related Tools

More from the Physics Calculators hub: the Skin Depth Calculator — why AC bridges meet a second complication — and the Drift Velocity Calculator, for what the bridge's currents are doing inside the wire.

Frequently Asked Questions

Who invented it — Wheatstone or Christie?

Samuel Hunter Christie described the diamond arrangement in 1833; Charles Wheatstone popularised it from 1843, crediting Christie, and history kept the populariser's name — a Stigler's-law exhibit the profession acknowledges cheerfully in the first lecture. Wheatstone's genuine contributions were the applications and the telegraph ecosystem that needed them (measuring line resistances over miles was the bridge's first industrial job). The calculator bears the conventional name, and this FAQ pays the priority where it is due.

Why is a null measurement so accurate?

Because detecting zero is categorically easier than measuring a quantity: the detector can be made arbitrarily sensitive without needing calibration across a range, systematic errors in its scale never enter, and the answer depends only on the standard arms and the ratio condition. The same philosophy powers the potentiometer (null voltage measurement), analytical balances (null torque) and modern auto-zero amplifiers. The bridge is its electrical archetype — the calculator's result inheriting, conceptually, an accuracy that belongs to the method rather than to any component in it.

What limits a real bridge's precision?

The standards' own tolerances and drift, thermal EMFs at junctions (dissimilar-metal contacts acting as tiny thermocouples, fought by reversing the supply and averaging), lead and contact resistance in the low-ohms ranges (fought by the Kelvin double bridge, the design's famous refinement), and the detector's noise floor near null. Metrology-grade bridges manage parts in 10⁷; student bridges parts in 10³; the calculator's arithmetic is exact and its note's silence about these limits is repaired here — the formula is the floor plan, the error budget is the building.

Can the bridge measure inductance or capacitance?

Yes — the AC bridges are its extended family: replace resistors with impedances, drive with AC, and balance now demands two conditions (magnitude and phase), met by adjusting two standards — the Maxwell, Hay and Schering bridges measure inductance and capacitance this way, and the Wien bridge doubles as an oscillator's frequency-setter. The calculator's jurisdiction is the DC resistive original; the family's principle (null the detector, read the standards) is identical, and the skin-depth page of this wave explains why AC arms bring their own complications.

What if my arms are arranged differently?

The balance condition is always "products of opposite arms equal" (R1 × Rx = R2 × R3 in this page's labelling) — if your physical bridge labels its arms differently, permute the inputs so the adjustable standard sits at R3 and the unknown opposite R1, or equivalently rearrange the formula: the unknown equals the product of the arms adjacent to it divided by the arm opposite. The topology sentence in the widget's note exists to make the permutation checkable in seconds — bridges punish label-guessing with answers off by the ratio squared, the classic student error this page is designed to prevent.

Why are bridges excited with AC in precision work?

To outrun thermoelectric drift: thermal EMFs at junctions are DC offsets that fake a resistance signal in DC bridges, while an AC excitation lets the measurement lock in to the carrier frequency and ignore those offsets entirely — the same reason precision strain systems and LVDTs run on carriers. The trade is that AC arms meet reactance (a resistor's stray inductance and capacitance unbalance the phase as well as the magnitude, demanding the two-condition balance of the AC-bridge FAQ). The calculator's DC balance is the carrier system's zero reference; state-of-the-art resistance metrology lives one modulation away from it.

What sensitivity can a bridge reach?

With microvolt-class detectors, resistance changes of one part in a million are routinely resolved — a strain gauge's working signals are exactly such fractional whispers (a 350 Ω gauge straining 0.1% changes by 0.7 Ω, and service measurements resolve a thousandth of that). The null architecture is what buys the sensitivity: the detector stares at a near-zero baseline, so its gain can be enormous without saturating. The calculator reports the balance point; the sensitivity story is why returning a sensor bridge to that point, degree by micro-degree, is a precision industry.

How do load cells use the bridge?

Four strain gauges are bonded to a flexing metal element, two stretched and two compressed by the load, wired as a full bridge: the load's signal adds across all four arms while temperature's effect (all gauges drifting together) cancels at the ratio — the worked principle of the sensing section above, industrialised into the weighing of trucks, the thrust stands of rocket tests and the kitchen scale's gram. Their excitation voltage and millivolt-per-volt output ratings are the bridge's bookkeeping in commercial dress; the balance equation this page computes is where every such datasheet begins.