Wheatstone Bridge Calculator

The Wheatstone bridge is a null instrument. Four resistances form a diamond, a source drives one diagonal, and a detector spans the other. The two halves act as independent voltage dividers, so the detector sees the supply multiplied by the difference between R3 over R1 plus R3 and Rx over R2 plus Rx. When those two fractions are equal the detector reads zero, and the balance condition, Rx equals R2 times R3 divided by R1, determines an unknown resistance purely from ratios of known ones. Because the answer rests on detecting a null rather than measuring a magnitude, it is largely immune to supply voltage drift and to the detector's own calibration, which is why bridge methods reach uncertainties of 0.01 percent or better where a direct ohmmeter reading struggles to reach 0.1 percent. Sensitivity, the output volts per ohm of imbalance, is greatest when all four arms are roughly equal, and it rises linearly with excitation voltage until self-heating begins shifting the resistances themselves. Most modern use is deliberately unbalanced: a strain gauge changes resistance by only about 0.1 percent at full scale, so a 350 ohm gauge bridge excited at 10 volts produces a few millivolts that must be amplified before use. The circuit is practical from roughly 1 ohm to 10 megohms. Below that range lead and contact resistance force a four-terminal Kelvin double bridge; above it, insulation leakage currents become comparable to the measurement current itself.

The circuit was published by Samuel Hunter Christie in the Philosophical Transactions of the Royal Society in 1833, where he described a diamond arrangement for comparing the conducting power of wires. It attracted little notice for a decade. Charles Wheatstone brought it to prominence in his 1843 Bakerian Lecture on the measurement of electrical resistance, crediting Christie for the arrangement, but the circuit acquired Wheatstone's name and has kept it since. William Thomson, later Lord Kelvin, extended the idea around 1861 with the double bridge that cancels lead and contact resistance, making accurate measurement of very low resistances possible. Alternating-current variants followed for reactive components: the Maxwell bridge for inductance, the Wien bridge for capacitance and frequency, and the Schering bridge for insulation loss measurement in high-voltage equipment, each requiring balance in both magnitude and phase and therefore yielding two independent conditions. The bridge's largest modern application arrived in 1938, when Edward Simmons at Caltech and Arthur Ruge at MIT independently developed the bonded resistance strain gauge. Wiring such gauges into bridge arms converts mechanical strain into an electrical signal, and quarter, half, and full bridge arrangements trade sensitivity against temperature compensation. Essentially every load cell, pressure transducer, and torque sensor in industrial service today is a Wheatstone bridge, as are the standard three-wire and four-wire resistance temperature detector circuits.