Wheatstone Bridge Calculator

Background.

Measuring a resistance by passing a current through it and reading the voltage works, but the answer can be no better than the two meters involved. The Wheatstone bridge, popularised by Charles Wheatstone in 1843, sidesteps that problem. It compares the unknown resistor against known ones and looks for a single condition, zero current through a detector, which can be judged far more precisely than any absolute reading.

The circuit is two voltage dividers side by side, fed from the same source. One divider is made of R1 and R2; the other of R3 and the unknown Rx, with R1 and R3 joined to the same supply terminal. A sensitive detector, traditionally a galvanometer, bridges the two midpoints. When the ratio R1 : R2 matches the ratio R3 : Rx, the midpoints sit at the same voltage, no current flows through the detector, and the bridge is said to be balanced. At that point the unknown follows from simple proportion.

A useful property of the balance is that it does not depend on the supply voltage. A drifting battery shifts both dividers together, so the null stays where it is. That is why bridges remain at the heart of precision measurement and of sensors. Strain gauges, platinum resistance thermometers and load cells all change resistance slightly under strain, heat or weight, and a bridge turns those small changes into a measurable signal.

The arithmetic here is the ideal balance only. The resistance of leads and contacts, heating of the resistors by the measuring current, the detector's limited sensitivity and the tolerance of the known resistors all affect a real measurement and are not included.

What is wheatstone bridge calculator?

A Wheatstone bridge is a four-arm resistor network used to find an unknown resistance by balancing it against three known ones. The bridge is balanced when the voltage across the detector, and so the current through it, is zero. That happens when R1/R2 = R3/Rx, giving Rx = R2 × R3 ÷ R1. The value reported here is the resistance Rx must have for the bridge to be in balance with the three arms you enter.

How to use this calculator.

1. 01Identify the arms. R1 and R2 are the pair in series on one side of the bridge; R3 is the arm on the other side that connects to the same supply terminal as R1, and Rx sits in series below it.
2. 02Enter R1, R2 and R3 in ohms, converting kilohms or megohms first, so 2.2 kΩ becomes 2,200.
3. 03If you balanced the bridge by adjusting R3, enter the setting at which the detector read zero.
4. 04Read the balanced unknown resistance in ohms. If it looks implausible, check that R1 and R2 were not entered the wrong way round, which inverts their ratio.

The formula.

Rx = R2 × R3 ÷ R1. At balance the two midpoint voltages are equal, so each side divides the supply in the same proportion: R2/(R1 + R2) = Rx/(R3 + Rx). Cross-multiplying and cancelling the common term reduces this to R1 × Rx = R2 × R3. The ratio R2/R1 therefore acts as a multiplier on R3; with equal ratio arms, Rx simply equals R3. No constants or supply voltage appear in the result. Because Rx is a product and quotient of the three known resistances, their relative errors combine: three resistors each within 0.1% can leave Rx uncertain by as much as about 0.3% in the worst case. Labelling matters as much as precision, since swapping R1 and R2 gives an entirely different answer.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST, Measurement of Resistance, Special Publication 250-60.
2. [2]OpenStax, University Physics Volume 2, chapter 10, Direct-Current Circuits.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.