Hong Life CalculatorsUnderstanding the Wheatstone bridge calculator — concept and principle
A Wheatstone bridge measures an unknown resistance by comparing it with three known ones. When the bridge is balanced, no current flows through the detector between its two midpoints, and the unknown can be calculated exactly from the others. The same circuit is the heart of strain gauges, load cells, pressure sensors and resistance thermometers, where tiny changes in resistance must be detected.
How it is calculated
- Balance condition: R1 / R2 = R3 / Rx
- Unknown resistance: Rx = R2 · R3 / R1
- Output with your actual Rx: V_out = Vs · (Rx / (R3 + Rx) − R2 / (R1 + R2))
The bridge consists of two voltage dividers fed from the same supply: R1 over R2 in one arm, R3 over Rx in the other. All resistances are in ohms. Vs does not appear in the balance formula, because balance depends only on the ratios; it scales the output voltage instead.
The principle
The midpoint of the first arm sits at Vs · R2 / (R1 + R2) and the midpoint of the second at Vs · Rx / (R3 + Rx). The detector reads the difference. It reads zero when the two fractions are equal, R2 / (R1 + R2) = Rx / (R3 + Rx), which simplifies to R1 / R2 = R3 / Rx. Because the method relies on detecting zero rather than reading a scale, it can be very accurate: the precision depends on the known resistors, not on the meter's calibration.
Worked example
- Inputs: R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω, Vs = 5 V.
- Rx = R2 × R3 / R1 = 200 × 150 / 100 = 30,000 / 100 = 300 Ω.
- Check the midpoints: 5 × 200 / 300 ≈ 3.333 V and 5 × 300 / 450 ≈ 3.333 V. The difference is zero, so the bridge is balanced and the output with the actual Rx of 300 Ω is 0 V; with Rx = 310 Ω it would be about 0.036 V.
| R1 (Ω) | Unknown Rx for balance (Ω) |
|---|---|
| 25 | 1,200 |
| 50 | 600 |
| 75 | 400 |
| 100 | 300 |
| 125 | 240 |
| 150 | 200 |
| 200 | 150 |
How to read the result
The value shown is the Rx that would make the bridge balance. In a measurement, you adjust a known resistor until the detector reads zero and then apply the formula. In sensor use the bridge starts balanced, and a small change in Rx produces a small output voltage, roughly proportional to the change for small deviations.
Common mistakes
- Mixing up the arm positions; the formula depends on which resistor sits above and below each midpoint.
- Expecting the supply voltage to change the balance value.
- Measuring very low resistances (below about 1 Ω) with a simple bridge, where lead and contact resistance dominate; a Kelvin double bridge is used instead.
Frequently asked questions
Why use a bridge instead of an ohmmeter?
A null measurement is independent of the meter's scale accuracy, so a bridge can reach much higher precision with good reference resistors.
How is a Wheatstone bridge used in a load cell?
Strain gauges form the bridge arms. Loading stretches some and compresses others, unbalancing the bridge and producing a millivolt signal proportional to force.
Sources: C. Wheatstone, "An account of several new instruments and processes for determining the constants of a voltaic circuit", Philosophical Transactions of the Royal Society 133 (1843) · P. Horowitz and W. Hill, The Art of Electronics, Cambridge University Press