About the Wheatstone Bridge Calculator
This Wheatstone bridge calculator covers the three ways a bridge is used. In balance mode it finds the unknown resistor Rx that makes the galvanometer read zero for given ratio arms. In output mode it takes all four resistors and the excitation voltage and returns the differential output voltage, the voltage at each midpoint, the bridge’s Thevenin resistance and the current through a meter of known resistance. In measured mode it works backwards from a measured output voltage to the unknown resistance — how strain-gauge, RTD and thermistor bridges are read.
It is for students learning the classic null-measurement method and for engineers designing sensor front ends, where the bridge turns a small change in resistance into a small voltage centred on zero that an instrumentation amplifier can boost. The chart shows how the output voltage moves as Rx drifts ±20% around the balance point, so you can see the bridge’s sensitivity and non-linearity.
Layout used here: R1 (top) and R2 (bottom) form the left divider; R3 (top) and Rx (bottom) form the right divider, both fed from the excitation voltage Vs. The output is measured from the left midpoint to the right midpoint (Vout = VB − VA). Lead resistance and meter loading are ignored except where the meter resistance is entered.
How to use the wheatstone bridge calculator
- 1Choose what to calculate: Rx at balance, the output voltage, or Rx from a measured voltage.
- 2Enter the excitation voltage and the resistors R1, R2 and R3.
- 3For output mode enter Rx and the meter resistance; for measured mode enter the reading in mV.
- 4Read the result, midpoint voltages and Thevenin resistance.
- 5Use the chart to see how sensitive the bridge is around balance.
Formula and method
A Wheatstone bridge is two voltage dividers fed from the same source. The left midpoint sits at VA = Vs·R2/(R1 + R2) and the right at VB = Vs·Rx/(R3 + Rx). When the ratios match (R1/R2 = R3/Rx) the two voltages are equal, the output is zero and no current flows through a meter between them — so the unknown follows from Rx = R2·R3/R1 without depending on the supply voltage or meter accuracy.
An unbalanced bridge produces Vout = VB − VA. Reading Rx from a measured voltage simply inverts the right-hand divider: Rx = k·R3/(1 − k) where k = Vout/Vs + R2/(R1 + R2). Seen from the meter, the bridge is a Thevenin source of Vout behind Rth = R1∥R2 + R3∥Rx, so a meter of resistance Rg draws Ig = Vout/(Rth + Rg).
- Vs
- Excitation (supply) voltage
- R1, R2
- Left ratio arm: top and bottom resistors
- R3, Rx
- Right arm: top resistor and unknown (bottom) resistor
- VA, VB
- Left and right midpoint voltages
- Rth
- Thevenin resistance seen between the midpoints
- Rg, Ig
- Meter resistance and current through it
Worked examples
Balancing with 1 kΩ, 1.5 kΩ and 2.2 kΩ arms
Rx = R2 × R3 ÷ R1 = 1,500 × 2,200 ÷ 1,000 = 3,300 Ω. Both midpoints are then at 10 × 1,500/2,500 = 6 V, so the meter reads zero. Rth = 600 + 1,320 = 1,920 Ω.
Unbalanced bridge: Rx = 3.4 kΩ, 100 Ω meter
VB = 10 × 3,400/5,600 = 6.0714 V and VA = 6 V, so Vout = 71.4 mV. The bridge looks like 71.4 mV behind 600 + 1,335.7 = 1,935.7 Ω, so a 100 Ω galvanometer carries 71.4 mV ÷ 2,035.7 Ω ≈ 35.1 µA.
Reading Rx from a 50 mV output
k = 0.05/10 + 0.6 = 0.605, so the right midpoint is at 6.05 V and Rx = 0.605 × 2,200 ÷ 0.395 = 3,369.6 Ω — about 2.1% above the 3.3 kΩ balance value.
Frequently asked questions
What is the Wheatstone bridge formula?+
At balance R1/R2 = R3/Rx, so the unknown is Rx = R2 × R3 / R1, using the labelling where R1 and R2 form one divider and R3 and Rx the other. Off balance, Vout = Vs × (Rx/(R3 + Rx) − R2/(R1 + R2)).
Why is a Wheatstone bridge more accurate than an ohmmeter?+
At balance no current flows through the detector, so the result depends only on the ratio of known resistors — not on the supply voltage or the meter’s calibration. A sensitive galvanometer only has to detect zero, which it can do very precisely.
How is a Wheatstone bridge used with strain gauges?+
A strain gauge forms one or more arms of the bridge. Strain changes its resistance by a tiny fraction, which unbalances the bridge and produces a millivolt-level output proportional to strain that an instrumentation amplifier then amplifies.
Is the bridge output linear in Rx?+
Only approximately for small changes. Vout depends on Rx/(R3 + Rx), which curves as Rx moves away from balance. Quarter-bridge circuits are non-linear by about 0.5% per 1% change; half- and full-bridge arrangements improve linearity and sensitivity.
What happens if I connect a low-resistance meter?+
The meter loads the bridge: the current it draws is Vout/(Rth + Rg), and the voltage it reads falls to Vout × Rg/(Rth + Rg). A high-impedance voltmeter or instrumentation amplifier reads the full open-circuit voltage.