Wheatstone Bridge Calculator — output, balance and sensitivity

Bridge output voltage and balance condition, with a strain-gauge mode.

Example: This bridge is balanced at 5 V excitation — both arms sit at 2.5 V and the output is zero.

Inputs

Excitation voltage(V)

R1(Ω)

R2(Ω)

R3(Ω)

R4 (the sensing element)(Ω)

In a quarter-bridge this is the strain gauge; the other three are fixed.

Gauge factor (optional)

About 2 for foil gauges, much higher for semiconductor types.

Result

Output voltage

0 V

Balanced: yes
Left node: 2.5 V
Right node: 2.5 V
R4 for balance: 350 Ω
Output impedance: 350 Ω
Excitation current: 14.29 mA
Implied strain: 0 µε
Sensitivity: 2.5 µV/µε

The bridge is balanced — both dividers produce the same voltage, so the output is zero. Balance needs the two ratios to match, not the four resistors to be equal.
A quarter bridge gives about 2.5 µV per microstrain at this excitation — microvolts. That is why a strain bridge needs an instrumentation amplifier with high CMRR, not a plain op-amp.
A half or full bridge multiplies sensitivity by two or four and cancels temperature effects, because the gauges expand together but strain in opposite directions. If you can fit more gauges, do.
Excitation dissipates 71.43 mW in the bridge. Self-heating changes gauge resistance directly, so more excitation buys sensitivity at the cost of drift — which is why bridge excitation is usually kept modest.

Formula

V_out = V_ex × (R2/(R1+R2) − R4/(R3+R4))    balance: R1/R2 = R3/R4

Worked example

This bridge is balanced at 5 V excitation — both arms sit at 2.5 V and the output is zero.

V_left = V_ex × R2 / (R1 + R2)
5 V × 350 Ω / 700 Ω
2.5 V
V_right = V_ex × R4 / (R3 + R4)
5 V × 350 Ω / 700 Ω
2.5 V
V_out = V_left − V_right
2.5 V − 2.5 V
0 V
Taking the difference is what cancels supply drift and temperature effects common to both arms.

Frequently asked questions

When is a Wheatstone bridge balanced?

When R1/R2 equals R3/R4 — the two divider ratios match, so both nodes sit at the same voltage and the output is zero. The four resistors do not have to be equal, only the ratios.

Why use a bridge instead of just measuring the resistance?

Because it measures a difference, and anything common to both arms cancels. Supply drift, temperature, lead resistance — all affect both halves equally and disappear from the output. That is what lets a bridge resolve a resistance change of a few parts per million.

Why is my strain gauge output only microvolts?

Because that is the physics. A quarter bridge with a gauge factor of 2 gives roughly V_ex × GF × ε / 4, so 1000 microstrain at 5 V excitation is about 2.5 mV — and typical strains are far smaller. You need an instrumentation amplifier with high common-mode rejection.

Should I increase excitation voltage for more output?

Only up to a point. Output scales with excitation, but so does self-heating in the gauge, and heating changes its resistance directly — indistinguishable from strain. Most gauge specifications recommend keeping power dissipation low for precisely this reason.

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