Wheatstone Bridge Calculator
Bridge output voltage, the resistance that would balance it, and the sensitivity in millivolts per ohm.
Results
Output voltage
12.56281
mV
Fourth resistance
1000.0000
Ω
Difference
-10.0000
Ω
Sensitivity
1.250000
mV/Ω
Percentage
-1.0000
%
What this tool does
The bridge works by subtracting two voltage dividers, so a tiny change in one arm produces a readable voltage while everything the two arms have in common — supply drift, temperature, ageing — cancels out. That cancellation is the whole point, and it is why every load cell and strain gauge in the world is wired this way. A balanced bridge reads exactly zero.
Formula
V out = V(R₂ ÷ (R₁+R₂) − R₄ ÷ (R₃+R₄)) ; balanced when R₁R₄ = R₂R₃
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ve | Input voltage | V |
r1 | Resistance R1 | Ω |
r2 | Resistance R2 | Ω |
r3 | Resistance R3 | Ω |
r4 | Fourth resistance | Ω |
VO | Output voltage | mV |
RB | Fourth resistance | Ω |
DR | Difference | Ω |
SN | Sensitivity | mV/Ω |
PC | Percentage | % |
Worked example
- Input voltage5 V
- Resistance R11000 Ω
- Resistance R21000 Ω
- Resistance R31000 Ω
- Fourth resistance990 Ω
- Output voltage12.56281 mV
- Fourth resistance1000.0000 Ω
- Difference-10.0000 Ω
- Sensitivity1.250000 mV/Ω
- Percentage-1.0000 %
Limitations
- Electrical installations are governed by national wiring rules. Cable sizing also depends on installation method, grouping, ambient temperature and protection devices, which this calculator does not evaluate.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.