Wheatstone Bridge Sensor Calculator
Calculate exact bridge output, balance, common-mode voltage, normalized mV/V response and resistor-tolerance offset for resistive bridge sensors.
SEN-003 handles the generic bridge electrical network. Strain gauge physics belongs to SEN-001, and load-cell rated output belongs to SEN-002.
Engineering tool
Wheatstone Bridge Sensor Calculator
Analyze exact Wheatstone bridge sensor output, balance, midpoint voltages, mV/V sensitivity, target R4 and resistor-tolerance offset using the shared SEN-001 bridge convention.
Calculation mode
Parameter panel
Result console
- Left Midpoint VL
- 2.5 V
- Right Midpoint VR
- 2.5 V
- Differential Output
- 0 V
- Output
- 0mV/V
- Normalized Output
- 0V/V
- Common Mode
- 2.5 V
- Balance Error
- 0%
- Bridge Status
- Balanced
Output polarity follows VOUT = VR - VL. Match this node convention to the measurement system.
Wheatstone bridge formula audit
| Adopted Bridge Topology | Top excitation rail feeds R1/R3; bottom rail is reference. |
|---|---|
| R1 Position | Upper-left arm from VEX+ to left midpoint. |
| R2 Position | Lower-left arm from left midpoint to VEX-. |
| R3 Position | Upper-right arm from VEX+ to right midpoint. |
| R4 Position | Lower-right arm from right midpoint to VEX-. |
| Left Midpoint Definition | VL = VEX × R2/(R1+R2). |
| Right Midpoint Definition | VR = VEX × R4/(R3+R4). |
| Output Polarity | VOUT = VR - VL, matching SEN-001 shared bridge utility. |
| Exact Bridge Equation | VOUT = VEX[R4/(R3+R4) - R2/(R1+R2)]. |
| Balance Condition | R1/R2 = R3/R4. |
| Cross-Product Identity | Balanced bridge satisfies R1R4 = R2R3. |
| Common-Mode Definition | VCM = (VL + VR)/2. |
| Normalized Output | B = VOUT/VEX. |
| mV/V Definition | mV/V = (VOUT/VEX) × 1000. |
| Single-Arm Approximation | |VOUT|/VEX ≈ |ΔR|/(4R) for small ΔR. |
| Half / Full Mapping | SEN-001 half/full additive mappings are reused. |
| Tolerance Corner Model | Worst-case offset enumerates 16 resistor min/max corners. |
Formula reference
Wheatstone Bridge Sensor Formulas
The calculator uses one fixed bridge labeling convention and separates exact bridge equations from small-signal sensor approximations.
VL = VEX × R2/(R1+R2)VR = VEX × R4/(R3+R4)VOUT = VR - VLVOUT = VEX[R4/(R3+R4) - R2/(R1+R2)]Balance: R1/R2 = R3/R4Cross product: R1R4 = R2R3VCM = (VL + VR)/2mV/V = (VOUT/VEX) × 1000Single arm: |VOUT|/VEX ≈ |ΔR|/(4R)Variable definitions
- R1/R2
- left bridge divider
- R3/R4
- right bridge divider
- VL
- left midpoint voltage
- VR
- right midpoint voltage
- VOUT
- differential bridge output
- VEX
- bridge excitation voltage
- VCM
- bridge common-mode voltage
Wheatstone Bridge Formula Audit
| Adopted Bridge Topology | R1/R2 form the left divider; R3/R4 form the right divider. |
|---|---|
| R1 Position | Upper-left arm from VEX+ to VL. |
| R2 Position | Lower-left arm from VL to VEX-. |
| R3 Position | Upper-right arm from VEX+ to VR. |
| R4 Position | Lower-right arm from VR to VEX-. |
| Excitation Polarity | VEX is applied from the top rail to the bottom reference rail. |
| Left Midpoint Definition | VL = VEX × R2/(R1+R2). |
| Right Midpoint Definition | VR = VEX × R4/(R3+R4). |
| Output Polarity | VOUT = VR - VL, matching SEN-001 shared bridge utility. |
| Exact Bridge Equation | VOUT = VEX[R4/(R3+R4) - R2/(R1+R2)]. |
| Balance Condition | R1/R2 = R3/R4. |
| Cross-Product Identity | R1R4 = R2R3. |
| Common-Mode Definition | VCM = (VL + VR)/2. |
| Normalized Output | B = VOUT/VEX. |
| mV/V Definition | mV/V = B × 1000. |
| Single-Arm Approximation | |VOUT|/VEX ≈ |ΔR|/(4R) for |ΔR| << R. |
| Half-Bridge Mapping | R1 = R + ΔR and R3 = R - ΔR, same as SEN-001. |
| Full-Bridge Mapping | R1/R4 increase and R2/R3 decrease, same as SEN-001. |
| Balance Solver | Balanced R4 = R2R3/R1. |
| Target Output Solver | R4 = xR3/(1-x), where x = VR/VEX and 0 < x < 1. |
| Tolerance Corner Model | All 16 resistor min/max corners are enumerated. |
Worked Examples
Balanced bridge
Known: R1=R2=R3=R4=350 Ω, VEX=5 V
VL=2.5 V, VR=2.5 V, VOUT=0.
Single R1 perturbation
Known: R1=351 Ω, R2=R3=R4=350 Ω, VEX=5 V
VL decreases slightly; with VOUT=VR-VL the output is positive.
Normalized output
Known: Same R1=351 Ω case
mV/V = (VOUT/VEX)×1000.
Balanced R4
Known: R1=100 Ω, R2=200 Ω, R3=150 Ω
R4=300 Ω because 100×300=200×150.
Balanced result
Known: R1=100, R2=200, R3=150, R4=300
VOUT=0 by exact equation.
Single active arm
Known: R=350 Ω, ΔR=0.7 Ω
ΔR/R=0.002; small-signal |VOUT|/VEX≈0.0005.
5 V excitation
Known: Single active arm above
Approximate |VOUT|≈2.5 mV.
Exact vs approximate
Known: ΔR/R=0.002
Exact output is close to the small-signal approximation.
Negative ΔR
Known: R1 active, ΔR=-0.7 Ω
Output polarity reverses.
R2 active
Known: R2 changes by +0.7 Ω
Polarity flips relative to R1 active under the adopted convention.
Half bridge additive
Known: R1=R+ΔR, R3=R-ΔR
Small-signal sensitivity is about 2× single-arm.
Full bridge additive
Known: R1/R4 increase, R2/R3 decrease
Small-signal sensitivity is about 4× single-arm.
Excitation scaling
Known: Double VEX
Exact VOUT doubles.
Normalized invariance
Known: Double VEX
VOUT/VEX remains the same for fixed resistance ratios.
Unknown R4 solver
Known: R1, R2, R3, VEX, target VOUT
Solved R4 round-trips through exact bridge analysis.
Invalid target
Known: Required midpoint outside excitation rails
Solver rejects without negative or infinite resistance.
Tolerance corner
Known: 350 Ω bridge, ±1% resistors
Worst-case output range contains zero.
Resistance unit check
Known: 350 Ω = 0.35 kΩ
Bridge output is unchanged.
Excitation unit check
Known: 5 V = 5000 mV
Bridge output is unchanged.
Large artificial ΔR
Known: ΔR no longer small compared with R
Exact and small-signal outputs diverge.
Common mode
Known: Balanced bridge
VCM = VEX/2.
Engineering Notes
| Wheatstone Bridge | A bridge converts resistance ratios into a differential voltage. |
|---|---|
| Bridge Sensor | Many pressure, force and resistive sensors use bridge behavior. |
| Differential Output | The useful signal is VR - VL under the adopted node convention. |
| Bridge Balance | A balanced bridge has zero ideal differential output. |
| Bridge Imbalance | Small mismatch can create microvolt or millivolt offset. |
| Resistance Change | Exact analysis should be used when ΔR is not negligible. |
| Bridge Excitation | Higher excitation increases signal and self-heating. |
| mV/V | mV/V normalizes bridge output to excitation voltage. |
| Common-Mode Voltage | Bridge common-mode voltage can be near mid-supply even when differential output is tiny. |
| Quarter Bridge | Single-arm approximations are small-signal references. |
| Half Bridge | Half-bridge mapping must define which arms change and in which direction. |
| Full Bridge | Full bridge sensitivity depends on the chosen additive mapping. |
| Tolerance | Resistor tolerance can dominate zero-load offset. |
| Self Heating | Bridge power can shift sensor resistance and measurement output. |
| Instrumentation Amplifier | Amplifiers must handle both the small differential signal and common-mode voltage. |
Common Mistakes
- Putting R1/R2/R3/R4 in different positions between schematic and formula.
- Changing VL and VR definitions across calculations.
- Using inconsistent output polarity.
- Writing the balance cross product backward.
- Treating small-signal approximation as exact.
- Confusing mV/V with mV.
- Ignoring excitation voltage.
- Assuming absolute resistor value matters more than resistor ratios.
- Ignoring common-mode voltage.
- Ignoring resistor-tolerance offset.
- Assuming higher excitation has no self-heating cost.
- Using a different topology from SEN-001 without documenting it.
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FAQ
What is a Wheatstone bridge?
A Wheatstone bridge is a four-resistor network that converts resistance ratios into a differential voltage.
How do I calculate Wheatstone bridge output voltage?
Calculate the left and right midpoint voltages, then subtract them using the adopted output convention.
When is a Wheatstone bridge balanced?
With the adopted labels, the bridge is balanced when R1/R2 equals R3/R4.
What is the balance equation?
The equivalent cross-product condition is R1R4 = R2R3.
How does a resistance change affect bridge output?
A small resistance change shifts one or more divider ratios, creating a differential output usually measured in mV or µV.
What does mV/V mean for a bridge sensor?
mV/V is the bridge output normalized to excitation voltage: VOUT/VEX multiplied by 1000.
How do I calculate bridge sensitivity?
For small resistance changes, compare normalized output to ΔR/R. A single-arm bridge is about one quarter of ΔR/R.
What is the difference between exact and small-signal bridge equations?
Exact equations use all four resistor values. Small-signal equations are approximations valid only when ΔR is much smaller than R.
Why is bridge output differential?
The useful signal is the voltage difference between the two bridge midpoints, not either midpoint alone.
What is bridge common-mode voltage?
Common-mode voltage is the average of the left and right midpoint voltages. Amplifiers must tolerate this voltage.
How do resistor tolerances create zero offset?
Tolerance changes divider ratios, so a nominally balanced bridge can produce output at zero sensor input.
How does excitation voltage affect bridge output?
For fixed resistor ratios, bridge output scales linearly with excitation voltage while normalized mV/V stays constant.
Why does a bridge need an instrumentation amplifier?
Bridge differential signals are often very small while common-mode voltage remains near mid-supply.
What is the difference between a Wheatstone bridge and a strain gauge?
A bridge is the electrical network. A strain gauge is a sensor element whose resistance changes with strain.
What is the difference between a Wheatstone bridge and a load cell?
A load cell is a calibrated mechanical sensor assembly, usually built around a bridge, and specified by rated load and mV/V output.
How does self-heating affect bridge sensors?
Higher excitation increases signal and bridge power, which can heat resistors or sensor elements and shift the measurement.
Engineering Disclaimer
This calculator provides ideal bridge network arithmetic. Critical bridge sensors require actual sensor data, input-loading review, excitation source analysis, self-heating checks, instrumentation amplifier design, ADC design, calibration and temperature testing.