Wheatstone Bridge Calculator
Solve a balanced bridge for any one resistor or calculate the differential output voltage of an unbalanced bridge.
Bridge inputs
Use positive finite values. Numbers follow the U.S. decimal convention.
Live results
All values are derived from the same canonical bridge model.
This value makes the two divider ratios equal.
Electrical breakdown
The detector branch is treated as high impedance, so it does not load the two voltage dividers.
| Metric | Value | Interpretation |
|---|---|---|
| Left branch current | 0.2 A | Current through the R₁ – R₂ series branch. |
| Right branch current | 0.3 A | Current through the R₃ – Rₓ series branch. |
| Midpoint D voltage | 1.2 V | Divider voltage V × R₁ ÷ (R₁ + R₂). |
| Midpoint B voltage | 1.2 V | Divider voltage V × R₃ ÷ (R₃ + Rₓ). |
| Ratio mismatch | 0% | Relative difference between R₁/R₂ and R₃/Rₓ. |
How to use the Wheatstone Bridge Calculator
What this calculator does
This calculator analyzes the ideal DC Wheatstone bridge as two resistive voltage dividers connected across the same supply. In a balanced bridge, the two midpoint voltages are equal and the differential bridge output is zero. The calculator can solve for any one of the four resistances under that balance condition, or it can use all four resistances and the supply voltage to calculate the output voltage of an unbalanced bridge. It also reports equivalent resistance, branch currents, midpoint voltages, total source current, power, and a ratio-mismatch indicator. These are circuit-model results, not a complete prediction of measurement uncertainty in real hardware.
When to use it
- Choose resistor values that balance a laboratory resistance bridge.
- Estimate the differential signal produced by a resistive sensor, strain gauge, thermistor, or RTD element.
- Check whether a proposed bridge and excitation voltage stay within current and power limits.
- Compare hand calculations with a reproducible Excel workbook before building or testing a circuit.
How to calculate
- The calculator opens with a complete demonstration: Calculation mode is “Balanced bridge: solve Rₓ,” Supply voltage V is 3 V, R₁ is 6 Ω, R₂ is 9 Ω, and R₃ is 4 Ω. The displayed Rₓ is 6 Ω, and the Excel workbook is immediately available.
- Select the required Calculation mode. The target resistance becomes read-only in a balanced mode. Select “Unbalanced bridge: solve Vᴳ” when all four resistors are known.
- Choose the Resistance unit and Voltage unit. A unit change converts the values already entered rather than merely changing the labels.
- Replace the demonstration values with your circuit data. Results update live. Read the primary result first, then use Bridge output Vᴳ, Equivalent resistance, Supply current, Total power, and the electrical breakdown table to check the design.
- Select Download Excel to generate a current-state OOXML workbook containing Summary, Inputs, Analysis, and Notes sheets. Select Reset to clear the demonstration and all calculated state. Reset may disable Excel export until a complete valid bridge is entered again.
Input guide
Calculation mode is required and determines the unknown. Balanced modes use the identity R₁/R₂ = R₃/Rₓ. The unbalanced mode calculates Vᴳ. Resistance unit is required and accepts Ω, kΩ, or MΩ; all resistance entries are converted together. Voltage unit is required and accepts V or mV; it applies to both the supply and output. Supply voltage V accepts a positive decimal such as 3 or 5. It is essential for Vᴳ, current, node-voltage, and power calculations. A common mistake is entering a millivolt value while the selector still shows volts.
Resistance R₁, Resistance R₂, Resistance R₃, and Resistance Rₓ accept positive finite decimals in the selected resistance unit. The target field in a balanced mode is calculated automatically; the other three are required. For example, 6, 9, and 4 in ohms produce Rₓ = 6 Ω. Increasing R₂ or R₃ raises the balanced Rₓ, while increasing R₁ lowers it. Zero and negative resistance are rejected because the ideal divider and balance equations would be undefined or outside the intended passive-resistor model. The parser uses a period as the decimal separator; a token such as 1,5 is rejected rather than silently interpreted as 15.
Output guide
Primary result is either the solved resistance or Vᴳ. A balanced resistance is an exact algebraic identity for the ideal model. Vᴳ is a signed differential estimate: zero means balanced, while the sign indicates which modeled midpoint is at the higher potential. Equivalent resistance is the parallel combination of the two series branches. Supply current equals V divided by equivalent resistance, and Total power equals V times supply current. High current or power may indicate that the excitation is impractical even when the ratio is correct.
The breakdown table lists Left branch current, Right branch current, Midpoint D voltage, Midpoint B voltage, and Ratio mismatch. The mismatch is zero at mathematical balance. A larger absolute mismatch generally produces a larger output-voltage magnitude, although the exact sensitivity also depends on the resistor values and supply voltage. The Bridge state label classifies the ideal bridge as balanced or unbalanced using a tight numerical tolerance. Formula used identifies the exact algebraic relationship applied for the selected calculation mode.
Worked example
With R₁ = 6 Ω, R₂ = 9 Ω, and R₃ = 4 Ω, the balanced unknown is Rₓ = R₂ × R₃ ÷ R₁ = 9 × 4 ÷ 6 = 6 Ω. At a 3 V supply, midpoint D is 3 × 6 ÷ (6 + 9) = 1.2 V. Midpoint B is 3 × 4 ÷ (4 + 6) = 1.2 V, so Vᴳ = 1.2 – 1.2 = 0 V. The two branch resistances are 15 Ω and 10 Ω; their parallel equivalent is 6 Ω, giving a supply current of 0.5 A and total power of 1.5 W. These values match the first-open display and workbook.
Learn more
For a detailed treatment of bridge sensors, differential measurement, excitation, sensitivity, and error sources, consult Texas Instruments' Basic Guide to Bridge Measurements. The resistance, current, voltage, and power quantities used here follow the International System of Units described in the NIST SI units guide.
How the bridge equations work
Each side of the bridge is an independent voltage divider. In the orientation used by this calculator, the first midpoint is V × R₁/(R₁ + R₂), and the second midpoint is V × R₃/(R₃ + Rₓ). Their difference is the bridge output:
At balance, Vᴳ = 0, so the divider ratios are equal. Rearranging gives R₁/R₂ = R₃/Rₓ and makes any one resistor solvable from the other three. A bridge is especially useful because it converts a small resistance change into a differential voltage that can be amplified and digitized. The bridge-circuit chapter from All About Circuits provides a practical derivation and measurement context.
Practical limits and common mistakes
- Do not treat ideal balance as guaranteed measurement accuracy. Resistor tolerance, temperature coefficient, wiring resistance, ADC offset, noise, and excitation drift can dominate a small signal.
- Check power dissipation. A mathematically correct low-resistance bridge can draw excessive current and self-heat the sensing elements.
- Keep the sign convention consistent. Reversing the detector leads reverses the sign of Vᴳ but not the physical degree of imbalance.
- Use matched, stable components for precision work. Ratio accuracy is usually more important than absolute resistance accuracy, but absolute values still determine loading and power.