Wheatstone Bridge Calculator

Compute unknown resistance, bridge balance condition, output voltage, and sensitivity for classic and strain‑gauge Wheatstone bridge circuits.

Standard Wheatstone bridge topology 

      R1               R2
  (top left)      (top right)
   ┌──Ω───┐       ┌──Ω───┐
   │      │       │      │
  (+)    (A)----- (B)    (+)
   │      │   Vout  │      │
   └──Ω───┘       └──Ω───┘
      R3               R4
  (bottom left)   (bottom right)

Supply: Vs between (+) top node and bottom reference node.

1. Balance / Unknown Resistance

Use this mode to design or analyze a Wheatstone bridge at balance. Enter any three resistances to solve the fourth, or check if a given set is balanced.

How the Wheatstone bridge works

A Wheatstone bridge is a four‑resistor network used to measure unknown resistance or small resistance changes with high precision. It compares two voltage dividers:

Balance condition

The bridge is balanced when the voltage at node A equals the voltage at node B, so the output Vout = 0:

\[ \frac{R_1}{R_2} = \frac{R_3}{R_4} \]

Node voltages and output voltage

With supply voltage \(V_s\) applied between the top and bottom nodes:

  • Left divider (R1 over R3): \( V_A = V_s \cdot \dfrac{R_3}{R_1 + R_3} \)
  • Right divider (R2 over R4): \( V_B = V_s \cdot \dfrac{R_4}{R_2 + R_4} \)

Output voltage

\[ V_{\text{out}} = V_A - V_B = V_s \left( \frac{R_3}{R_1 + R_3} - \frac{R_4}{R_2 + R_4} \right) \]

Solving for an unknown resistance at balance

If the bridge is balanced and one resistor is unknown, you can solve it directly from the ratio:

From \( \dfrac{R_1}{R_2} = \dfrac{R_3}{R_4} \) you can solve for any missing resistor. For example, if R4 is unknown:

\[ R_4 = R_3 \cdot \frac{R_2}{R_1} \]

Strain‑gauge Wheatstone bridge formulas

In sensor applications (load cells, pressure sensors, torque sensors), one or more resistors are strain gauges whose resistance changes slightly with strain:

\[ \Delta R = GF \cdot R \cdot \varepsilon \]

  • \(GF\) – gauge factor (typically 2.0–2.2 for metal foil gauges)
  • \(R\) – nominal gauge resistance (e.g. 120 Ω, 350 Ω)
  • \(\varepsilon\) – strain (dimensionless). 500 µε = 500 × 10⁻⁶.

Approximate Vout for small strain

For small changes (ΔR ≪ R) and a symmetric bridge, the output is approximately linear in strain:

Quarter‑bridge (1 active gauge)

\[ V_{\text{out}} \approx \frac{1}{4} \, GF \, \varepsilon \, V_s \]

Half‑bridge (2 active gauges, opposite arms)

\[ V_{\text{out}} \approx \frac{1}{2} \, GF \, \varepsilon \, V_s \]

Full‑bridge (4 active gauges)

\[ V_{\text{out}} \approx GF \, \varepsilon \, V_s \]

The calculator uses these expressions to report both the expected output voltage and the sensitivity in V/strain and mV/V per 1000 µε.

Typical use cases

  • Precision resistance measurement – unknown resistor in one arm, others as reference.
  • Strain‑gauge sensors – load cells, pressure transducers, torque sensors.
  • Temperature compensation – using dummy gauges in adjacent arms.
  • Instrumentation front‑end – feeding instrumentation amplifiers or ADCs.

Design tips

  • Choose resistor values so that bridge currents are reasonable and self‑heating is low.
  • Use precision, low‑drift resistors for reference arms in measurement bridges.
  • For strain‑gauge bridges, match gauge resistances and wiring to minimize offset.
  • Use differential measurement and proper shielding to reduce noise pickup on Vout.

FAQ

What is the main advantage of a Wheatstone bridge?

It converts small resistance changes into a measurable differential voltage while rejecting common‑mode effects such as supply variation and some temperature drift. This makes it ideal for precision sensing.

Do the absolute resistor values matter, or only the ratios?

For balance, only the ratios matter. However, absolute values affect current, power dissipation, noise, and the output magnitude for a given ΔR, so they are important in practical design.

Can I use this calculator for non‑strain sensors?

Yes. Any resistive sensor (thermistor, RTD, LDR, potentiometer, etc.) can be placed in one or more arms. Use the general Vout mode with the appropriate resistance values.