Wheatstone Bridge Calculator
Enter the four arms and excitation for balance and output, or switch to sensor mode for strain gauge and RTD bridges.
Step-by-step
- Enter valid values to begin.
Layout used in every formula: excitation Vex is across the top and bottom nodes (bottom = 0 V). R1 is top-left, R2 bottom-left, R3 top-right, Rx bottom-right; the output is taken between the left midpoint (R1/R2) and the right midpoint (R3/Rx), Vout = Vright − Vleft, so it is positive when Rx rises above its balance value. The detector or amplifier is assumed to draw no current. In sensor mode all four arms start at R0; half bridge uses R3 = R0 − ΔR and Rx = R0 + ΔR, and full bridge uses R1 and Rx = R0 + ΔR with R2 and R3 = R0 − ΔR. Strain gauges commonly have a gauge factor near 2 and are 120, 350 or 1000 Ω; the 10 mW and 50 mW self-heating levels are typical rule-of-thumb figures, not standards, and depend on gauge size and the structure it is bonded to. RTD values use the Callendar–Van Dusen equation with the IEC 60751 coefficients (A = 3.9083×10−3, B = −5.775×10−7, C = −4.183×10−12); lead-wire resistance is ignored.
Wheatstone Bridge: Balance, Sensitivity and Self-Heating
Core Engineering Principles
We draw the bridge with R1 top-left, R2 bottom-left, R3 top-right and Rx bottom-right, excitation across the top and bottom nodes, and the output taken between the two midpoints. Each side is a voltage divider, so the output is the difference of two divider voltages. It is zero when R1/R2 = R3/Rx. The null is independent of excitation voltage and ignores changes that move all four arms equally, such as temperature.
With a strain gauge or RTD we look at tiny fractional changes, so the bridge arrangement decides the signal. One active arm, a quarter bridge, gives about Vex/4 × ΔR/R. Two arms that change oppositely give twice that, and four give four times, and they also cancel temperature and lead effects. The limit is heat. Every arm dissipates power, the gauge warms the structure it is bonded to, and the reading drifts. Excitation is therefore a trade between signal size and self-heating; we usually keep gauge arms near 10 mW or less on poor heat sinks, and accept more only on a thick metal specimen.
Quarter Vout ≈ Vex/4 × GF × ε • half ×2, full ×4 • Parm = I² R
NEC & Standard References
IEC 60751 defines industrial platinum resistance thermometers, with R0 = 100 Ω for a Pt100, a temperature coefficient of 0.00385 per °C and the Callendar–Van Dusen coefficients A and B (and C below 0 °C) used here. ASTM E251 sets test methods for the performance characteristics of metallic bonded resistance strain gauges, including gauge factor and temperature behaviour. Load-cell accuracy classes are covered by OIML R 60. Strain-gauge excitation and self-heating limits are manufacturer recommendations, not standard values, so check the gauge datasheet.1. Left midpoint = 5 × 1 / 2 = 2.500 V.
2. Right midpoint = 5 × 1.1 / 2.1 = 2.619 V.
3. Vout = 2.619 − 2.500 = 119.05 mV, which is 23.81 mV/V.
4. Balance needs Rx = 1 × 1 / 1 = 1 kΩ, so the sensor is 100 Ω off.
5. Current = 2.500 + 2.381 = 4.88 mA, total power 24.4 mW, and 6.24 mW in Rx.
6. In sensor mode, a 350 Ω gauge with GF 2.0 at 1000 µε (ΔR = 0.7 Ω) gives 2.4975 mV at 5 V, but dissipates 17.9 mW; at 2.5 V it falls to 4.5 mW and 1.25 mV.
- Self-heating is a systematic error. The gauge warms, the specimen warms, and zero drifts; reduce excitation or use a pulsed supply.
- Lead wires matter. A quarter bridge adds lead resistance to one arm; use a three-wire connection or a half or full bridge.
- Don’t load the bridge. The output resistance can be hundreds of ohms, so use a high-impedance instrumentation amplifier.
- Keep the sign convention. Swapping R3 and Rx with the amplifier inputs reverses the polarity.
- Quarter-bridge non-linearity. At large strain use the exact formula.