Wheatstone Bridge Calculator
Enter the three known resistances and supply voltage to find the unknown resistor in a balanced bridge, or enter all four resistances to calculate the differential output voltage, equivalent resistance, and supply current for an unbalanced bridge. Results update as you type and a step-by-step panel shows the working.
Formula
Worked example
Balanced bridge: R1=1 kOhm, R2=2 kOhm, R3=1.5 kOhm. Rx = (2000/1000) x 1500 = 3000 Ohm. With 5 V supply the equivalent load is (3000 x 4500)/7500 = 1800 Ohm, drawing 2.78 mA. Unbalanced: same resistors but Rx=3200 Ohm (slightly off null). Vout = 5 x (2000/3000 - 3200/4700) = 5 x (0.6667 - 0.6809) = -0.0710 V (-71.0 mV).
What is a Wheatstone bridge?
A Wheatstone bridge is a circuit of four resistors arranged in a diamond (rhombus) shape, with a voltage source applied across two opposite corners and a detector (historically a galvanometer, today an instrumentation amplifier) connected across the other two. It was invented by Samuel Hunter Christie in 1833 and popularised by Sir Charles Wheatstone in 1843. Its principal virtue is that the output is zero when the ratios of adjacent arm resistances are equal, so even a tiny change in one resistance produces a measurable voltage. That property makes it the standard interface circuit for resistive sensors including strain gauges, thermistors, platinum resistance thermometers (RTDs), and photoresistors. Modern load cells, pressure transducers, and precision thermometry all rely on Wheatstone bridge principles.
How a balanced bridge works
Label the four arms R1 (upper-left), R2 (lower-left), R3 (upper-right) and Rx (lower-right). Supply voltage Vs feeds the top node; the bottom node is ground. When R1/R2 = R3/Rx the two mid-node voltages are identical, so the detector reads exactly zero. Rearranging gives Rx = (R2/R1) x R3. In a laboratory measurement, R2 is a calibrated variable resistor. The operator adjusts R2 until the galvanometer reads null, then reads Rx directly from the dial. This null method is extremely precise because the measurement does not depend on the exact value of Vs or the detector sensitivity, only on the ratio of the known resistors. The ratio R2/R1 is the bridge ratio, and choosing a ratio close to one gives the smallest measurement uncertainty.
Output voltage of an unbalanced bridge
When Rx departs from the null value (for example a strain gauge stretches slightly), the two mid-node voltages diverge and the detector sees a differential voltage. The exact formula is Vout = Vs x (R2/(R1+R2) - Rx/(R3+Rx)). For small deviations from balance the output is nearly linear in the fractional resistance change dRx/Rx, which is why strain gauges express their response as the gauge factor (GF = (dR/R) / strain). The sensitivity of the bridge in mV per volt of supply is (Vout/Vs) x 1000. Real bridge amplifiers specify this sensitivity in mV/V as it removes the supply dependence. Increasing Vs boosts the signal but also increases self-heating of the sensing element, which matters particularly for RTDs and thermistors.
Practical considerations and bridge configurations
Full-bridge, half-bridge, and quarter-bridge are the standard configurations used in structural testing. A quarter-bridge uses one active sensing element (one arm changes) and three fixed resistors. A half-bridge uses two adjacent or opposite active elements, which either doubles the output or cancels the temperature-induced common-mode drift. A full bridge uses all four arms as active elements, doubling the output again and cancelling temperature drift simultaneously. Modern bridge amplifier ICs (such as the INA125, AD8221, or HX711) provide regulated excitation voltage, high-gain differential amplification, and analog-to-digital conversion in one package. When designing for stability, keep all four resistor values within a factor of 10 of each other to maximise sensitivity and minimise loading effects from the detector input impedance.
Common Wheatstone bridge arm configurations
| Configuration | R1 | R2 | R3 | Rx (balanced) | Use case |
|---|---|---|---|---|---|
| Equal arms | 1 kOhm | 1 kOhm | 1 kOhm | 1 kOhm | Precision resistance measurement |
| 2:1 ratio | 1 kOhm | 2 kOhm | 1 kOhm | 2 kOhm | Extended measurement range |
| 10:1 ratio | 1 kOhm | 10 kOhm | 1 kOhm | 10 kOhm | Wide-range sensor interface |
| Strain gauge (120 Ohm) | 120 Ohm | 120 Ohm | 120 Ohm | 120 Ohm (+/-) | Strain gauge measurement |
| Platinum RTD | 1 kOhm | 1 kOhm | 100 Ohm | 100 Ohm | Temperature sensing (PT100) |
Typical resistor values used in precision measurement bridges. All arms equal gives the most sensitive null measurement.
Frequently asked questions
What is the Wheatstone bridge formula?
For a balanced bridge: Rx = (R2/R1) x R3. This comes from setting the two voltage-divider ratios equal: R1/R2 = R3/Rx. For an unbalanced bridge the output voltage is Vout = Vs x (R2/(R1+R2) - Rx/(R3+Rx)), where Vs is the supply voltage.
How do I use this calculator for a balanced bridge?
Select "Balanced bridge" mode, enter the three known resistances (R1, R2, R3), and the calculator solves for Rx. Enter a supply voltage as well and it will also show the equivalent load resistance and the supply current.
What does a negative Vout mean?
Vout is defined as the left mid-node voltage minus the right mid-node voltage. A negative result means the right node is at a higher potential than the left node. In a strain-gauge application, the sign tells you the direction of strain (tension vs compression). Which sign is positive and which is negative depends on how you wire the bridge and the amplifier.
What is bridge sensitivity and why does it matter?
Bridge sensitivity is the output voltage divided by the supply voltage, expressed in mV/V. It tells you how much signal you get per volt of excitation regardless of the exact supply value. A typical strain-gauge full bridge has a sensitivity of about 2 mV/V at full scale. Knowing the sensitivity lets you choose the right gain for your instrumentation amplifier.
What is the equivalent resistance of a Wheatstone bridge?
Looking into the supply terminals, the bridge appears as two series strings in parallel: Req = (R1+R2)||(R3+Rx) = (R1+R2)(R3+Rx)/(R1+R2+R3+Rx). This determines the current drawn from the supply and the power dissipated in the bridge.
Why is the Wheatstone bridge so accurate?
The balanced (null) measurement method means the result depends only on the ratio of the known resistors, not on the supply voltage or the internal resistance of the detector. Small instabilities in the supply or the galvanometer sensitivity do not affect the measurement, making it far more precise than a direct Ohm-law measurement.