Voltage Divider Calculator

About the Voltage Divider Calculator

A voltage divider is two resistors in series: the output, taken across R2, is Vin × R2 / (R1 + R2). Enter the input and both resistors to get the output, or enter the output you need and solve for R1 or R2. The calculator then rounds to the standard values you stock (E6 to E192), lists the best standard pairs with their exact output and error, and shows the divider current, the power in each resistor and the output (Thevenin) resistance.

Add a load resistance — the input of an ADC, a meter or the next stage — and every figure includes it, including how far the load pulls the output down. Separate modes cover the current divider, the Wheatstone bridge (balance point and output voltage) and strain-gauge bridges in quarter-, half- and full-bridge form, from strain to millivolts and back.

Formulas

• Output: Vout = Vin × R2′ / (R1 + R2′), where R2′ = R2 ‖ RL = R2·RL / (R2 + RL) with a load RL (R2′ = R2 without one).
• Solving: R2′ = R1 × Vout / (Vin − Vout), then R2 = 1 / (1/R2′ − 1/RL) with a load; R1 = R2′ × (Vin − Vout) / Vout.
• Thevenin equivalent (what the output looks like to whatever you connect): Vth = Vin × R2 / (R1 + R2) and Rth = R1 ‖ R2. The lower Rth is compared with the load, the less the load changes the output.
• Current divider: Ik = I × (1/Rk) / Σ(1/Rj); for two resistors I1 = I × R2 / (R1 + R2).

Choosing the resistor values

The ratio sets the output; the size of the resistors sets the current and the output resistance. Small values waste current (and power in the resistors); large values make the output easily pulled down by the load and more sensitive to noise. A common rule is to make the divider current at least ten times the load current, or Rth well below the input resistance of whatever reads it — an ADC datasheet usually gives a maximum source impedance. The best-pairs table keeps one resistor within a factor of about three of the value you entered, so the current stays similar.

Wheatstone bridge

Two dividers side by side, fed from the same excitation voltage Vex: R1 (top left) and R2 (bottom left), R4 (top right) and R3 (bottom right). The output between the two midpoints is Vout = Vex × (R3/(R3 + R4) − R2/(R1 + R2)), and it is zero — the bridge is balanced — when R1 × R3 = R2 × R4. Wheatstone published the method in 1843; it is still how strain gauges, RTDs and load cells turn tiny resistance changes into a measurable voltage.

Strain-gauge bridges

With gauge factor GF and strain ε (x = GF × ε), the output per volt of excitation Vr = Vout / Vex is:

• Quarter bridge, one active gauge: Vr = (x/4) / (1 + x/2)
• Half bridge, bending (+ε and −ε gauges in adjacent arms): Vr = x/2
• Half bridge, axial with a Poisson gauge (+ε and −ν·ε): Vr = (1 + ν)·x / (4 + 2(1 − ν)·x)
• Full bridge, bending (four active gauges): Vr = x
• Full bridge, bending with Poisson gauges: Vr = (1 + ν)·x / 2
• Full bridge, axial with Poisson gauges: Vr = (1 + ν)·x / (2 + (1 − ν)·x)

The quarter and axial bridges are slightly nonlinear: the calculator shows the exact output, the linear approximation and the difference (about 0.1% per 1000 µε for a quarter bridge with GF = 2). Metal-foil gauges have a gauge factor of about 2; take the exact value from the gauge package. Poisson’s ratio ν is about 0.3 for steel and 0.33 for aluminium. Going from a reading back to strain, an output the bridge cannot produce, or one that would mean more than 100,000 µε (10%), is reported as a likely typo rather than turned into a strain.

Sources

• IEC 60063:2015, Preferred number series for resistors and capacitors (E-series)
• Vishay Micro-Measurements Tech Note TN-507-1, Errors Due to Wheatstone Bridge Nonlinearity
• NI, Measuring Strain with Strain Gages (quarter-, half- and full-bridge configurations; about 0.5 mV/V at 1000 µε for a quarter bridge and 2.0 mV/V for a full bridge; gauge factor about 2 for metal gauges)
• Wheatstone, C. (1843), “An account of several new instruments and processes for determining the constants of a voltaic circuit”, Phil. Trans. R. Soc. 133: 303–327

Limitations

• Resistors are taken at their nominal value: a ±1% resistor pair can move the output by up to about ±1%. The best-pairs errors are from nominal values only.
• The load is treated as a resistance. Inputs that draw a pulsed or changing current (such as a sampling ADC) may need a buffer or a capacitor across R2.
• A divider is not a power supply: the output voltage falls as soon as current is drawn. Use a regulator to power anything.
• Strain results assume identical gauges, no lead-wire resistance and no temperature change; long leads on a quarter bridge reduce the output and need compensation.

Privacy

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.