OpenSpecEngineering

Works out a two-resistor voltage divider. Give the input voltage and both resistors to get the output voltage and the current through the divider. Or give a target output and one resistor to get the other, with the nearest standard value from an E-series. Use it to scale a voltage down for an ADC input, set a regulator’s feedback, or make a bias voltage.

Equations

V_out = V_in·R₂/(R₁ + R₂)     I = V_in/(R₁ + R₂)

V_in is the voltage across the whole divider, R₁ the top resistor (from V_in to the output), R₂ the bottom resistor (from the output to ground), V_out the voltage across R₂ and I the current through both [1]. Solved for either resistor:

R₁ = R₂·(V_in − V_out)/V_out     R₂ = R₁·V_out/(V_in − V_out)

The nearest standard value comes from the IEC 60063 preferred-number series you pick [2], and the page says how far above or below the exact value it lies.

Limits and common mistakes

• The equations assume nothing draws current from the output. A load across R₂ acts in parallel with it and pulls V_out down. Keep the load resistance at least 10 times R₂, or include it in R₂.
• The target output must lie between 0 and V_in. A divider can only scale down.
• Picking the resistor values is a trade-off. Low values waste current and heat; very high values let leakage and input currents shift the output and pick up noise.
• Don’t power a circuit from a divider. Its output sags as the load changes; use a regulator.
• Rounding to a standard value moves V_out. Re-solve with the part you choose, and allow for the resistors’ tolerance too.

Worked example

A microcontroller with a 3.3 V ADC must read a 24 V battery. The top resistor is 100 kΩ, and 24 V should give about 3.0 V at the pin, leaving headroom below 3.3 V.

1. Choose Solve for R2 (bottom resistor).
2. Enter Input voltage (V_in) 24 V, R1 (top resistor) 100 kΩ and Target Output Voltage (V_out) 3 V.
3. Choose Also show the nearest standard resistor from E24 (±5 %) and press Solve. The Solution shows: Required R2: 14,285.7 Ω
   Nearest E24 value (±5 %): 15 kΩ (5.0 % above)
   Divider current (I): 2.1e-4 A
4. To check the part chosen, choose Solve for Output Voltage (Vout), enter R2 (bottom resistor, Vout taken here) 15 kΩ and press Solve: Output voltage (V_out): 3.13043 V
   Divider current (I): 2.08696e-4 A

Check by hand: R₂ = 100 kΩ × 3/21 = 14.29 kΩ, and with 15 kΩ the output is 24 × 15/115 = 3.13 V, still below 3.3 V. The divider draws only about 0.2 mA from the battery.