Electrical Engineering

Voltage Divider

Vout = Vin * R2 / (R1 + R2)

Last reviewed: How we build & verify
V
ohm
ohm

How it works

Two resistors in series split a supply voltage in proportion to their resistances, with the output taken from the junction between them. The same current passes through both, so each resistor drops a share of the total equal to its share of the total resistance.

Formula
Vout = Vin × R2 / (R1 + R2)
I = Vin / (R1 + R2)
Variables
  • Vinsupply voltage across the series pair
  • R1upper resistor, between the supply and the output node
  • R2lower resistor, between the output node and ground
  • Voutvoltage at the node between R1 and R2, unloaded
  • Istanding current through the divider
Worked example
Inputs: Vin = 12 V, R1 = 10 kΩ, R2 = 4.7 kΩ
  1. Total resistance: 10,000 + 4,700 = 14,700 Ω
  2. Divider ratio: 4,700 / 14,700 = 0.3197
  3. Vout = 12 × 0.3197 = 3.837 V
  4. I = 12 / 14,700 = 0.8163 mA
  5. Standing power: 12 × 0.8163 mA = 9.80 mW
Result: Vout = 3.84 V, drawing 0.816 mA
Notes
  • The formula assumes nothing is connected to the output. Any load sits in parallel with R2 and pulls the voltage down, so either keep the load impedance at least ten times R2 or buffer the tap with an op-amp follower.
  • A divider is not a regulator. Vout tracks Vin proportionally, so supply ripple passes straight through and the output sags as soon as the load draws real current.
  • Raising both resistances cuts the standing current but raises output impedance and picks up more noise. Somewhere between 1 kΩ and 100 kΩ is the usual compromise for a sensing tap.
  • Tolerances stack in the same direction. Two 5% resistors can shift this ratio by close to 7% at the worst-case corner, even though the nominal numbers look exact.

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