Voltage divider formula

Vout = Vin × R2 / (R1 + R2)

The two resistors form a series circuit. The output is taken across R2. Current through the divider: I = Vin / (R1 + R2).

Common uses

Level shifting - reduce a 5 V signal to 3.3 V for a microcontroller
Biasing transistors
Reference voltages for ADC inputs
Volume controls (potentiometer)

Circuit diagram

A voltage divider consists of two resistors in series between the supply voltage and ground. The output is measured at the junction between R1 and R2:

   Vin
    │
   [R1]
    │
    ├───► Vout
   [R2]
    │
   GND

R1 is the top resistor (between Vin and Vout). R2 is the bottom resistor (between Vout and ground). To get a higher Vout, decrease R1 or increase R2. The formula Vout = Vin × R2 / (R1 + R2) confirms that Vout is always less than Vin (for positive resistances).

Load effect warning

When you connect a load (RL) across R2, it is in parallel with R2. The effective lower resistance is R2 ∥ RL = (R2 × RL) / (R2 + RL), which is always less than R2. This lowers Vout. For a stable Vout, choose R1 and R2 such that the divider current is at least 10× the load current, making the load’s effect negligible.

Resistor selection guide

Standard resistor values follow the E12 and E24 series, which contain 12 or 24 values per decade. When designing a voltage divider, choose a ratio R1/R2 matching your target and round to the nearest standard values.

Example: 5 V source to 3.3 V output requires Vout/Vin = 0.66, so R2/R1 ≈ 0.515. From the E24 series: R1 = 15 kΩ, R2 = 27 kΩ gives Vout = 5 × 27/(15+27) = 3.21 V (within 3.3% of target - acceptable for most digital logic level conversion).

Power dissipation calculation

Total power dissipated by the resistor network is:

P = Vin² / (R1 + R2)

For battery-powered circuits, use large resistor values (100 kΩ+) to keep quiescent current low. For a 5 V source and R1+R2 = 200 kΩ: P = 25/200,000 = 0.125 mW - negligible even for coin-cell batteries.

Zener diode comparison

A Zener diode shunt regulator maintains a more stable output voltage under varying load conditions than a resistive divider:

Stability: Zener ≪ resistive divider under variable load.
Cost: a Zener diode + one resistor is often inexpensive.
Current draw: Zener regulators waste current as heat; not ideal for ultra-low-power designs.
Recommendation: use a resistive divider for signal conditioning and level shifting; use a Zener or IC regulator for powering loads.