Voltage Divider Circuits Explained: Formula, Design, and Applications

What Is a Voltage Divider?

A voltage divider is a passive circuit that produces a fraction of its input voltage at the output. It consists of two resistors in series: the output is taken from the junction between them.

         Vin
          │
         [R1]
          │
Vout ─────┤
          │
         [R2]
          │
         GND

The output voltage is:

Vout = Vin × R2 / (R1 + R2)

Worked Examples

Example 1: Basic divider

R1 = 10kΩ, R2 = 10kΩ, Vin = 10V

Vout = 10 × 10000 / (10000 + 10000) = 10 × 0.5 = 5 V

Equal resistors always give half the input voltage.

Example 2: Produce 3.3V from 5V

We need Vout/Vin = 3.3/5 = 0.66. Choose R2/(R1+R2) = 0.66.

R2 / (R1 + R2) = 0.66
R1 = R2 × (0.34 / 0.66) = R2 × 0.515

If R2 = 10kΩ, then R1 = 5.15kΩ. Nearest standard value: 4.7kΩ or 5.6kΩ.

With R1 = 4.7kΩ:

Vout = 5 × 10 / (4.7 + 10) = 5 × 0.68 = 3.4 V

Close enough for a logic level converter.

Choosing Resistor Values

Higher resistance values draw less current (more power-efficient) but are more susceptible to loading effects. Lower resistance values are less susceptible to loading but draw more current.

General guidance:

Keep R1 || R2 (parallel combination) at least 10× lower than the load impedance
For battery-powered circuits, use higher values (100kΩ range) to minimise quiescent current draw
For signal-level dividers, keep values in the 1kΩ–100kΩ range

Loading Effect

The voltage divider formula assumes no current flows out of the Vout terminal. In practice, connecting a load (RL) in parallel with R2 lowers the effective R2:

R2_eff = (R2 × RL) / (R2 + RL)

This reduces Vout. The error is small when RL >> R2. As a rule of thumb, the load resistance should be at least 10× R2 for less than a 10% voltage drop from the ideal value.

Practical Applications

Logic level shifting (5V to 3.3V)

Many microcontrollers (Arduino, RPi, STM32) use 3.3V I/O logic. When interfacing with 5V devices, a voltage divider can shift the logic levels safely:

5V signal → R1 = 2kΩ → Vout → R2 = 3.3kΩ → GND
Vout = 5 × 3.3/(2+3.3) = 5 × 0.623 = 3.1V ≈ 3.3V ✓

For signals above a few MHz, consider a dedicated logic level translator IC — the resistors add capacitance and parasitic delay that can degrade fast signals.

Potentiometer as a variable divider

A potentiometer is effectively a tapped voltage divider. The wiper position sets R2/(R1+R2), making it continuously variable. Used for volume controls, position sensors, and user-adjustable inputs.

NTC Thermistor temperature sensing

An NTC (negative temperature coefficient) thermistor changes resistance with temperature. Paired with a fixed resistor in a voltage divider, the output voltage changes with temperature and can be read by an ADC:

Vin ─── R_fixed ─── Vout ─── NTC ─── GND
Vout = Vin × NTC / (R_fixed + NTC)

At a target temperature, set R_fixed ≈ NTC resistance to maximise sensitivity (steepest voltage change per °C) and centre the output around Vin/2.

ADC Reference voltage

Some ADCs require a reference voltage lower than the supply. A voltage divider from the supply to a stable reference resistor network is a simple (though less precise than a dedicated voltage reference IC) way to generate a Vref.

What Voltage Dividers Are NOT Good For

A resistive voltage divider is not a voltage regulator. The output voltage changes with load current. For a stable supply voltage, use a linear regulator (LDO) or switching regulator (buck/boost converter). Use voltage dividers for measurement and biasing, not for powering loads.

Try It Online

The Voltage Divider Calculator on DevGizmo calculates output voltage, current, and power dissipation for any resistive voltage divider — enter any three values to solve for the fourth.