Voltage Divider Circuits Explained: Formula, Design, and Applications
A voltage divider is one of the simplest and most useful circuits in electronics. Learn the formula, how to design a divider for any output voltage, understand loading effects, and see practical applications like sensor interfaces and logic level shifting.
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.