What Is a Voltage Divider?
A voltage divider is one of the most fundamental circuits in electronics — two resistors connected in series between a supply voltage and ground, with the output taken from the junction between them. Despite its simplicity, it is used everywhere: from biasing transistors and setting reference voltages to scaling sensor outputs for ADC inputs.
The Voltage Divider Formula
For a divider with resistors R1 (top, connected to supply) and R2 (bottom, connected to ground), the output voltage Vout is:
Vout = Vin × R2 / (R1 + R2)
For example, if Vin = 12V, R1 = 10kΩ, and R2 = 4.7kΩ:
Vout = 12 × 4700 / (10000 + 4700) = 12 × 0.32 = 3.84V
This is useful for scaling a 12V sensor output down to the 3.3V or 5V range of a microcontroller ADC input.
Designing for a Target Output Voltage
If you know Vin and the desired Vout, you can choose a ratio for R2 / (R1 + R2). The absolute resistor values are then chosen based on current consumption and load requirements (more on this below). A practical design process:
- Calculate the required ratio: ratio = Vout / Vin
- Choose a standard R2 value (e.g., 10kΩ).
- Calculate R1: R1 = R2 × (1 − ratio) / ratio
- Round R1 to the nearest E24 or E96 standard value and verify the output voltage with the formula.
The Load Effect: The Most Critical Practical Consideration
The voltage divider formula assumes no current is drawn from the output. In reality, any load connected to Vout adds a parallel resistance to R2, which reduces the effective R2 and lowers Vout. This is called loading.
As a rule of thumb, the load resistance should be at least 10× greater than R2 for the loading error to remain below approximately 10%. For better accuracy, aim for a load resistance of 100× R2 or buffer the output with an op-amp voltage follower.
When Loading Is a Problem
- Driving a low-impedance load directly from a divider (e.g., a relay coil)
- ADC inputs with sample-and-hold capacitors that draw transient charge current
- Multiple loads connected in parallel to the same divider output
Resistor Value Selection
Choosing the right absolute resistance values involves a trade-off:
| Resistor Values | Pros | Cons |
|---|---|---|
| Low (100Ω–1kΩ) | Low load sensitivity, good for fast signals | High quiescent current, power dissipation |
| Medium (10kΩ–100kΩ) | Balance of power and load sensitivity | Moderate loading effect |
| High (1MΩ+) | Very low current draw | Very sensitive to load, susceptible to noise pickup |
For most general-purpose analog circuits, resistor values in the 10kΩ to 100kΩ range offer a good compromise.
Power Dissipation in Divider Resistors
Don't forget to check that the resistors can handle the power. The total power dissipated by the divider is:
P = Vin² / (R1 + R2)
With Vin = 12V and R1 + R2 = 14.7kΩ, P = 144 / 14700 ≈ 9.8mW — well within the capacity of a standard 1/8W or 1/4W resistor. However, if Vin = 12V and R1 + R2 = only 100Ω, P = 1.44W, which would destroy a standard 1/4W resistor.
When Not to Use a Simple Voltage Divider
- Powering loads — a voltage divider is not a voltage regulator. Use a proper linear or switching regulator instead.
- Driving low-impedance inputs — add a buffer op-amp stage.
- Precision references — use a dedicated voltage reference IC for accuracy better than a few percent.
- High-frequency signals — stray capacitance across resistors alters the frequency response; use resistor-capacitor compensation.
Summary
The voltage divider is simple, elegant, and useful in a huge number of circuit designs. Mastering its formula, understanding the loading effect, and selecting appropriate resistor values will serve you well across virtually every area of electronics design.