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Vin (+)
│
┌┴┐
│ │ R1
└┬┘
├───── Vout
┌┴┐
│ │ R2
└┬┘
│
GND (−)Vout = Vin × R2 / (R1 + R2)
| Ratio | R1 | R2 | Output |
|---|---|---|---|
| 1:1 (50%) | 10k | 10k | Vin/2 |
| 2:1 (33%) | 20k | 10k | Vin/3 |
| 1:2 (67%) | 10k | 20k | 2Vin/3 |
| 9:1 (10%) | 9k | 1k | Vin/10 |
| 3.3V from 5V | 5.1k | 10k | 3.31V |
| 3.3V from 12V | 26.4k | 10k | 3.30V |
A voltage divider is one of the most fundamental circuits in electronics, consisting of two resistors connected in series between a voltage source and ground. The output voltage is taken from the junction between the two resistors and is always a fraction of the input voltage, determined by the ratio of the resistor values. The formula Vout = Vin × R2 ÷ (R1 + R2) governs this relationship. Voltage dividers are used extensively in electronics for signal conditioning, sensor interfacing, biasing transistor circuits, and creating reference voltages. Arduino and Raspberry Pi projects frequently use voltage dividers to scale down sensor signals (such as 0–12V) to match the 3.3V or 5V ADC input range. While simple and elegant, voltage dividers have a critical limitation: their output voltage drops under load, making them unsuitable for power delivery. For power applications, engineers use voltage regulators (linear or switching) instead, per standard circuit design practices described in IEEE and IEC guidelines.
Determine Vin (your source voltage) and the desired Vout. For example, you might need to convert a 12V sensor signal to 3.3V for a microcontroller ADC input.
The ratio R2 ÷ (R1 + R2) must equal Vout ÷ Vin. For 3.3V from 12V: ratio = 3.3 ÷ 12 = 0.275. This means R2 must be 0.275 times the total resistance (R1 + R2).
Pick R2 first (e.g., 10kΩ), then calculate R1. For our example: R1 = R2 × (Vin ÷ Vout - 1) = 10k × (12 ÷ 3.3 - 1) = 26.36kΩ. Use the nearest standard value: 27kΩ (gives 3.24V) or a precise 26.4kΩ resistor.
Ensure the load impedance is at least 10× R2 to maintain output accuracy. For a 10kΩ R2, the load should be 100kΩ or higher. Microcontroller ADC inputs typically have >1MΩ impedance, making them ideal loads for voltage dividers.
Voltage dividers scale analog sensor outputs to match microcontroller ADC ranges, enabling Arduino and Raspberry Pi projects to safely read higher-voltage signals without damaging components.
When connecting 5V and 3.3V logic systems, voltage dividers provide a simple, cost-effective method for unidirectional signal level translation without dedicated ICs.
Transistor amplifier circuits rely on voltage dividers to set stable bias points, ensuring consistent operation across temperature variations and component tolerances.
| Conversion | R1 | R2 | Actual Vout | Error |
|---|---|---|---|---|
| 5V to 3.3V | 5.1kΩ | 10kΩ | 3.31V | +0.3% |
| 12V to 5V | 14kΩ | 10kΩ | 5.0V | 0% |
| 12V to 3.3V | 26.4kΩ | 10kΩ | 3.30V | 0% |
| 24V to 5V | 38kΩ | 10kΩ | 5.0V | 0% |
| 24V to 3.3V | 62.7kΩ | 10kΩ | 3.30V | +0.1% |
| 9V to 5V | 8kΩ | 10kΩ | 5.0V | 0% |
No. Voltage dividers are not suitable for power delivery because the output voltage drops significantly when current is drawn by a load. The load effectively appears in parallel with R2, changing the divider ratio. For power delivery, use a linear voltage regulator (like LM7805) for low current or a switching regulator (buck converter) for higher efficiency and current.
For most signal-level applications, use resistors in the 1kΩ to 100kΩ range. Lower values (1k–10kΩ) provide better noise immunity and load regulation but consume more current. Higher values (47k–100kΩ) minimize power consumption but are more susceptible to noise pickup and stray capacitance effects. For battery-powered circuits, favor higher values to conserve energy.
Any load connected to the output appears in parallel with R2, reducing the effective lower resistance. This causes the output voltage to drop below the calculated unloaded value. The rule of thumb is that load resistance should be at least 10 times R2 for the output to remain within 10% of the calculated value. For precision applications, use a buffer amplifier (op-amp voltage follower) between the divider and load.
To read a higher voltage signal with a microcontroller, design a voltage divider that scales the maximum input voltage to the ADC reference voltage (5V for Arduino Uno, 3.3V for Raspberry Pi). For example, to read 0–12V with an Arduino: use R1 = 15kΩ and R2 = 10kΩ, giving Vout = 12V × 10 ÷ 25 = 4.8V, safely under the 5V ADC limit.
Yes, purely resistive voltage dividers work identically with AC and DC signals and maintain the same attenuation ratio at all frequencies. This makes them useful in audio circuits and measurement applications. For frequency-dependent voltage division, capacitive dividers are used in high-voltage probes and RF circuits, while inductive dividers serve in power system measurement transformers.