Voltage Dividers: The Most Useful Circuit You'll Ever Build

A voltage divider is two resistors in series. That's it. Connect the top to your input voltage, the bottom to ground, and the middle point gives you a fraction of the input. It's the most fundamental analog circuit, and you'll use it constantly — level shifting, sensor reading, bias networks, and reference voltages.

The formula

V_out = V_in × R2 / (R1 + R2)

Where R1 connects V_in to V_out, and R2 connects V_out to ground.

V_in ──[ R1 ]──┬── V_out
                │
              [ R2 ]
                │
              GND

The voltage divider calculator lets you enter any three values and solve for the fourth. Enter V_in, R1, and R2 to get V_out — or enter V_in, V_out, and one resistor to find the other.

Practical examples

5V to 3.3V for a microcontroller input

You have a 5V sensor output but your Raspberry Pi GPIO expects 3.3V max. You need V_out/V_in = 3.3/5 = 0.66.

Pick R2 = 10 kΩ. Then R1 = R2 × (V_in/V_out − 1) = 10k × (5/3.3 − 1) = 10k × 0.515 = 5.15 kΩ.

Nearest standard: 5.1 kΩ. That gives V_out = 5 × 10k / (5.1k + 10k) = 3.31V. Close enough.

12V battery monitoring with an ADC

An Arduino ADC reads 0–5V. To monitor a 12V battery, divide by about 3. Use R1 = 20 kΩ, R2 = 10 kΩ:

V_out = 12 × 10k / (20k + 10k) = 4.0V — safely within ADC range. A fully charged 12.6V battery gives 4.2V. A dead battery at 10.5V gives 3.5V. Plenty of range.

Audio signal attenuation

Line-level audio is about 1V peak-to-peak. To reduce it to microphone level (~10 mV), use R1 = 100 kΩ and R2 = 1 kΩ:

V_out = 1 × 1k / (100k + 1k) = 0.0099V ≈ 10 mV.

The loading problem

Here's where beginners get burned. The voltage divider formula assumes no current flows out of the V_out node. In reality, whatever you connect to V_out draws current, which changes the output voltage.

Rule of thumb: The load impedance should be at least 10× the value of R2. If R2 = 10 kΩ, the load should be 100 kΩ or higher.

This is why voltage dividers work well for:

• High-impedance ADC inputs (typically >1 MΩ)
• MOSFET gate drives (near-infinite impedance)
• Op-amp inputs (very high impedance)

And poorly for:

• Directly powering LEDs (low impedance)
• Driving relay coils
• Any load that draws significant current

If you need to supply current at a reduced voltage, use a voltage regulator, not a divider.

Power dissipation

Current flows through R1 and R2 continuously, wasting power. With V_in = 12V and R_total = 30 kΩ:

I = 12 / 30,000 = 0.4 mA P = 12 × 0.0004 = 4.8 mW

That's negligible. But with R_total = 100 Ω:

I = 12 / 100 = 120 mA P = 12 × 0.12 = 1.44 W

Now you're dissipating real power. For battery-powered devices, use high-value resistors (100 kΩ range) to minimize idle current. Use the power calculator to check dissipation for your specific values.

Choosing resistor values

For signal conditioning (sensors, ADCs): Use 10 kΩ – 100 kΩ range. Low enough to avoid noise pickup, high enough to minimize power waste.

For high-voltage monitoring: Use 100 kΩ – 1 MΩ range. Minimizes current draw from the source.

For audio: Use 1 kΩ – 100 kΩ range. Must be low enough relative to the source impedance but high enough for the load.

To identify the resistors in your bin, the resistor color code decoder reads 4-band and 5-band markings instantly.

Voltage dividers in the real world

You'll find voltage dividers everywhere:

• Potentiometers — a pot is a variable voltage divider. The wiper position sets the ratio.
• Sensor interfaces — thermistors, photoresistors, and FSRs are typically read as one leg of a voltage divider.
• Feedback networks — voltage regulators use a resistor divider to set the output voltage (the chip compares the divided output to an internal reference).
• Biasing — transistor and op-amp circuits use voltage dividers to set DC operating points.

Common mistakes

1. Ignoring load current. If your divider says 3.3V but the load drops it to 2.8V, your R2 is too high relative to the load impedance.
2. Using for power delivery. A voltage divider is a signal-level tool, not a power supply. Use regulators for powering circuits.
3. Forgetting about tolerance. Two 5% resistors can shift V_out by up to 10%. For precision references, use 1% resistors.
4. AC signals and capacitance. At high frequencies, parasitic capacitance across R2 creates a low-pass filter effect. For RF work, this matters.