Current I = Vin / (R1 + R2) — the same current flows through both resistors
Power PR1 = I² × R1 — power dissipated in top resistor
Power PR2 = I² × R2 — power dissipated in bottom resistor
Ratio = Vout / Vin — the attenuation factor
Worked Examples
1 Arduino 5 V → 3.3 V ADC
Vin5 V
R110 kΩ
R220 kΩ
Vout = 5 × 20k / 30k3.33 V
2 12 V → 5 V reference
Vin12 V
R114 kΩ
R28.6 kΩ
Vout = 12 × 8.6k / 22.6k≈ 4.57 V
3 Find R1 for 2.5 V output
Vin5 V
Vout2.5 V
R210 kΩ
R1 = 10k × (5−2.5) / 2.510 kΩ
4 Sensor bias 3.3 V → 1.65 V
Vin3.3 V
R1100 kΩ
R2100 kΩ
Vout = 3.3 × 100k / 200k1.65 V
Frequently Asked Questions
What is a voltage divider?▾
A voltage divider is a simple circuit with two resistors in series. The output is tapped from the junction between them. It produces an output voltage that is a fixed fraction of the input — set by the ratio R2 / (R1 + R2). Common uses include ADC input scaling, sensor biasing, and reference voltage generation.
What is the voltage divider formula?▾
Vout = Vin × R2 / (R1 + R2)
R1 is the top resistor (between supply and output), R2 is the bottom resistor (between output and ground). Output is measured across R2.
When does the formula become inaccurate?▾
The formula assumes an unloaded output. When a load (like a microcontroller pin or sensor) is connected, it draws current through R2, lowering Vout. The error stays below 10% when the load resistance is at least 10× larger than R2. For low-impedance loads, use an op-amp buffer after the divider.
Can I use a voltage divider to power a circuit?▾
No — not reliably. A voltage divider has high output impedance (R1 ∥ R2), so any load current causes the voltage to drop. For powering circuits, use a linear voltage regulator (LM7805, LM317) or a switching regulator instead. Voltage dividers are only suitable for signal conditioning and biasing.
How do I choose resistor values?▾
Two rules:
1. Ratio: R2 / (R1 + R2) must equal Vout / Vin. Start with a standard R2 value, then calculate R1. 2. Total resistance: Higher total resistance (R1+R2) means less idle current (more efficient), but higher output impedance (worse with loads). 10–100 kΩ total is a good starting range for most digital circuits.