Voltage Divider Formula
Calculate the output voltage when two resistors divide a voltage source.
One of the most common circuits in electronics.
The Formula
V_out = V_in × R₂ / (R₁ + R₂)
A voltage divider uses two resistors in series to produce a lower output voltage from a higher input. The output voltage is a fraction of the input, determined by the resistor ratio.
Variables
| Symbol | Meaning |
|---|---|
| V_out | Output voltage (volts) |
| V_in | Input (source) voltage (volts) |
| R₁ | First resistor (between V_in and V_out) |
| R₂ | Second resistor (between V_out and ground) |
Example 1
V_in = 12 V, R₁ = 10 kΩ, R₂ = 10 kΩ
V_out = 12 × 10,000 / (10,000 + 10,000)
V_out = 6 V (equal resistors split the voltage in half)
Example 2
Need 3.3 V from a 5 V supply. R₂ = 10 kΩ. Find R₁.
3.3 = 5 × 10,000 / (R₁ + 10,000)
R₁ + 10,000 = 50,000 / 3.3 = 15,152
R₁ ≈ 5.15 kΩ (use a standard 5.1 kΩ resistor)
When to Use It
Use the voltage divider formula when:
- Reducing a voltage to a lower level for a sensor or microcontroller
- Creating reference voltages in circuit design
- Reading analog sensor values with a known resistance range
- Biasing transistors and setting operating points