Voltage Divider Formula
Calculate the output voltage of a two-resistor voltage divider from input voltage and resistor values.
Includes Vout = Vin*(R2/(R1+R2)) with practical examples.
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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
Key Notes
- The formula assumes negligible load current — when a load R_L is connected, V_out drops because R_L parallels R₂; the loaded output is V_in × (R₂‖R_L) / (R₁ + R₂‖R_L)
- The "10:1 rule": for accurate division, load resistance should be at least 10× R₂ — lower load resistance drags V_out below the calculated value significantly
- A voltage divider wastes power continuously: P_waste = Vin² / (R₁ + R₂); use large resistor values (kΩ–MΩ range) to minimize standby current drain in battery-powered circuits
- A potentiometer is mechanically adjustable voltage divider — the wiper slides along a resistive element, setting R₂ as a fraction of the total resistance
Key Notes
- Voltage divider formula: V_out = V_in × R₂ / (R₁ + R₂): Two resistors in series split the input voltage proportionally. V_out is taken across R₂. The formula works because the same current flows through both resistors: I = V_in/(R₁+R₂); V_out = I × R₂.
- Current divider (dual problem): I₁ = I_total × R₂ / (R₁ + R₂): Note the subscript flip — R₂ controls I₁ because more current takes the lower-resistance path. For two parallel resistors: I₁/I₂ = R₂/R₁. Lower resistance always carries more current.
- Loading effect — the critical limitation: Connecting a load resistance R_L in parallel with R₂ changes V_out because it changes the effective resistance. The loaded output: V_out = V_in × (R₂ ‖ R_L) / (R₁ + R₂ ‖ R_L). Loading is negligible only when R_L ≫ R₂ (rule of thumb: R_L > 10 × R₂).
- Potentiometer: A three-terminal variable resistor acts as an adjustable voltage divider. Moving the wiper changes R₁ and R₂ in opposite directions, varying V_out smoothly. Used in volume controls, joystick position sensing, and manual bias adjustment in circuits.
- Applications: Voltage dividers are ubiquitous in electronics: biasing transistor bases and op-amp inputs, scaling sensor outputs (e.g., 0–5V sensor to 0–3.3V microcontroller), setting reference voltages, attenuating signals, and implementing resistor networks for DAC (digital-to-analog converter) circuits.