Voltage Divider Guide: Formula, Circuit Design & Calculator
Voltage Divider Formula
A voltage divider uses two resistors to produce an output voltage that is a fraction of the input:
Vout = Vin × R2 / (R1 + R2)
- Vin = input voltage
- Vout = output voltage (across R2)
- R1 = upper resistor (series)
- R2 = lower resistor (to ground)
Common Voltage Divider Outputs
| Vin | R1 | R2 | Vout | Ratio |
|---|---|---|---|---|
| 12V | 10 kΩ | 10 kΩ | 6.00V | 50% |
| 12V | 20 kΩ | 10 kΩ | 4.00V | 33% |
| 12V | 10 kΩ | 20 kΩ | 8.00V | 67% |
| 5V | 10 kΩ | 10 kΩ | 2.50V | 50% |
| 5V | 33 kΩ | 10 kΩ | 1.16V | 23% |
| 24V | 100 kΩ | 10 kΩ | 2.18V | 9.1% |
| 120V (AC) | 100 kΩ | 10 kΩ | 10.9V | 9.1% |
Loaded Voltage Divider
When a load is connected to Vout, it acts as a parallel resistance with R2, reducing the output voltage:
Vout(loaded) = Vin × (R2 ‖ RL) / (R1 + R2 ‖ RL)
Where R2 ‖ RL = (R2 × RL) / (R2 + RL)
Loading Effect Example
Unloaded: 12V, R1=10kΩ, R2=10kΩ → Vout = 6.00V
With 10kΩ load: R2‖RL = 5kΩ → Vout = 12 × 5/(10+5) = 4.00V (33% drop!)
With 100kΩ load: R2‖RL = 9.09kΩ → Vout = 12 × 9.09/19.09 = 5.71V (5% drop)
With 1MΩ load: R2‖RL = 9.90kΩ → Vout = 12 × 9.90/19.90 = 5.97V (0.5% drop)
Design Rule: RL >> R2
For stable output, the load resistance should be at least 10× larger than R2. This keeps the loading effect under 10%.
For high-current loads, use a voltage regulator (LM7805, LM317) instead of a voltage divider.
Practical Applications
- ADC input scaling: Scale 12V to 3.3V for a microcontroller ADC (R1=26.4kΩ, R2=10kΩ)
- Battery voltage monitoring: Divide 12V battery to <5V for Arduino analog input
- Reference voltage: Create a precise reference from a regulated supply
- Biasing transistors: Set base voltage for BJT amplifier circuits
- Sensor signal conditioning: Scale sensor output to ADC input range
Common Mistakes
- Using a divider for power supply: Voltage dividers are for signal-level currents only. A divider with 1kΩ/1kΩ can't power a 100mA load — it wastes 12V / 2kΩ = 6mA just in the divider, and the output sags dramatically.
- Ignoring loading: Always check that RL >> R2. If RL is comparable to R2, the output voltage will be much lower than expected.
- Power dissipation: Small resistors can overheat. With R1=R2=100Ω and Vin=12V: PR1 = (12−6)²/100 = 0.36W — needs ½W resistors minimum.
Standards Reference
- IEEE Standard 100 — Electrical Definitions
- IEC 60063 — Preferred Number Series for Resistors
- IPC-2221 — PCB Design (voltage clearance)
Frequently Asked Questions
What is a voltage divider?
A voltage divider is a simple circuit using two resistors in series to produce an output voltage that is a fraction of the input. The formula is V_out = V_in × R2 / (R1 + R2). It's used for signal scaling, reference voltages, and sensor conditioning — not for powering loads.
How do I calculate a voltage divider?
Use V_out = V_in × R2 / (R1 + R2). For 12V with R1=33kΩ and R2=10kΩ: V_out = 12 × 10/(33+10) = 12 × 10/43 = 2.79V. The output is always less than the input. Choose R2/(R1+R2) to get your desired ratio.
Can I use a voltage divider as a power supply?
No. Voltage dividers are for signal-level currents (microamps to a few milliamps) only. They waste power, have poor regulation, and the output voltage changes drastically with load. For power supply applications, use a voltage regulator (LM78xx, LDO, or buck converter).
What happens when I add a load to a voltage divider?
The load resistance acts in parallel with R2, reducing the effective R2 and lowering the output voltage. If R_L = R2, the output drops to about 67% of the unloaded value. Keep R_L > 10× R2 for less than 10% voltage drop.
How do I choose resistor values for a voltage divider?
Use moderate values (1kΩ–1MΩ). Too low (<1kΩ) wastes power. Too high (>1MΩ) is susceptible to noise and has poor drive capability. For ADC inputs, 10kΩ–100kΩ is typical. For battery monitoring, 100kΩ–1MΩ minimizes current draw.