The Voltage Divider Calculator determines the scaling down of input voltage through a passive series resistor network. It calculates both unloaded and loaded divider systems, accounting for load resistance pull-down.
What is a Voltage Divider?
A voltage divider is a simple passive linear circuit that scales down a higher input voltage to a lower output voltage. It consists of two resistors connected in series across an input voltage source, distributing the voltage proportionally across each component.
Voltage division relies on Ohm's Law to calculate the drop across the lower resistor relative to the total loop resistance. It is standard practice to use dividers for reference signals, sensor readings, and signal-level matching.
The Voltage Divider Formula
Use these mathematical formulas to determine output voltage under unloaded or loaded configurations:
| Configuration | Formula | Description |
|---|---|---|
| Unloaded Divider | Vout = Vin × R2 / (R1 + R2) | Calculated when no electrical load is connected to the output node. |
| Loaded Divider | Vout = Vin × Req / (R1 + Req) | Calculated when a load resistor (RL) is in parallel with R2, where Req = (R2 × RL) / (R2 + RL). |
How to Calculate Output Voltage
- Measure the input voltage (Vin) supplied to the series circuit.
- Determine the resistance values of R1 (connected to input) and R2 (connected to ground).
- Divide R2 by the sum of R1 and R2 to find the scaling ratio.
- Multiply the input voltage by the scaling ratio to obtain the unloaded output voltage.
Worked Example
This worked example calculates the loaded output voltage of a divider circuit where Vin = 12 V, R1 = 1 kΩ, R2 = 2 kΩ, and a load resistor RL = 2 kΩ is connected in parallel with R2.
| Step | Description | Calculation | Result |
|---|---|---|---|
| 1 | Calculate equivalent parallel resistance (Req) of R2 and RL. | (2 kΩ × 2 kΩ) / (2 kΩ + 2 kΩ) | 1 kΩ |
| 2 | Add R1 and Req to find total loop resistance. | 1 kΩ + 1 kΩ | 2 kΩ |
| 3 | Divide Req by the total resistance to find the ratio. | 1 kΩ / 2 kΩ | 0.5 |
| 4 | Multiply Vin by the ratio. | 12 V × 0.5 | 6 V |
Why the Loaded Divider Effect Occurs
Connecting a load resistor (RL) in parallel with R2 reduces the total resistance of the bottom half of the divider. This physical load alters the voltage division ratio, pulling the output voltage (Vout) lower than the unloaded calculation.
Designers avoid this loading effect by making the load resistance at least ten times larger than R2. This ensures that the parallel equivalent resistance remains close to R2's nominal value.
Practical Applications
- Creating a reference voltage to bias transistors in amplifier circuits.
- Interfacing a 5V sensor output to a 3.3V microcontroller input pin safely.
- Measuring battery voltage levels using analog-to-digital converter (ADC) pins.
Common Mistakes
- Forgetting the load resistance (RL) in calculations, leading to lower output voltage in real-world testing.
- Sizing resistors too low, causing high current draw and thermal failure.
- Sizing resistors too high, causing signal distortion from the input capacitance of the load component.