Voltage Divider Guide
How It Works
A voltage divider consists of two resistors (R1 and R2) connected in series between a voltage source and ground. The output voltage is taken from the node between the resistors:
Vout = Vin × R2 / (R1 + R2)
The current through the divider is: I = Vin / (R1 + R2)
When to Use a Voltage Divider
- Sensor reading: Scale a 0-5V sensor output to 0-3.3V for a microcontroller
- Voltage measurement: Measure high voltages with a low-voltage ADC
- Transistor biasing: Set the operating point for BJT amplifiers
- Reference voltage: Create a stable reference for comparators
- Level shifting: Interface between circuits running at different voltages
Load Impedance Warning
The output voltage formula assumes no load (or infinite load resistance). When a load is connected, it appears in parallel with R2, effectively lowering the combined resistance and dropping the output voltage.
Rule of thumb: Load resistance should be at least 10× the value of R2 for the output to remain within 10% of the calculated value.
Practical Design Tips
- Use 1% tolerance resistors for precision applications
- Keep total resistance between 1k and 100k ohms
- Add a buffer (op-amp voltage follower) if driving any significant load
- Consider temperature effects on resistor values for precision work
Note: This calculator assumes ideal resistors with no load connected to the output.
Voltage Dividers in Real Circuits
Voltage dividers are the first circuit every electronics student builds — and the most commonly abused. Loading effect is the classic pitfall: a 10 kΩ / 10 kΩ divider from 5 V outputs 2.5 V unloaded, but drops to 1.67 V if a 10 kΩ load is added. Rule of thumb from Horowitz & Hill's Art of Electronics: the divider's Thevenin resistance should be ≤ 1/10 of the load resistance to maintain <10% voltage error.
Arduino's analog-input impedance is roughly 100 MΩ, making voltage dividers for sensor scaling effectively unloaded. A common 12 V → 5 V divider uses 10 kΩ upper and 7.2 kΩ lower (or the 20 kΩ/15 kΩ safer variant) to read car battery voltage through a 5 V ADC. Real-world builders forget that the ATmega328P sampling capacitor (14 pF) requires source impedance <10 kΩ for accurate reads — a 100 kΩ divider introduces measurable error.
Precision applications use 0.1% metal-film resistors instead of 5% carbon composition. A 0.1% divider holds ±0.2% total-error vs. a 5% divider's ±10% error — 50x better accuracy for ~10x the cost ($0.05 vs $0.005 each in reels of 5,000). Temperature coefficient matters too: carbon resistors drift 500-1,000 ppm/°C versus 25-50 ppm/°C for metal film, which is why industrial transmitters specifying ±0.25% accuracy over -40 to +85°C use thin-film dividers exclusively.
Sources: Horowitz & Hill Art of Electronics, Atmel ATmega328P datasheet, Vishay resistor specs
Methodology & Assumptions
This calculator implements standard formulas drawn from primary-source authorities. Values are point-in-time estimates; consult a licensed professional for high-stakes decisions. See the per-input definitions and source citations below.
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| Input | Default | Source / authority |
|---|---|---|
| All inputs | Domain-typical defaults | Editorial methodology, CalcMesh 2026 |