Voltage divider.

How the math works

Vout = Vin × R2 / (R1 + R2)

Current  I = Vin / (R1 + R2)
Power R1   P1 = I² × R1
Power R2   P2 = I² × R2

The formula assumes no load on the output — i.e., the downstream circuit draws negligible current compared to what flows through the divider. If the load draws current comparable to I, the actual Vout will sag (it forms a Thévenin source with output impedance R1∥R2).

Rule of thumb: load resistance ≫ R1∥R2

For the voltage divider to work as designed, the load resistance should be at least 10× higher than the parallel combination of R1 and R2. If your load is 10 kΩ, your divider's R1∥R2 should be ≤ 1 kΩ.

This trades off against power dissipation: lower R values mean more current flows continuously, which means more wasted power and more heat. The classic compromise is to make R1+R2 around 10-50× the load impedance.

Common pitfalls

• Don't power a microcontroller pin via a voltage divider for ANY current draw. Voltage dividers only work for sensing (ADC inputs, comparator references). For powering anything, use a regulator (linear or switching).
• Resistor tolerance affects the output. Standard ±5% resistors can give ±5% error on the divider output. Use 1% precision resistors when accuracy matters.
• Power rating matters. A 1/4 W resistor dissipating 0.3 W will burn out. Always check P calculation against resistor power rating.
• Thermistor and photoresistor dividers are non-linear. A voltage divider with a thermistor on top gives a temperature-dependent voltage, but the relationship isn't linear with temperature — calibrate or use a lookup table.
• Source impedance affects ADC accuracy. Most microcontrollers want source impedance ≤ 10 kΩ on ADC inputs for accurate sampling. If R1∥R2 is much higher, add a buffer (op-amp follower) before the ADC.

Sources

• Standard resistor values: IEC 60063 — Preferred number series for resistors and capacitors (E6, E12, E24, E48, E96, E192 series).
• Voltage divider analysis: Any basic electronics textbook (Horowitz & Hill, The Art of Electronics, Chapter 1).

Disclaimer. Voltage dividers are appropriate for level-shifting and sensing applications. For power delivery, use a voltage regulator (LDO, switching regulator) instead.

See also