Voltage divider: get any voltage from two resistors

Two resistors in series split the voltage between them. Take the voltage from the middle and you have a voltage divider. It's probably the most used little circuit in electronics.

Change the values below. Then put a load on the output and see what happens.

The formula

Vout = Vin × R2 ÷ (R1 + R2)

R1 is the top resistor, connected to the input. R2 is the bottom one, connected to ground. The output is the point between them. With two equal resistors you get exactly half: 9 V with 10 kΩ and 10 kΩ gives 4.5 V.

The ratio is what matters, not the values. 1 kΩ and 1 kΩ also give 4.5 V. The difference is the current: 9 V through 2 kΩ is 4.5 mA, through 20 kΩ only 0.45 mA. Bigger resistors waste less battery.

The mistake: loading it

Here's the catch. Whatever you connect to the output sits in parallel with R2. That lowers the bottom resistance, so the output drops.

Try it above: 9 V, 10 kΩ and 10 kΩ, then a 10 kΩ load. The output falls from 4.5 V to 3 V. That's a big miss.

• Rule of thumb: the load should be at least 10 times bigger than R2. Then the output stays close to what you calculated.
• Don't power things from a divider. Motors, LEDs, lamps and most boards pull too much current. The voltage collapses as soon as they start. Use a voltage regulator for power.
• Do use it for signals. Inputs of microcontrollers and sensors draw almost nothing, so a divider works great there.

Where you'll actually use one

5 V to 3.3 V

Many newer boards and sensors use 3.3 V and don't like 5 V signals. Put the 5 V signal into a divider. With R1 = 10 kΩ you'd need 19.4 kΩ for R2. The closest standard value is 18 kΩ, which gives about 3.2 V. Good enough for a logic input. The calculator above finds this for you.

Measuring a battery

A microcontroller input can't take 9 V directly. A divider brings it down to a safe level, and the code multiplies it back. Use big resistors here, like 100 kΩ, so the divider doesn't drain the battery while it sits there.

Sensors

A light sensor (LDR) or a thermistor changes resistance. Put it in a divider with a fixed resistor and its change becomes a voltage change you can measure.

The potentiometer

A potentiometer is a voltage divider in one part. The track is R1 plus R2, and the wiper is the middle point. Turn it and you move the split. That's how a volume knob or a dimmer input works.

Dividers are just series resistors with a tap in the middle, and everything here is Ohm's law.