Lesson 3 of 4 in Step 2 · Working with resistors
The voltage divider
By Mihai Dumitru · · · 6 min read
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On the series and parallel page you saw that two resistors in series share the supply voltage in proportion to their values. If you take a connection from the point between them, you get a voltage that is a fixed fraction of the supply. That arrangement is called a voltage divider, and it is one of the most common small circuits in electronics.
Try changing the values below, then add a load on the output and see what happens to it.
Voltage divider calculator
Two resistors and one output. Change any value and the output is recalculated.
- Output voltage
- 4.5 V
- Current through the divider
- 0.45 mA
Need a specific output? Find R2
R2 = 5.79 kΩ. Closest standard value: 5.6 kΩ, which gives 3.23 V.
The formula
The resistor connected to the supply is usually called R1, and the one connected to ground is R2. Ground is the reference point of a circuit, normally the minus side of the supply, which is taken as 0 V. The output is the point between R1 and R2:
Vout = Vin × R2 ÷ (R1 + R2)
With two equal resistors, the output is exactly half of the input: 9 V with 10 kΩ and 10 kΩ gives 4.5 V. The output depends only on the ratio between the resistors, so 1 kΩ and 1 kΩ also give 4.5 V. What changes is the current: 9 V through 2 kΩ in total is 4.5 mA, while 9 V through 20 kΩ is only 0.45 mA. Larger resistors waste less of the battery.
What a load does
A divider works as calculated only when nothing draws current from its output. Anything you connect to the output is in parallel with R2, which lowers the bottom resistance and pulls the output voltage down. In the tool, 9 V with two 10 kΩ resistors and a 10 kΩ load gives 3 V instead of 4.5 V.
As a rule of thumb, the load should be at least ten times larger than R2 for the output to stay close to the calculated value. That is why dividers are used for signals, which draw almost no current, and not to power things. A motor, a lamp or an LED connected to a divider would pull the voltage down as soon as it starts. To power something from a lower voltage, use a voltage regulator instead.
Typical uses
Reducing a 5 V signal to 3.3 V
Many newer boards and sensors work at 3.3 V and can be damaged by a 5 V signal. A divider brings the signal down. With R1 = 10 kΩ, the exact R2 for 3.3 V would be about 19.4 kΩ. The nearest standard value is 18 kΩ, which gives about 3.2 V, close enough for a logic input. The calculator finds this for you.
Measuring a battery
A microcontroller input can't take 9 V directly. A divider reduces it to a safe level, and the program multiplies the reading back. Large resistors such as 100 kΩ are used here, so that the divider doesn't drain the battery while it is connected all the time.
Sensors
Some sensors are simply resistors whose value changes with light (an LDR) or temperature (a thermistor). Put one in a divider with a fixed resistor, and the change in resistance becomes a change in voltage that a microcontroller can measure.
A potentiometer is a voltage divider built into a single part with a knob. It gets its own page, next in the course.
Check yourself
Two 10 kΩ resistors form a divider across 9 V. What is the output voltage?
Show the answer
Equal resistors split the voltage in half: 9 × 10 ÷ (10 + 10) = 4.5 V.
A divider has 20 kΩ at the top and 10 kΩ at the bottom, across 12 V. What is the output?
Show the answer
Vout = 12 × 10 ÷ (20 + 10) = 4 V.
In the first question, a 10 kΩ load is connected to the output. What happens to the voltage?
Show the answer
The load is in parallel with the bottom resistor, so together they make 5 kΩ. The output drops to 9 × 5 ÷ (10 + 5) = 3 V. This is why a divider only works well with loads much larger than its own resistors.
Why is a voltage divider a bad way to power a motor?
Show the answer
The motor draws a large current that would pull the output voltage down, and the resistors would waste a lot of power as heat. Dividers are for signals and references, not for powering loads.