You want to measure a voltage? But it’s outside the range of your microcontroller’s 0 to 3.3v or 5v? We can achieve this with resistors.

There are three distinct problems, each with its own solution.

The positive voltage is above 3.3v or 5v

If we apply double our maximum voltage over two identical resistors in series, we expect to measure half our voltage at the midpoint. It is this midpoint we are going to measure.

Simple resistor divider, voltage at midpoint is half the voltage at the top

Simulation of the voltages in a resistor network, all the voltages are evenly scaled

The voltage at the top can be calculated by multiplying the analog-read-voltage by 2. In this example I will assume a 5V microcontroller.

If we add another identical resistor, we add another 5V to the maximum voltage we can read, we can extend this as many times as we like.

With three identical resistors, we can now measure three times the maximum voltage of our microcontroller

We do only intend to measure after the first resistor, and then multiply the measured voltage by three to get the correct voltage. This means we can group the other resistors together by adding them up.

Final solution, measure three times the voltage on your analogRead pin

The voltage is below ground/negative

If we want to measure below ground, we have to set this resistor network upside down. This example assumes a 3.3V microcontroller.

Reading a negative voltage can be done with an up-side-down resistor network

Instead of connecting the bottom end to the ground, we now connect the top to the maximum of our controller. And it is now after the top resistor where we read our voltage.

Once again, we simplify the network to only use two resistors by adding them up.

Final solution for reading a negative voltage on a microcontroller

Calculating the actual voltage is not that complicated. First we multiply the voltage on the analog input by three and then add the lowest voltage we can read on the network, which is -6.6V. On the positive network we did not do this because that value was 0V.

So if we read +3.3V the actual value = (3.3 x 3) – 6.6 = +3.3V.

And if we read 0V the actual value = (0 x 3) – 6.6 = – 6.6V.

Both voltages are out of range

When the input can be below ground as well as above the controller’s maximum, we can’t tie one end of the network to ground or max-voltage. We need to tie it in the middle, using another resistor divider. This example assumes a 5V controller.

The standing resistors on the left are equal, and without any voltage to measure would produce +2.5V at the middle for the analog pin to read.

The to-measure-voltage applied to the right will then pull that voltage up or down through the third resistor.

Then, how to calculate that third resistor? And how to translate the value read at the analog pin back to the real world value? I could not figure this out in a simple way, so I wrote a tool for it.

You find this tool further down this page.

Arduino code

It doesn’t matter how many resistors your divider has, the voltage at the measuring point always has a linear relation to the actual voltage you are trying to measure.

Therefore, all you need to do is measure two sets of voltages and store them in the map() function. It will then ‘translate’ your new reading into the new actual voltage using these data points.

const int analogPin = A0; // define analog input pin
const float voltageMax = 5.0; // maximum voltage the Arduino can read

void setup() {
  Serial.begin(9600); // initialize serial communication
}

void loop() {
  int analogValue = analogRead(analogPin); // read analog value on pin A0
  float voltageValue = (analogValue / 1023.0) * voltageMax; // convert analog value to voltage

  /*
  To setup the map function we need to sample two voltages and record 
  both the actual and midpoint voltage.
  Example: 1K - 1K resistor divider.
  Sample 1: Measure 0V, midPoint is 0V 
  Sample 2: Measure 10V, midPoint is 5V
  float actualVoltage = map(midPointVoltage, sampleMP1, sampleMP2, sampleActual1, sampleActual2);
  */
  float actualVoltage = map(voltageValue, 0, 5, 0, 10);
  
  Serial.print("Analog Value: ");
  Serial.println(analogValue);

  Serial.print("Voltage Value: ");
  Serial.print(voltageValue);
  Serial.println("V");

  Serial.print("Actual Voltage: ");
  Serial.print(actualVoltage);
  Serial.println("V");

  delay(1000); // wait for 1 second
}