Voltage divider reverse formula

Question

I have this schematic, with an power supply of 24V and I want to read this voltage with my arduino so i need a voltage divider, the formula for voltage divider is Vout = (Vin * R2)/R1+R2, so with my data, Vout is 2.824V (24 * 10000)/75000+10000.

So what is the reverse formula to convert 2.824V to 24V, for printing on my serial monitor?

Answer 1

It will look something like this:

$$V_{OUT} = ADC\cdot \frac{V_{REF}}{1024} \cdot (1 + \frac{R_1}{R_2}) $$

Where \$ADC\$ is a value (between 0...1023) read by Arduino ADC. and \$V_{ref}\$ is an Arduino ADC reference voltage.

Or to answer your question directly

$$V_{CC} = V_{ADC} \cdot (1+\frac{R_1}{R_2}) = 2.824V \cdot8.5 = 24V $$

Answer 2

So,

$$V_{out}=V_{in}\dfrac{R_2}{R_1+R_2}$$

Reverse function is

$$V_{in}=V_{out}\dfrac{R_1+R_2}{R_2}$$