Asking you guys because i would like to confirm the voltage drop for following datas.

copper wire with length of 120ft

input load : 20A

When i check voltage drop from Easycalculation.com

The calculator shows result as "1.2 volts". Is the answer value is correct for my automatic POWERON circuit?

Kindly help me to use the exact voltage drop for my digital circuit.

 

It entirely depends upon the wire gauge, which you did not state.
What does an automatic POWERON circuit have to do with it?

 

My chart shows that 12 AWG wire has 1.588 ohms per thousand feet at 20 degrees C.
That and Ohm's Law will get you an answer.

 

If the power source and the load are 120 feet apart you have 240 feet minimum of wire between them.

 

Ohming in on homes law.