What is the difference in the input from inbuilt microphone and an external microphone amplifier?
Without precise data from the laptop manufacturer the best procedure may be:


Get a tone generator app for your phone.
Play a 1 kHz tone on a loudspeaker.
Position both measuring systems equidistant from the sound source.
Perform some measurements.


You then have a choice of calibrating one against the other using a potentiometer (if the Arduino is more sensitive than the PC) or performing a software calibration / scaling.