Let us first of all understand what is meant by Loudness of sound.
Loudness of sound is a subjective term which describes the strength of perception of ear of a sound signal. In other words it is psycho-physiological correlation of amplitude of the sound by ear-brain combination.
Though loudness is related to sound intensity but it can not be considered identical to intensity of sound being heard, as the relationship is not linear. The magnitude of loudness sensation is known to be proportional to the logarithm of the physical stimulus which produced it.
Unit of loudness of sound is decibel, dB. A decibel expresses the relative intensity of sound on a scale from zero, (average least perceptible sound) to around 100 dB, (the level most people find uncomfortably loud). Normal speech is around 50 to 60 dB.
Mathematically Loudness or Acoustic intensity level
It can also be stated in terms of Sound pressure Level
Given is atmospheric pressure
We know that
Intensity of Sound
In the absence of either sound pressure generated or Amplitude of the sound wave, Loudness can not be calculated.