this earlier today, but I think it deserves to be put in the blog - if nothing else so I can find it again next time ... and there always seems to be a next time when it comes to calculating headphone amplifier gains.
Starting at the beginning, the encoded data on a CD goes from 0 to 1 in 2^16 steps, but in a typical CD player or soundcard, the DAC output is -2.8 V to 2.8 V or 2 V rms or 6 dB. Many sources, such as phono stages and portable audio, are lower, perhaps as low as 250 mV.
How loud the sound is depends on the source signal amplitude, the position of the volume control, the circuit gain, and the impedance and sensitivity of the headphones.
As a practical matter, most people would want the volume control at the 9-10 o'clock position for "normal" listening.
For standard "line level" source, the gain required to keep the volume control at a 9-10 o'clock varies depending on the impedance...