Is it possible to know the maximum db output of a pair of headphones based on your laptop volume level?

[cosmoscosmos]

Hello all, I just joined the forum on advice from r/audioengineering. I asked this question over there and they thought you would be better to answer. This doesn't seem like the ideal place to ask, but it's where I am allowed to post as a newb. 
 
My question is fairly straightforward (may not be simple).
 
Is there a way to know the maximum db output of a pair of headphones (such as SONY MDR 7506) at a set system output on a macbook pro (for example 4 bars)?
 
Ideally I would like to know that the headphones cannot exceed a level (say 75db) no matter what I throw at it. Then I can set the volume level of the mac, and stop worrying about headphone volume for ear damage.
 
I produce music on my laptop for hours on end and the volume of the sound can vary widely quickly when different effects and sounds are introduced. 
 
I know there are headphones that limit the db output, but the limit is too high (usually 95 or 100 db) from what I have seen.
 
Thank you for your help (if possible)

 

[MindsMirror]

You can use the sensitivity rating of the headphones to find the sound pressure level they create at a given power. The SONY MDR 7506 has a sensitivity of 106 dB at 1mW. Their impedance is 63 Ohms, which you will need for calculations as well.
 
This thread lists some specs about the maximum output of the Macbook Pro's audio jack.
 

During playback of a 1 kHz, full-scale sine wave (44.1 kHz output sample rate, 24-bit sample depth, 100 kΩ load, unless otherwise specified) the audio line output has the following nominal specifications:

Jack type: 3.5 mm stereo
Maximum output voltage: 2 VRMS (+8.24 dBu)
Output impedance: < 24 Ω

 
You can then perform some calculations to find the maximum sound pressure level the headphones and Mac together can produce.
 
VRMS across the headphones at 1mW = 0.251V
Max VRMS across 63 Ohm load = 1.45V
Decibel difference = 15.2dB
Maximum SPL = 121.2dB
 
Therefor, if you set the volume to full and play the loudest possible 1KHz sound, the headphones will produce 121.2dB SPL. To achieve 75dB you would need a volume setting of -46.2dB. I don't know how many bars that is, maybe you can find it somewhere else. If not, you could use some software that has a decibel scale volume control, set the system volume to full and set -46.2dB on the software to hear how loud that is.
 
The music you are producing won't be as loud as a full scale 1KHz sine wave. The loudest CD I have is at -6dBFS, music that's mastered properly should be at around -14 to -20 dBFS, and modern CDs are often around -10dBFS. So depending on how loud the music you're mixing can get, you may only need a volume setting somewhere from -40 to -26 dB.

 

[cosmoscosmos]

Awesome... So I basically need to find out what volume level on the mac corresponds to -46.2dB.
 
I posted over on the mac forums but no response yet.
 
​Really looking forward to finding out the answer