• Registered: 2014-07-11
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Topic: Any audio engineers or electrical engineers that can check my math?

I have an ADI-2 DAC that I use to drive Sennheiser HD 800S headphones. I'm trying to work out volume level on the dial vs SPL output of the phones to make sure I don't start pushing the volume level too high.

The 800S are spec'd to 102dbSPL at 1VRMS which is 1dBV if I understand correctly. That should mean 102dBSPL at 3.2dBu. So to get them to 90dBSPL I would want to run them at about -9dBu and for 85dBSPL about -14dBu. All sound correct so far?

Then with the ADI-2 running in low power its output level on the phones jack should be +7dBu with the dial set to 0dB since these are high impedance phones.  That would mean to be at about 90dBSPL I'd want the volume dial set at -16dB and for 85dBSPL at about -21dB.

So is my logic of the situation and math right, or am I confused and risking blowing out my ears? smile

2 Reply by ning (edited by ning 2021-04-24 01:16:17)

  • ning
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Re: Any audio engineers or electrical engineers that can check my math?

Pretty much right, except safe hearing range is defined in dba throughout the time so your calculation is based on the worst case scenario. So you are very safe in this respect.

However headphone sensitivity is defined at certain frequency (usually 1khz), but higher frequencies usually have much higher response (usually 10 db more at several kHz). So in this respect you are under calculating.

And the above analysis is entirely based on health research that link hearing damage threshold to sound exposure level in dba, which is just a convenience approximation. Not really precise. It’s also used to address different problems such as exposure to occupational noise such as construction noise with regards to loss of hearing in human voice frequency range, not music one.

Most of the time hearings are damaged by other means(aging, illness such as cold or flu that caused inflammation in inner ear, concussion, sleep disorder, mental issues, your genes, etc. ), not just overexposure to noise. so just enjoy your music, NOW:)

  • Registered: 2014-07-11
  • Posts: 16

Re: Any audio engineers or electrical engineers that can check my math?

Basically I'm just looking for a sanity check on the volume dial. Something I'm used to from my speaker days (I'm transitioning back to headphones for the first time in over a decade) where I have them calibrated to 105dB SPL being 0dB on the volume dial per the THX reference levels. So I'm just looking for a similar sanity check. Not a hard limit on where the dial is set, for more dynamic things it'll get turned up, just to make sure I don't start creeping it up during long sessions in to dangerous territory

waedi: We absolutely DO have a formula for blowing out ears. The NIOSH has a table of recommended max safe exposure levels vs time, as well as extensive research as to why and so on: https://www.cdc.gov/niosh/docs/98-126/pdfs/98-126.pdf. The EU has similar rules (Directive 2003/10/EC). The NIOSH's findings are that 80dBSPL or below is safe for any amount of time. 85dB is recommended for no more than 8 hours a day, 90dB for no more than 2.5 hours a day.

  • ning
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Re: Any audio engineers or electrical engineers that can check my math?

Sycraft wrote:

Basically I'm just looking for a sanity check on the volume dial. Something I'm used to from my speaker days (I'm transitioning back to headphones for the first time in over a decade) where I have them calibrated to 105dB SPL being 0dB on the volume dial per the THX reference levels. So I'm just looking for a similar sanity check. Not a hard limit on where the dial is set, for more dynamic things it'll get turned up, just to make sure I don't start creeping it up during long sessions in to dangerous territory

that's what the second paragraph in my above reply is about: speakers are a little bit different than headphones. Speakers usually have  very flat frequency response compared to headphones.  Take your hd800s as example, at 5.5khz, it's almost 10db louder than 1khz, with the same input rms voltage. your sensitivity value is measured at 1khz. so for the treble, you are under calculating a lot.

  • Registered: 2014-07-11
  • Posts: 16

Re: Any audio engineers or electrical engineers that can check my math?

Understood but I'm not too worried. For one, I've equalized down that 5.5khz peak (the PEQ on this thing is partially what sold me on it). Likewise, music content tends to fall as frequency rises. If you look at a spectrum analysis of music it tends to slope downward 3-6dB per octave.

So yes, if the sound was something like a sine wave at a high frequency, that could be an issue. However with musical content the overall SPL level should be fine, particularly as a general check.

6 Reply by KaiS (edited by KaiS 2021-04-25 23:04:45)

  • KaiS
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Re: Any audio engineers or electrical engineers that can check my math?

Sycraft wrote:

I have an ADI-2 DAC that I use to drive Sennheiser HD 800S headphones. I'm trying to work out volume level on the dial vs SPL output of the phones to make sure I don't start pushing the volume level too high.

The 800S are spec'd to 102dbSPL at 1VRMS which is 1dBV if I understand correctly. That should mean 102dBSPL at 3.2dBu. So to get them to 90dBSPL I would want to run them at about -9dBu and for 85dBSPL about -14dBu. All sound correct so far?

Then with the ADI-2 running in low power its output level on the phones jack should be +7dBu with the dial set to 0dB since these are high impedance phones.  That would mean to be at about 90dBSPL I'd want the volume dial set at -16dB and for 85dBSPL at about -21dB.

So is my logic of the situation and math right, or am I confused and risking blowing out my ears? smile

The theoretical approach has too many uncertainties:

• Very important: the music tracks you are listening to.

• Loudness exposure is measured as Leq A-weighted, that is completely different (more than 10dB) to the values your calculation is based on, which are Peak linear.

• The headphones frequency response and specially the ear coupling and HRTF, which is very non-linear, and beyond what can be easily calculated.

With all this you are likely way more than 10 dB off with calculation-based SPL.


There are 2 possible approaches and a simplistic estimate:

1. I do some HD 800 (I have one) measurements for you on the Bruel&Kjaer 4153 Artificial Ear.

• Tell me several representative music pieces that are available in (Tidal) streaming for this.


2. More precise, individually calibrated to you, like the audiologist would do:

• Get yourself iOS app AudioTools from Andrew Smith, use the SPL Pro modul.
https://apps.apple.com/de/app/audiotools/id325307477
This changes the iOS device into a precise SPL meter.
There is is cost free try out period.

• Set measurement to Leq A-weighted.

• Play your representative music tracks on loudspeakers, set volume to 85 dB Leq A.

• Compare and subjectively set ADI-2’s headphones volume until you reach the same loudness. Concentrate on midrange and treble (vocalist) doing so.
Ignore the bass.

This approach is precise within few dBs.


Simplistic estimate:

• Sit someone 1 m close to you, make him talk with slightly above normal voice.

• Set headphones volume to about the same level for the vocalist / singer.

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