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Safe listening levels and headphone voltage/power requirements

Phorize

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Heya,

there's a couple of threads asking about safe listening levels and people asking about voltage/power requirements in almost any amp/headphone thread.
Here's my take on this:


Noise Exposure Limits
The EPA and WHO recommend that noise should be kept below 70 dBA over 24 hours and below 75 dBA over 8 hours. Additionally, the CDC makes the rough recommendation to keep noise exposure below 2 hours for 80-85 dBA loud noise as (based on the same data and 3 dB exchange rate) to prevent hearing damage.

NIOSH defines a 3 dB exchange rate: permissible exposure time halves for every 3 dB increase in noise intensity.
NIOSH recommends a limit of occupational noise exposure to 85 dBA over an 8-hour time-weighted average.
EPA recommends noise exposure to be limited to 85 dBA over 45 minutes.
View attachment 233575

Why this discrepancy? The answer is in the:


Fine print
The EPA limits were chosen to protect 96% of the general population against impairment of physical (hearing loss) and mental (like discomfort) health.
The NIOSH limits were chosen solely to protect against hearing loss in the workplace accepting that 8% of the workforce will still develop hearing loss.
Therefore, NIOSH recommends hearing protection if noise levels exceed 85 dBA regardless of exposure duration.

The EPA limit is averaged over 24 hours.
The NIOSH limit is averaged over 8 hours (average workday) with rest/recovery periods between exposures.

The EPA limit is based on 365 days/year exposure.
The NIOSH limit is based on 250 workdays/year exposure.

The NIOSH limit considers implementation cost for businesses to stay within limits (sacrificing human health for economic reasons).

Note: both recommendations are based on audiometric tests of hearing loss up to 4 kHz.
Note: OSHA (which records occupational hearing loss cases) defines a significant decrease in hearing as a "standard threshold shift" which is a change of 10 dB averaged over 2, 3, and 4 kHz.


A-Weighting
A-weighting significantly attenuates low frequencies, while giving a slight boost to frequencies between 1 kHz and 6 kHz (the peak is about +1.3 dB at 2.5 kHz):
View attachment 233555


Conclusions
85 dBA should not be considered a universally safe limit, especially not for children, people with sensitive hearing, when regularly listening for several hours, or when being exposed to other potentially louder noise sources throughout the day.
Therefore, I recommend to stay below 85 dBA when listening to music.



Power/Voltage Requirements
This depends on headphone sensitivity and type of music you're listening to:


Headphone sensitivity
You can find this in product datasheets. If it's just specified as "x dB" then it is usually at 1 mW. Sensitivity is sometimes also specified at 1 Vrms.
Both are typically measured with a 500 Hz or 1 kHz sine wave.

To convert from dB SPL@1 mW to dB SPL@1 Vrms and vice-versa, calculate:
Code:
sensitivity_Vrms = sensitivity_mW - 10*log10(0.001 * impedance)
sensitivity_mW = sensitivity_Vrms + 10*log10(0.001 * impedance)

Note that a sine wave's RMS value is 3 dB lower than its peak magnitude. This needs to be considered when we analyze the RMS value of music tracks.
Additionally, we have to apply the A-weighting.


Music
Let's look at two extremes: classical recordings and highly dynamic range compressed modern pop/rock.
Note: the selection of tracks used for this analysis is random. Ymmv.


Classical:
View attachment 233576
Total RMS value: -24.1 dB
Total RMS value with A-weighting: -26.85 dB.

Modern pop/rock
View attachment 233581

Total RMS value: -11.2 dB
Total RMS value with A-weighting: -15 dB.

The differences in A-weighting (-2.75 dB for classical and -3.8 dB for modern pop/rock) is explained due to the fact that modern pop/rock has significantly more energy in bass/lower mids and also upper treble, which is exactly what the A-weighting filter attenuates.


So how much power/voltage do I need?
Now we have all the information we need:
  • The target SPL: 85 dB SPL
  • Sensitivity in dB SPL either @1 mW or @1 Vrms
  • Weighted total RMS value
Note: for a 1 kHz sine wave, the weighted total RMS value would be -3 dB, hence the need to subtract an extra 3 dB from the target SPL.

power_mW = 10^((target_spl - sensitivity_mW - weighted_rms - 3)/10) voltage_rms = 10^((target_spl - sensitivity_Vrms - weighted_rms - 3)/20)


Amplifier gain, volume setting and headroom
Knowing the required voltage and the output voltage of your source device, calculating the required gain with optional added headroom is as simple as:
Code:
headroom_x = 10^(headroom_dB/20)
min_amp_gain_x = voltage_rms/source_rms * headroom_x
min_amp_gain_dB = 20*log10(min_amp_gain_x)

The actual gain of your amp may be higher, which means you'll have to turn down the volume. By how much? Calculate:
Code:
volume_x = min_amp_gain_x / amp_gain_x
volume_dB = 20*log10(volume_x)


I've also published a Headphone power spreadsheet that contains these calculations. Feel free to clone/download it.




Sources
  1. CDC. What Noises Cause Hearing Loss?. https://www.cdc.gov/nceh/hearing_loss/what_noises_cause_hearing_loss.html
  2. EPA [1974]. Information on levels of environmental noise requisite to protect public health and welfare with adequate margin of safety. EPA/ONAC 550/9-74-004. http://nepis.epa.gov/Exe/ZyPDF.cgi/2000L3LN.PDF?Dockey=2000L3LN.PDF
  3. NIOSH [1998]. Criteria for a recommended standard: occupational noise exposure. DHHS (NIOSH) Publication Number 98-126. https://www.cdc.gov/niosh/docs/98-126/
Good work, thank you!
 
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VladDracule

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Wow, great work.
I've just updated my spreadsheet to version 8 with your data. Thank you again for letting me use it.

If I didn't mess up then the number of entries increased from 664 to 746 (+82). I saw that you consolidated some model variations into single entries so the number of actual additions is probably higher.

So need some help with the spreadsheet. Im using a chord mojo 2, and u12t headphones. I cant find a gain value to put in for the spreadsheet?

I think i got the right numbers otherwise but im not sure

vRMS i put as 5.2, which is the mojo spec @30ohms, but the u12ts are lower impedance at 12. Zout of the mojo is .06...im not really sure where to go from there
 

solderdude

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127dB/V so you will need 0.45V to reach 120dB SPL, this requires 37mA and draws 17mW.
You can easily drive it from a E.U. phone to impressively loud levels.
 

VladDracule

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127dB/V so you will need 0.45V to reach 120dB SPL, this requires 37mA and draws 17mW.
You can easily drive it from a E.U. phone to impressively loud levels.
Appreciate the numbers, what do i put into the spreadsheet to calculate all that? also whats the easiest way to figure out what "volume" setting that is on the mojo? probably a voltmeter? 120 is obviously too high i want to keep it around the 85 as max
 
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xnor

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@VladDracule I found an image that apparently describes the volume settings for the Chord 2:
e942d0b54117720d85b0e95e26b674a26c7d4688.jpeg


So in the spreadsheet I'd set Source Max Vout to 4.75468 [Vrms], Headphone Amp gain to 0 [dB], Zout to 0.06 [Ω].
This is because the theoretical max output voltage is independent of the load and we want a volume setting of 0 dB to correspond to 4.75468 [Vrms]. The Chord 2 is a bit special in that the volume control also has gain and therefore allows positive values up to +18 dB.
(In the spreadsheet any volume settings above +0 dB will turn red to indicate a lack of gain because it assumes that volume controls only attenuate ... with the Chord 2 you'd only lack gain if the value went above +18 dB.)

For the headphone you can simply use one of the _custom entries on top. Set Sensitivity to 127 [dB SPL / Vrms], impedance (Z) to 12 [Ω].

That's 5 values to enter and you're done.

Assuming all values are correct the results show that for the 80 dB(A) target level with -18 LUFS loudness target (using loudness normalization) you need to turn the volume down to -38 dB for Jazz, Pop/Rock, Hypercompressed.
If you set Loudness Target to "disabled" (no loudness normalization) then you need to turn the volume down to -39, -48, -53 dB for Jazz, Pop/Rock, Hypercompressed respectively.
 
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VladDracule

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@VladDracule I found an image that apparently describes the volume settings for the Chord 2:
View attachment 298399

So in the spreadsheet I'd set Source Max Vout to 4.75468 [Vrms], Headphone Amp gain to 0 [dB], Zout to 0.06 [Ω].
This is because the theoretical max output voltage is independent of the load and we want a volume setting of 0 dB to correspond to 4.75468 [Vrms]. The Chord 2 is a bit special in that the volume control also has gain and therefore allows positive values up to +18 dB.
(In the spreadsheet any volume settings above +0 dB will turn red to indicate a lack of gain because it assumes that volume controls only attenuate ... with the Chord 2 you'd only lack gain if the value went above +18 dB.)

For the headphone you can simply use one of the _custom entries on top. Set Sensitivity to 127 [dB SPL / Vrms], impedance (Z) to 12 [Ω].

That's 5 values to enter and you're done.

Assuming all values are correct the results show that for the 80 dB(A) target level with -18 LUFS loudness target (using loudness normalization) you need to turn the volume down to -38 dB for Jazz, Pop/Rock, Hypercompressed.
If you set Loudness Target to "disabled" (no loudness normalization) then you need to turn the volume down to -39, -48, -53 dB for Jazz, Pop/Rock, Hypercompressed respectively.
where did you get the Vrms value? are you just assuming its linear based on the impedance?

Im trying to do the same thing now just for the element iii with hd800s
 
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xnor

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where did you get the Vrms value? are you just assuming its linear based on the impedance?
I assume there is no load sensing circuitry in the Chord 2 so the theoretical output voltage only depends on the volume setting. In the image/table I posted you can see that at 0 dB it apparently outputs 4.75468 V.

You can always double check by measuring the output voltage using a multimeter in AC voltage mode and playing a low frequency (check multimeter specs for accuracy) full-scale sine wave. Very simple to do with something like a 3.5mm male to 3.5mm male adapter cable - measure between the tip (left channel) or middle ring (right channel) and the sleeve of the jack.

Im trying to do the same thing now just for the element iii with hd800s
Its auto gain function seems to operate similarly to Chord 2. According to https://blog.jdslabs.com/2022/01/jds-labs-element-iii-official-release-benchmarks/ volume goes to +13.5 dB above 0 dB. Given the max output voltage of 9.37 Vrms into 600 ohms, that would mean 0 dB = 2 Vrms.

So you can again set this as the source voltage, set amp gain to 0, and Zout to 0.7 ohm.
 
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xnor

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I analyzed the voltage/power requirements for all 756 headphones in the spreadsheet.

To reach a 85 dB(A) target level:
In the worst case ("Classical" music sample) 75% of all headphones require less than 1.1 Vrms and 95% of all headphones require less than 3.1 Vrms.
In the "Modern Pop/Rock" case 75% of all headphones require less than 0.25 Vrms and 95% of all headphones require less than 0.7 Vrms.
In the best case ("Hypercompressed Metal") 75% of all headphones require less than 0.15 Vrms and 95% of all headphones require less than 0.4 Vrms.

On average (regardless of music) 75% of all headphones draw less than 0.2 mW and 95% of all headphones draw less than 1 mW.


edit: added more numbers
 
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xnor

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I've updated the spreadsheet again.

There is now a Loudness Normalization combo box that allows easy selection of common services.

I've also reworked the Source/Amp Parameters sections and combined them. Source "Max Vout" is now called "Vsource" and is explicitly described as the fixed output voltage of a DAC or the output voltage of a DAC/amp combo device at a 0 dB volume setting.

I've also added configurable Min/Max Volume, and Max Volume can be positive (providing extra gain). In the results, the resulting volume setting will now turn red if it goes outside the Min/Max Volume range.

---

So for the Chord 2, for example, you can now enter:
Vsource: 4.75468 [Vrms]
Min Volume: -108 [dB]
Max Volume: +18 [dB]
Amp Gain: 0 [dB]
Amp Zout: 0.06 [Ω]

Note that Max Vsource/Vout will say 37.768 [Vrms] but the Chord 2 can only output 5.3 V according to the table above, so it would already clip at about +1 dB. Headphones.com says it already starts clipping above 4.3V... With low impedance loads it will probably start clipping even sooner.

So all the extra gain in the Chord 2 basically works like digital amplification. It only makes sense to be used if the digital audio signal itself has a very low level.
 

VladDracule

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So I think I understand the spreadsheet a bit more now

For the JDS Labs Element 3 i put in these values:
Vsource: 9.37
Min Volume -127.5 (this only seems to show 127.5 but the negative sign still shows in the cell, is it working right?)
Max Volume: +13.5
Amp Gain: 0dB
Zout: 0.7
SNR: 117.7dB

Not sure on the amp SNR reference value

and when i look at the results, for HD800s
that means for
Classical: -3.1dB
Jazz: -5.6dB
Modern Pop/Rock: -5.9

should be my max volume settings, does that seem correct?
 
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Vsource for a combo DAC/amp should be set to the output voltage at 0 dB volume setting, so in this case that seems to be precisely 1.98 Vrms.
The calculated Max Vout (at full volume) will then be 9.37 Vrms, which matches the product's specs ("Max Continuous Power @ 600 Ω")

I've corrected the Min Volume number format. Now Excel also displays the negative sign. Thanks for reporting this and please download the latest version.
Note that the value that you enter here is only for color coding of the results but doesn't change the results' values. For example imagine having a high gain amp that has bad channel balance below -40 dB. Although the amp volume control goes much lower (possibly to negative infinity aka total silence) setting this to -40 dB will color the Vol result cell red if it goes below -40 dB.

For SNR, the specs provide "Noise Level: -112 dBV" which is even better than using their SNR measured at an unknown level because dBV is an absolute number referenced to 1 Vrms. So you can enter SNR: 112 dB, Amp SNR Reference: 1 Vrms.
The whole SNR/Noise thing is something I've also added recently to show how loud the noise will be played through the headphones, see the color coded Noise result column.

Regarding your results, I can only compare the numbers if you also tell me what you set the Target Level to.
 

Gershy13

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Am i doing this correctly? I am using a Sabaj A10h as my amp for TYGR 300R headphones, with a UMC204HD as my output (i believe the RCA out is around 0.75v?). I have a -5db preamp on the output using voicemeeter because of EQ.

When using spotify to listen to music (usually pop) with normal loudness equalization, i usually only have my volume set to -30 to -25db on the sabaj in H2 mode (+9db).
Is 80db really so loud that i would have to turn it to -10 on the amp? This means that i usually listen at around 60-65db?

Also in voicemeeter its showing the spotify input at -5dbfs during the loud parts of the song, is this normal? Is the max spotify output set to -5db? Or is this a windows/voicemeeter thing?

Do these results look correct?

Capture.PNG
 
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Hmm, the UMC204HD quick start guide says "max output: +3 dBu" which would be about 1 Vrms and most likely applies to the TRS main outputs. I don't know the output level of the RCA outputs! Unless you can find some reliable info I would measure this with a multimeter to be sure.

You mentioned digital preamp and EQ. There's a small catch: the spreadsheet's results are based on the headphone's sensitivity. This is typically measured at 1 kHz.
Therefore, the "fixed attenuation" value should also be based on the attenuation at that frequency.

Let me give you an example to clarify: let's say you have a +5 dB bass boost at 100 Hz and a -2 dB peak at 1 kHz and then apply -5 dB preamp to avoid clipping, so 1 kHz ends up at -7 dB and you would therefore enter 7 in the spreadsheet.

The voicemeeter input meter is most likely a peak meter that shows the result of Spotify's properly working loudness normalization. You can test this yourself by temporarily disabling loudness normalization in Spotify's settings.
This also makes sense according to the spreadsheet: Spotify (normal) normalizes to -14 LUFS. The "modern pop/rock" loudness is -8 LUFS. So you'd expect Spotify to attenuate such songs by roughly 6 dB.
 

Gershy13

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Hmm, the UMC204HD quick start guide says "max output: +3 dBu" which would be about 1 Vrms and most likely applies to the TRS main outputs. I don't know the output level of the RCA outputs! Unless you can find some reliable info I would measure this with a multimeter to be sure.

You mentioned digital preamp and EQ. There's a small catch: the results are based on the headphone's sensitivity. This is typically measured at 1 kHz.
Therefore, the "fixed attenuation" value should also be based on the attenuation at that frequency.

Let me give you an example to clarify: let's say you have a +5 dB bass boost at 100 Hz and a -2 dB peak at 1 kHz and then apply -5 dB preamp to avoid clipping, so 1 kHz ends up at -7 dB and you would therefore enter 7 in the spreadsheet.

The voicemeeter input meter is most likely a peak meter that shows the result of Spotify's properly working loudness normalization. You can test this yourself by temporarily disabling loudness normalization in Spotify's settings.
This also makes sense according to the spreadsheet: Spotify (normal) normalizes to -14 LUFS. The "modern pop/rock" loudness is -8 LUFS. So you'd expect Spotify to attenuate such songs by roughly 6 dB.
Thank you! My EQ is just a 4db wide boost at 20hz (only really affects up to around 100hz). So i would assume that it would just be -5db preamp that i would factor in?

I believe this is referring to the RCA output. That is where i got the 0.75v from.


EDIT: I may have read it wrong, I think that was referring to the output voltage after reduced by -3db (to avoid clipping with the umc204hd). So original voltage was 1v, and after the reduction of -3db, it would be around ~0.75v. Im not sure if the output voltage of the RCA Playback outputs are the same as the TRS main out (1v).

Assuming the UMC204HD is the same as the UMC404HD, there is a video showing that the RCAs also output at 1V.

I believe @solderdude has/had one of these units? Can you confirm what the output voltage of RCA 1/2 and 3/4 are? And does the clipping at 0dbfs happen for them too or is it just the TRS output with that issue?
 
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Thank you! My EQ is just a 4db wide boost at 20hz (only really affects up to around 100hz). So i would assume that it would just be -5db preamp that i would factor in?
Correct.

I also watched the linked video and it would make sense for the UMC204HD to be the same regarding the playback outputs also being +3 dBu or as Krause measured +1 dBV, both of which round to 1.1 Vrms to be a bit more precise. (You can use this calculator.)

So with those numbers the result would be roughly -15 dB on the volume control for a 80 dB(A) target. As explained in other posts this level is not necessarily safe for long term listening for every individual. For children or people with sensitive hearing the suggested max listening time is suggested to be only 12,6 hours per week.
 

solderdude

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Max. output voltage is around 1.1V BUT it is best NOT to use it at those levels because it already has somewhat high (onset of clipping) distortion there (0.5%).
Ensure the max output voltage is -3dB (opposite max voltage) in which case distortion is much better and below audible levels is around 0.75V.
I used it with the volume control in windows set to 75% (-3dB) which works fine.

Headphone out is pretty much worthless.
 
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Btw, those headphones do have a bit of a dip in their frequency response at and above 1 kHz. Maybe that is also the reason why Beyerdynamic measures sensitivity at 500 Hz instead.
They specify 96 dB/mW (32 ohm, 500 Hz) which translates to 111 dB/Vrms. That would be 3 dB higher sensitivity than DIY-Audio-Haven measured, bringing the resulting volume further down to roughly -18 dB.
 

Gershy13

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Max. output voltage is around 1.1V BUT it is best NOT to use it at those levels because it already has somewhat high (onset of clipping) distortion there (0.5%).
Ensure the max output voltage is -3dB (opposite max voltage) in which case distortion is much better and below audible levels is around 0.75V.
I used it with the volume control in windows set to 75% (-3dB) which works fine.

Headphone out is pretty much worthless.
Is the distortion on the RCA as well as the TRS main out? According to Julian's video he said distortion improves even at max volume when using the RCAs. However maybe it is different for the 204HD. I assume to be safe i should just apply a -3db preamp in eqAPO or voicemeeter to both my outputs? The main volume knob (for the TRS only) on the front doesnt have any effect on the distortion does it?

Btw, those headphones do have a bit of a dip in their frequency response at and above 1 kHz. Maybe that is also the reason why Beyerdynamic measures sensitivity at 500 Hz instead.
They specify 96 dB/mW (32 ohm, 500 Hz) which translates to 111 dB/Vrms. That would be 3 dB higher sensitivity than DIY-Audio-Haven measured, bringing the resulting volume further down to roughly -18 dB.
Interesting! I changed the sensitivity to 96db/mw and dac voltage to 1.1, and now the result is -17.1 for pop/rock @80db (with a 6db attenuation as that is what i usually set on the output).

A comfortable listening level for me is usually around -30db on the amp, which seems to roughly be equivalent to around 65-67dba. So this should mean that the volume i daily listen at is considered pretty safe? And for short periods i can go up to -18db on the amp (80dba) which is still considered safe for 40h a week?
 
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