# How can I find the maximum SPL of my headphones?

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### How can I find the maximum SPL of my headphones?

Hello!

Is there any mathematical formula to find out what is the maximum SPL that a pair of headphones can produce when connected to a headphone output?

- My soundcard's headphone output (RME Babyface) has an impedance of 30 Ohm and its output level at 0 dBFS is +7 dBu.
- My headphones (Shure SE535) are 36 Ohm (at 1KHz) and have a sensitivity of 119 dB SPL/mW (at 1KHz).

If I play a 1KHz sine wave file at 0dBFS and Totalmix is set to unity gain (0dBFS) as well, then how many SPL am I going to get out of the headphones?

Thank you in advance for your help and I apologize for my ignorance of physics/electronics!
ElGreco
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### Re: How can I find the maximum SPL of my headphones?

Well I get that +7dBu is 21mW into 36 Ohms and thus an SPL of 132dB, a seriously loud and damaging level (in fact the phones might crack before that is acheived).

But I bow to my betters if I am wrong.

Dave.
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### Re: How can I find the maximum SPL of my headphones?

Don't forget the 30 ohm output impedance of the headphone amp Dave. With these headphones the +7dBu is into 76 ohms.

James.
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### Re: How can I find the maximum SPL of my headphones?

James Perrett wrote:Don't forget the 30 ohm output impedance of the headphone amp Dave. With these headphones the +7dBu is into 76 ohms.

James.
Didn't do that James! I was bit lazy tho' and took the attenuation to be ~6dB giving 0.867V across 36 R.

Dave.
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### Re: How can I find the maximum SPL of my headphones?

Thank you both for your replies!

So, the total resistance is 36 or 76 Ohm? Or 66? (30+36)
And what is the formula to calculate it?

Thanks!
ElGreco
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### Re: How can I find the maximum SPL of my headphones?

ElGreco wrote:Thank you both for your replies!

So, the total resistance is 36 or 76 Ohm? Or 66? (30+36)
And what is the formula to calculate it?

Thanks!
There are several: First you need to get a voltage from +7dBu (daft archaic nonsense!) and I got 1.74volts. The total resistance is 66R and as I say I took V load to be 1/2 that= 0.867 so from vsqrd/r we get ~21mW.
SPL = 10x log W+S where W is power(21mW) and S is sensitivity( 119dB/mW)=132dB?

Nobody has shouted WRONG yet!

Dave.
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### Re: How can I find the maximum SPL of my headphones?

ef37a wrote:
There are several: First you need to get a voltage from +7dBu (daft archaic nonsense!) and I got 1.74volts. The total resistance is 66R and as I say I took V load to be 1/2 that= 0.867 so from vsqrd/r we get ~21mW.
SPL = 10x log W+S where W is power(21mW) and S is sensitivity( 119dB/mW)=132dB?

Nobody has shouted WRONG yet!

Dave.

If I use your formula and calculate with R=66 instead of R=36 (in your calculation) then the resulting SPL is 129.56dB. Is this calculation correct? The resistance was almost doubled but the result is only 2.5dB lower?
ElGreco
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### Re: How can I find the maximum SPL of my headphones?

ElGreco wrote:
ef37a wrote:
There are several: First you need to get a voltage from +7dBu (daft archaic nonsense!) and I got 1.74volts. The total resistance is 66R and as I say I took V load to be 1/2 that= 0.867 so from vsqrd/r we get ~21mW.
SPL = 10x log W+S where W is power(21mW) and S is sensitivity( 119dB/mW)=132dB?

Nobody has shouted WRONG yet!

Dave.

If I use your formula and calculate with R=66 instead of R=36 (in your calculation) then the resulting SPL is 129.56dB. Is this calculation correct? The resistance was almost doubled but the result is only 2.5dB lower?

No because the voltage across the whole system is 1.74V but you only "hear" that votage across the 36R of the phones so,,, ****n you, you have made me work out the ACTUAL voltage! It is 0.936 giving 24mW but that is still just a smidge higher at 132.8dBSPL.

But why do you want to know? Tis just fekkin' loud!

Dave.
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### Re: How can I find the maximum SPL of my headphones?

ef37a wrote:
No because the voltage across the whole system is 1.74V but you only "hear" that votage across the 36R of the phones so,,, ****n you, you have made me work out the ACTUAL voltage! It is 0.936 giving 24mW but that is still just a smidge higher at 132.8dBSPL.

But why do you want to know? Tis just fekkin' loud!

Dave.

Thank you for your time and effort to help me man! I wanted to know in order to set my output fader in Total Mix correctly and avoid hearing damage!! Knowing that the maximum SPL is 133 then I could set my fader to -53dB and get 80dB SPL. Please correct me if my rationale is wrong!!
ElGreco
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### Re: How can I find the maximum SPL of my headphones?

I see your reasoning (I get 86dB?) but I doubt the fader is anything like accurate enough!

The only way to tell is one of these..
http://www.maplin.co.uk/mini-sound-level-meter-226470 But I would use noise not a sine tone for testing.

Dave.
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### Re: How can I find the maximum SPL of my headphones?

ef37a wrote:I see your reasoning (I get 86dB?) but I doubt the fader is anything like accurate enough!

The only way to tell is one of these..
http://www.maplin.co.uk/mini-sound-level-meter-226470 But I would use noise not a sine tone for testing.

Dave.

The output volume is controlled by a software fader. Shouldn't be accurate enough?

Thanks for the link, but I guess that it would be difficult to measure the SPL of an in-ear phone! (Shure SE535 are in-ear phones)
ElGreco
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### Re: How can I find the maximum SPL of my headphones?

"but I guess that it would be difficult to measure the SPL of an in-ear phone"

Don't see why? A bit of rubber tube and gaffer tape? After all you just want a "safety level check" you are not submiting data to the NPL! (or even SoS!)

Bit OT: Can anyone tell me why these in ear phones are so confoundedly expensive? I mean 350 quid buys you more than two pairs of very acceptable "studio" quality phones. (and ones moreover at a very much more sensible impedance!)

Dave.
ef37a
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### Re: How can I find the maximum SPL of my headphones?

Well, I bought them for live gigs. I think they are so expensive because they are so small and good sounding!
ElGreco
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