SPL formula (1 Viewer)

[Bob_M]

Hi all,
What is the formula for calculating total watts needed to reach a given SPL with a given Speaker sensitivity? I can write a table but just can;t get the forula worked out. thanks Bob

 

[Bob_M]

I think I got it:
SPL = Sensitivity + 10 (log(watts))

 

[Eric S]

Alternatively, if you don't have a calculator handy, start with the speaker's rated sensitvity at 1 watt, and just add 3 dB each time you double the power.
For speakers with 90dB efficiency, just double the power each time until you ballpark your amp:
1 watt = 90 dB
2 watts = 93 dB
4 watts = 96 dB
8 watts = 99 dB ... and so on. Not as exact as the formula, but it will get you close enough.

 

[Greg Monfort]

Yes, this is correct for just this value, but for comparisons at different powers:
SPL = sens + [10*(log P2/P1)]
where:
P2 = peak power
P1 = reference power (1W in your case)
If you want to know how much power is required for a given SPL, then:
P = 2^[(dB2 - dB1) / 3.01]
where:
dB2 = peak SPL
dB1 = reference SPL (speaker sens in your case)
GM
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Loud is beautiful, if it's clean

 

[Robert Fellows]

Bob:
Email me and I'll send you an Excel graph/table.
------------------
Bob
p.s.: This advice is worth exactly what you paid for it...

 

[Bob_M]

Hi Greg,
>P = 2^[(dB2 - dB1) / 3.01]<
How did you come up with this? Can you get that by solving for P in the SPL equation, SPL = Sens + 10 (log(p))?
Thanks Bob

 

[Greg Monfort]

I got it from a long out-of-print book.

Yes, it's derived from: dB = 10*[log(P2/P1)],
which is a different way of expressing:
y = 10*{log[x^(10*log2)]/log2,
and P = 2^[(dB2 - dB1)/3.01] is from:
x = 2^[y/(10 log 2)]
where:
x = change in power (new power/old power)
y = change in dB (new dB - old dB)
BTW, the 'P' in SPL is for 'pressure', not power. For 'sound power level', the abbreviation is PWL.
GM
------------------
Loud is beautiful, if it's clean

 

[Rob Roth]

Using this formula indicates that my 150wpc receiver will achieve clean levels of 108 dB with 87 dB sensitivity speakers. Actually, I doubt the power supply would handle the combined load. Are these instantaneous levels or sustained? Is the reference standard of 105 dB for peak or sustained?
thanks

 

[Greg Monfort]

This is transient peak power, unless you're playing sine waves.

Since the peak-to-average SPL varies with frequency, the average 'loudness' without the amp clipping will be based on the 250-500Hz BW (assuming no organ music), which has up to 30dB peaks in music, reducing max average SPL to ~79dB, or 20dB for movies/~89dB/m.
HT reference is 105dB peaks for all speakers, except the sub, 'at the listening position'. So if you're not within