I have answered questions about the relative ‘loudness’ of different guitar amplifier wattages, speaker types, and cabinet arrangements many times over the years, but I thought I would put up a blog post about it so that I can just direct people here when they have questions:
Here is the wattage math:
100 watt to 50 watt amp = 81% as loud (-3dB)
100 watt to 25 watt amp = 66% as loud (-6dB)
100 watt to 10 watt amp = 50% as loud (-10dB)
100 watt to 1 watt amp = 25% as loud (-20dB)
100 watt to 0.1 watt amp = 12.5% as loud (-30dB)
Here is the speaker math:
4×12″ speakers to 2×12″ speakers = 75% as loud (-3dB)
4×12″ speakers to 1×12″ speaker = 66% as loud (-6dB)
+3dB sound level = 1.23x loundess = 2x more speakers/power
+6dB sound level = 1.52x loudness = 4x more speakers/power
+10dB sound level = 2x loudness = 10x more speakers/power
-3dB sound level = 81% loundess = half the speakers/power
-6dB sound level = 66% loudness = a quarter the speakers speakers/power
-10dB sound level = 50% loudness = a tenth the speakers/power
That works with speaker sensitivity ratings as well, so if you have a cab with quiet 94dB speakers like the budget Celestion Rocket50 ( I know they say 95dB sensitivity… they’re 94dB) and replace them with something like a skull-crushingly-loud Jensen C12N, which is 102dB (I know they say 98.4dB sensitivity, but Ted Weber tested them at 102dB… which was 3dB louder than the Celestion Vintage30’s which he tested at 99dB), then you can increase your volume by 33% at the same power. So if you need more juice form your setup and don’t want to spring for a new amp… check the specs on your speakers and see if they have an unusually-low sensitivity rating like Celestion EVH, g12t-75, etc.
So compared to a 100 watt amp through a 4×12″ cabinet (in descending order of loudness):
50 watt + 4×12″ = 81% as loud
100 watt + 2×12″ = 75% as loud
25 watt + 4×12″ = 66% as loud
50 watt + 2×12″ = 60% as loud
10 watt + 4×12″ = 50% as loud
25 watt + 2×12″ = 50% as loud
10 watt + 4×12″ = 50% as loud
10 watt + 2×12″ = 37.5% as loud
And here are some micro-power amp numbers:
1 watt + 4×12″ = 25% as loud
1 watt + 2×12″ = 18.8% as loud
1 watt + 1×12″ = 16.5% as loud
0.1 watt + 4×12″ = 12.5% as loud
0.1 watt + 2×12″ = 9.4% as loud
0.1 watt + 1×12″ = 8.3% as loud
While it seems counterintuitive that a 10 watt amp is half as loud as a 100 watt amp: that is just how it works. So now you can see why people are so blown away when they plug their little ‘Smokey’ 1/2 watt cigarette pack amps into their 4×12″ cabs… those little, pocket-sized, battery-operated things can put out 20% of the volume of a 100 watt monster.
As real-world example, here is my old setup:
I used to use a 2×12″ Earcandy cabinet with ~99dB-rated-sensitivity speakers (or a 4×12″ cabinet with total ~98dB speakers) and a ~12-17 watt EL84 amp (later a ~25-watt, class-A El34 amp since some smaller clubs didn’t mic up the cabs), so I could hit ~112dB at a meter away (~118dB with the 4×12″). That was fine by my standards, and I built my setup like that on purpose so that I could stand between my amp and the drum kit and hear both equally well at max volume and know that I was being exposed to 112dB minus ~22dB from my earplugs and know that I was in the ‘safe zone’ for a 2-3 hour practice session (<90dB).
I occasionally would run into situations where the other guys in the band, who were standing 8-9 feet away, could not hear me over their instruments — my reply was usually TURN DOWN THEN or move away from the drums… because I knew my setup was calibrated to the maximum safest volume level for a practice session. The 25W + 4×12″ setup pushed things into the ‘danger zone’ for practice sessions volume-wise, so I had to switch from hi-fi earplugs to the crappy orange foam types during practice or stand further up front to keep my hearing safe… and I kept a few different pairs around for shows since I never knew how loud they would run the stage volume. Musicians: it is not worth permanent hearing loss for the sake of rehearsal.
For small gigs where they don’t mic the cabinets, 12-17watts + 2×12″ cabinet was not quite enough, so I would run through a 50-watt poweramp into my 2×12″. Later I switched to the 25-watt, 4×12″ setup so that I would not have to do that.
And as a closing note: if any of you crazies think you want double the loudness of your 100 watt, 4×12″ setup you’ll have to spring for a 1,000 watt amp… or cart around 10 speaker cabinets.