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Working in live sound can encompass venues of all sizes from a small and intimate bar all the way up to the biggest sports stadium seating 100,000 or more.
So is there a way to calculate how much power you need to fill the venue with sound?
Firstly, we need to be a little more precise about this. "Fill the venue with sound" needs quantifying. One way to do this would be to say that the system should be capable of a level of 100 dB SPL over the whole seating area of the venue. Or a map of levels could be produced that allows some areas to be louder than others.
So now let's consider the variables in the system...
Let's say that you have 1000 watts of power available. This will be supplied to loudspeakers that have a certain efficiency rating. If a loudspeaker can convert 1000 watts of electrical power to 20 watts of sound power, it is doing pretty well at 2% efficiency. The rest of the energy is wasted as heat.
So now we have 20 watts of sound power to play with. All loudspeakers focus their output to a greater or lesser extent. The more focused the output, the higher the level in the direction of 'throw'.
Now for the difficult part - reflections from the room...
Any room (in acoustics, 'room' means an enclosed space of any size) holds and contains sound energy to an extent. A reverberant room will allow sound energy to bounce back and forth. A well-damped room will absorb sound energy. The reverberant room will be louder for the same sound power input because you get the opportunity to hear the same sound several times as it bounces back and forth.
Plainly, we are talking about some difficult calculations here. But there is an alternative... good old-fashioned 'rule of thumb'!
I don't think you will find a better rule of thumb than that provided by the experts at Crown Audio who collectively probably have at least as much and possibly more experience than anyone else in providing amplification for venues of varying sizes, and for different purposes.
So here it is...
Crown also provide a calculator, but this does not account for the directional properties of the loudspeakers, nor for reflections in the room. Still, it makes for a good starting point. (You could bear in mind that they want to sell you more amplifiers!)
Opinions from live sound practitioners would be welcome.