What actually determines volume power? Is it watts?

@dman

If, as some suggest, you look at changing both your speakers and your integrated amplifier, could I suggest you look at powered speakers where the manufacturer has effectively done the matching for you?

The little KEF LS50s are the knockout class-leader in their price range and play much, much louder than their appearance suggests. Each active speaker includes a 260-Watt class D amplifier for the bass and a 100-Watt class A/B amplifier for the treble.  So you effectively get bi-amplification and monobloc operation.  A bonus is that these units have concentric bass and treble drivers, so they throw a coherent wavefront resulting in a massive soundstage and a much bigger than usual listening area.

There are much more expensive powered speakers in the KEF range worth considering as well.

As others have said, one important role of the power amplifier is to control the momentum of a dynamic speaker, so it actually stops moving in short timeframes.  Eliminating speaker wires allows the amplifier feedback circuit to directly interact with the speaker

dman77

For every 3 db SPL increase in output volume requires a doubling of the amplifier watts being used. So if your speaker sensitivity is 88 db, which means that it takes 1 watt of amplifier power to drive that speaker output to 88 db at 1K Hz measured 3 feet away. It will take 2 watts to drive it to 91 db, 4 watts to get to 94 db, 128 watts to get to 109 db and 256 watts to get to 111 db and that is before we consider the effects of the inverse square law which states that you will loose 6 db of SPL for every doubling of distance from the source.

To answer your question more directly, it’s a combination of amplifier power, speaker sensitivity, source level, room size, music type (low frequencies will eat more power than high) and I’m sure there are other factors I don’t know about. A 200 watt amp is a 200 watt amp and will drive a speaker close to the same volume regardless of price, but a better amp may do it a little cleaner, with better low end or  better peak output, etc. etc.

My 48 watts/ch tube amp creates the same amount of volume as my 250watt/ch ss amp ( that doubles down to 400 watts/ch at 4 ohms). The reason has to do with the ability of the transformers and the amount of current delivery to my speakers. Not wattage. 

So what spec do I look at instead of wattage?

Depends on your speakers.

What are you playing?

The issue may be the speaker / amp matching and knowing your speakers would help.  Your speakers may be out of dynamic range or they may have a difficult impedance profile. 

Assuming you had easy to drive speakers, and they were not even a little stressed, then Wattage would help you understand how much more you needed.  Doubling of power = 3 dB SPL.  Doubling perceived volume = 10x the power, and 10 dB louder.

OP:

Lets simplify.  If you feel you are "almost there" with your current amp and you are looking for a reason to upgrade, go ahead.  However if you feel there's a big gap between how loud you can play and how loud you want to play the math isn't in favor of a 2x power difference being your solution.

It's also possible your amp has plenty of juice but it's your speakers which are compressing and reaching their thermal and/or mechanical limits.  They do have limits. 

So, if you feel you have a big gap between where you are and where you want to go, it's more likely to be solved by higher efficiency speakers.

Have fun shopping!

Erik