What numbers are important in SS amps specs

I'm tired of assuming and am now ready to admit I know nothing.
In solid state watts are watts however there are other factor to consider when looking over the spec sheets.
There has to be two or three other specifications with which a consumer should be fimiliar.
How about a little education.
FWIW - Watts ain't watts, you've got to know measurement conditions before even that measure is meaningful.
Anyway, your speaker manufacturer should provide you with a specification for minimum reccomended power & approximate nominal impedance. Once you have that in hand (e.g. 60 wpc continuous and 120wpc short term peak @ 4 ohms) then I'd reccomend looking at amps at and above that power range & trying to make the selection by listening to different amps paired to your speakers if at all possible.
It would be great if you could by the best sound just by looking at the numbers, but it doesn't work that way.
As Jeff_Jones stated, you'd want to be concerned with how many watts are output into the load nominally presented by your speakers. When choosing my amp, I also looked closely at input impedance and power bandwidth. With SS amps THD will generally be less than 0.1%, so that's a spec that is often a wash, and not always that useful when stated by the manufacturer as just THD+Noise, without specifying full power, etc. Some audiophiles also make a big deal over slew rate, which tends to vary significantly between amps. I've owned high and low slew rate amps and liked both. Ultimately it is useful to check out what amps other owners of your speakers are using with them, and seeing how those are spec'ed, then just trust your ears...
Hbarrel, your very reasonable question is made complex by the experience many of us have had that none of the specifications are meaningful and consistent indicators of what an amp will actually sound like in real world listening experiences. The power output is useful ballpark information once you know the sensitivity of the speakers you plan to drive, and some specifications may tell you about a likely incompatibility (e.g., impedance at input and output). But in my experience, little to nothing in the way of specifications is a reliable indicator of what the unit will actually sound like.

For example, while it is certainly true that lower distortion is usually better than higher, an amp that has materially lower distortion achieved through the liberal application of negative feedback will most likely sound inferior to an amp with higher measured distortion but more judicious (or zero) use of negative feedback. It is also certainly true that higher slew rate capability (or "rise time", etc) can be a positive factor in achieving greater resolution and clarity, but high slew rate coupled with ringing and overshoot will sound terrible.

Over the years, I've given up looking at any specifications as indicators of good sound. If I need some indicator of what may be worthwhile auditioning, I instead consider build quality, robustness of power supply, parts quality and manufacturer's track record/reputation. Ultimately, I only care how the unit actually sounds when I listen to it and I refuse to even think about specifications as a substitute indicator of sound quality.
Trying to judge a component by the numbers is like trying to judge a person by their height and weight and color of their eyes, hair, skin, etc. Those details are meaningless, IMHO. Also, they are entirely subjective when it comes to the synergy within a given system, room and listener. Use the ears, heart and soul you were gifted with to judge such things.

This reminds me of folks who buy motorcycles by the performance specs, or cameras by resolution specs: You are going to be riding the motorcycle, right? Likely you have a specific agenda in mind for the use of the bike...how are the specs going to tell you anything about what you are specifically going to use it for (unless of course you are purchasing it solely to run 1/4 miles at the dragstrip, and or roll-ons and stoppies). Likewise the camera may offer remarkable resolution, which may not make one wit of difference in creating a beautiful image if relied upon to do so...unless you happend to find great beauty in images resolution charts. I exaggerate, I know, but really, c'mon...short of a truly intimate understanding of how such things manifest themselves within the performance of a given component, which I'd guess only a precious few of those posting here have time and expertise to cultivate, of what use can such specs be to anyone. In a case like this, I think "a little education" has the potential to do more harm than good. Forgive me if I am misinterpreting your motivations here, which is entirely possible. Are you really going to make a decision about an amplifier based upon slew rate or THD? How will knowing and understanding those details actually weigh in when you are comparing one amp to another in your system. Are you going to decide, "I love the sound of the Pass Labs amp, but the Levinson, which I don't like nearly as much, has 'superior' THD figures so......?"

Take the advice of the wise folks who have already said it above: trust your own ears.

If you really want to get a sense of how amps compare, start listening to some yourself and see which directions your preferences lean. Then start to read some reviews, as well as real-world criticism of those amps and see where that research may lead you. Numbers are a dead end.

WATTS are multiple of current AND voltage or a physical ability to do the WORK per unit of TIME(Joules per second).

Where's the solid state WATTS?

WATTS are important and so is important a condition under which these watts had been measured. Hence the most important spec you should pay attention for is sufficient number of CONTINUOUS WATTS i.e. continuous power which is likely neccessary to drive your speakers.

Then knowing the possible range of your speaker impedances you should verify if the amplifier will be able to handle the peak speaker loads.

Such specs as THD, peak power, S/N are now pointless...

And finally, WATTS are for all WATTs.
The spec wars are over. Numbers, even power ratings (wpc)can be completely deceiving. There seems to be many factors that come into play that determmine how well an amp will drive a speaker. Ask about the experiences of others with specific combinations. The only real way to know is advice from those who you trust and first hand listening.
I seemed to get the best results from my Totem Ones with the most powerful amp I tried. My friend who has them now gets great sound with his Bedini 25/25.
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Viridian - you forgot to factor in the number of fins, thickness of faceplate, and finally multiply that all by the number of blue LED's on the unit. Doing this will give you the THI or 'Total Hype Index'.

Marty, my amp weighs in at: 0.266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666… pounds per watt. Is that a good rating, and how might I make improvements to avoid that annoying repeating decimal?!
Agree completely with Viridan. Weight is important, say at least 50 pounds. Also look for rows of external heat sinks. They're not cheap and so won't find their way onto underperforming equipment.

The answer is obvious. Get a heavier power cord.

Wow, I finally understand the move to big diameter solid copper PCs. Its all about the Amp Index.
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Jeez, you're slipping Viridian!!! You didn't even include PI or the conversion for pounds to pounds per square inch...