Integrated Amplifier

How does speaker wattage apply to amplifier wattage?

I have two, 300 watt, speakers. Does that mean I would want a 300+ watt amp? Or a 600+ watt amp? Or something completely different? Also, would the wattage be the same for all receivers, amplifiers, and integrated amplifiers? I don't know much about speakers, so the more info the better. Thanks.

300 watts is the maximum power those speakers can handle. That doesn't mean they need 300 watts, it just means they can handle a receiver or amp that puts out 300 watts per channel.
That said, you need to make sure that all ratings are RMS (root mean squared). Sometimes speakers and receivers are rated at "peak power" and several other terms are used as well.
The standard in the U.S. is RMS so just make sure you're comparing apples to apples, in that all ratings are expressed as RMS.
Stereo and surround sound receivers (and amplifiers and integrated amplifiers) are rated in watts per channel, so in that case the maximum you'd want to go is a receiver or amp rated at 300 watts per channel RMS. That's a very big expensive amp for a home theater setup. Unless your room is very large, you won't need nearly that much power.
The other thing to look at is the sensitivity rating on the speakers. The more efficient they are, the less power they need to produce a given volume level. A speaker with a sensitivity rating of 88db takes twice as much power as a speaker with a sensitivity rating of 91db to produce the same volume level.
Unless these speakers are very inefficient, a receiver or amplifier with 100 to 120 watts per channel should be plenty loud and clean.

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