One of the most commonly misunderstood concepts in audio are the wattage figures that show up on amplifier, receiver and speaker advertisements and specifications. The most common thing we think of when it comes to wattage are light bulbs. The socket has a specification, you buy a light bulb that matches, or is smaller than, that number. That’s the wrong way to think about speakers and amplifiers. Depending on how loud a speaker is playing, it uses a variable amount of power (measured in watts), and the amplifier supplies it. So all you need is an amplifier or receiver that can deliver as much power as the speaker needs to create sound.
The wattage rating on a speaker only tells you how much power the speaker can take before it breaks irrevocably. Even then, playing certain types of signals, even at low power, can damage a speaker. In normal use you wouldn’t ever run into this issue.
[I removed a large section of math here 8/6/2015]
The amount of power used by a speaker in your house is pretty small. You’ll generally won’t peak at more than 10 watts. Within 20 feet and at typical listening volumes, a speaker doesn’t need that much power to operate.
So the question becomes, “does the power rating of an amplifier matter once it’s more than the level I just calculated?” The answer is yes. Even if a 15 watt amp can provide all the power you need, distortion is an issue faced by every amplifier. The following graph shows an input versus output for two cases. The first is for a fictitious distortionless amplifier, it linearly maps an input voltage to an output voltage. The second graph is a theoretical example of an amplifier with distortion. It’s similar to the first stage of most home theater receiver amplifiers. While at low voltages it behaves close to the ideal case, at higher voltages it produces proportionally smaller outputs. This means that the peaks and valleys of an audio signal are smaller and broader in the output than in the input. In other words, the signal has been distorted.
Different manufacturers will rate the wattage of their devices differently, usually based on how much power can be delivered under a distortion constraint. One might think of the % distortion as the difference between the red and blue lines. Ultimately though, using less power on an amplifier means that it distorts less. So buying an amp with more power than you need can be advantageous.
In summary, here are a few rules for dealing with wattages on speakers, amplifiers and receivers.
1. Most amplifiers and receivers will work with most speakers provided you are using them reasonably. Most amplifiers and receivers can damage a speaker if you are using them unreasonably.
2. Speaker wattage ratings don’t impact the quality of the sound, they are warnings about what can make the speakers break.
3. Amplifiers with less than 10 watts should only be bought if you have confidence you are doing the correct thing. Amplifiers with 10-100 Watts are ones that will have noticeable differences in sound quality as you increase the wattage. Above 100 Watts, you should have a good justification for spending money on more watts.