A watt is a unit of power. When discussing an amplifier or speaker, wattage describes how much energy per second the audio device is capable of converting into sound. This figure is often a good approximation for what level of volume and clarity your audio device is capable of producing. Knowing the wattage of the different components of an audio system is valuable, as underpowering a device will produce inferior sound and overpowering a device could permanently damage the hardware. As long as you know some basic information about your audio device, it is fairly easy to calculate wattage using an electrical engineering relation known as Ohm's Law.
Determine the voltage at which the audio device in question operates. Technical specifications, including voltage, are often printed on the back or bottom of audio devices. If not, consult the manual that came with the device. If the manual is nowhere to be found, PDF versions of many audio hardware manuals are available for free online.
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Determine the recommended current the wiring of your audio device is designed to carry. Whatever documentation you found helpful in the previous step should also contain this information.
Note Ohm's Law for power:
P = V * I
where P is power, V is voltage and I is current.
Plug in your determined values for V and I, then solve for P. This value is the wattage of your amplifier or speaker.
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Audio device in question
In the first step, note the voltage of the outlet you plug your audio device into is not necessarily the actual operating voltage of that device. Many audio devices use transformers that convert the high (110-120 VAC) voltages of wall outlets into lower voltages usable by the device.
Note the approach used a direct current approximation for Ohm's Law for what is actually an alternating current system. The only difference between the two, however, is the AC version includes a cosine of the phase angle -- this can be omitted to greatly simplify the calculations while minimally impacting the end result.
Make sure your units agree before attempting any calculations. Otherwise, you will receive a nonsensical value for the wattage.