Wattage and Efficiency from HARMONY CENTRAL Website.
“So let's assume we have a speaker with a sensitivity of 90dB @ 1W / 1m and a power handling capacity of up to 100W. If we power that speaker with 1W of power, it will generate 90dB when measured at a distance of 1 meter. If we double that power to 2W, the SPL measurement will increase to 93dB. If we increase the power to 10W, then the SPL measurement will increase to 100dB, which is "twice the perceived loudness" when compared to 1W. So it actually takes ten times more power to give us a perceived doubling of volume level. Since this imaginary speaker is rated to safely handle up to 100W, we could double that volume level yet again, and in theory, hit up to 110dB SPL by increasing the power all the way up to 100W. One watt = 90dB. One hundred watts, or 100X more power = 110dB. That's a huge increase in power but only a "doubled double" (4X) increase in terms of perceived volume levels!
As you can see, it takes considerable increases in power - in the wattage of the amplifier - to "double" the perceived "volume". This is where speaker sensitivity / efficiency comes into the equation. If we replace that 90dB @ 1W / 1m speaker with a model that has a sensitivity of 100dB @ 1W / 1m, the numbers change dramatically. For starters, 1W of input power will give us 100dB SPL. Remember, the first speaker required 10W to achieve that same volume level! So by installing a more efficient speaker, we can get the same perceived volume level from a 1W amp as we could from a 10W amp that is coupled to a less efficient speaker. Again, this applies all the way up to the maximum power handling capacity of the speaker. Assuming our 100dB @ 1W / 1m speaker can also handle up to 100W, it can give us up to 120dB SPL; again, that's double the perceived "volume level" of the 90dB @ 1W / 1m 100W speaker's maximum level of 110dB SPL.
AMPLIFIER POWER PLUS SPEAKER EFFICIENCY AND POWER HANDLING = MAXIMUM VOLUME
So remember, while increasing the amplifier power can make you louder, increasing the speaker sensitivity will make more efficient use of the available power from any amplifier. This means it's impossible to make generalizations about the "loudness" of any amplifier based solely on its wattage. You simply must factor in the power handling capacity and sensitivity of the speakers in order to know "how loud" it will be capable of getting. If your 15W amp has a relatively inefficient speaker installed, but is still "almost" loud enough for your needs, you may not need a higher wattage amp - simply installing a more efficient speaker, such as the Electro-Voice EVM 12L in Fig. 2, may give you all the increase in volume you seek, without having to replace the entire amplifier. Similarly, you may not need a 100W amp; replacing the stock 95dB @ 1W / 1m speakers in your 50W amp with new speakers that are rated at 101dB @ 1W / 1m will more than make up the difference in terms of the "volume levels" you will be able to generate... it will actually be capable of "sounding louder" than that 100W amp will when it is running into the less efficient speakers”.
The above may help to explain Wattage and Efficiency.