What is The Formula for RMS Wattage?

Don't know about square wave. For sine first divide peak voltage by sqrt(2) the square that result and divve by resistance/impedance.

W= ( (Vp/sqrt(2)) * (Vp/sqrt(2)) )/ R

Example: Peak volage =42, assume the load is 8 ohms
RMS voltage = 42/ sqrt(2)= 42/1.4=30
W=(30*30)/3 = 112.5

This does not take into account losses the fact that if you are taking impedance rather than resistance, it often varies with frequency.
excuse me guys, but Vpeak/sqrt(2) is the effective value of a sinusiodal wave, and if P=(Vpeak/sqrt(2))^2/R, then I (and my teachers at the high school) call "P" as the effective power. not RMS (root means square).
The "Vpeak/sqrt(2)" is the effective value of the sinusoidal wave. This sqrt(2) comes from a very "dirty" maths.... Some integrals are involved grrr :)
At square wave the effective valua is simply the duty cycle of the square wave.
For a sine wave, power is peak-to-peak squared divided by eight times resistance (that is, peak squared divided by twice resistance)

Which if you use my starting point of 42Vp comes out to 110.25. Virtually the same result.

I mention this not to be contentious but to keep the original poster from getting confused. We are really just manipulation Ohms Law and the definition of RMS to get the same result by a different sequence.

If you want more precision look at:


The example I stated with will come out more like 100W in the real world.

Ok, this is getting confusing.

As for RMS, are not amplifiers rated to deliver so many watts per channel RMS???

When I say peak-to-peak, I mean it! 60 v peak-to-peak is the same as plus AND minus 30 volts, so on a scope at 10V/div, the wave would go up 3 div and down 3 div, for a total of 6 div. being occupied vertically by the wave on the screen.


diyAudio Member
2002-10-11 8:15 am
Re: confused

lgreen said:
.....As for RMS, are not amplifiers rated to deliver so many watts per channel RMS???...

"A serious and reliable measure of the power output of a loudspeaker or audio amplifier is average power, commonly called watts RMS. RMS stands for root mean square and is actually a misnomer here but has nonetheless become the common term. The "RMS" power is found by averaging the instantaneous power output over a long period of time, so it is actually the average power or mean power. The term RMS is used due to the fact that the mean power is calculated from the RMS voltage and current (or one of them and the impedance)."
a squarewave puts out exactly twice as much power as a sinusoidal voltage if the squarewave bandwidth extends to infinity.
For reference the extra power of the square wave is all above the second harmonic which is why tweeters burn out in a clipping amp. So a 100w single frequency 1kHz signal into a two way passive speaker should put almost zero power into the tweeter but a similar drive voltage square wave will put 100w out at 1kHz and another 100w out at 3kHz and above (if perfect squarewave).