# RMS Voltage



## xrotaryguy (Jul 26, 2007)

The easy way to calculate rms voltage is to divide the peak voltage by the square root of 2.

(Vpeak)/(sqrt(2))=Vrms or Vpeak=(Vrms)*(sqrt(2))

Vpeak is the voltage of the battery pack that one would use in order to achieve the desired Vrms value.

But what does RMS actually mean? When discussing and researching AC motors a useful term that frequently comes up is the RMS rating of the motor or controller. RMS stands for "root mean square" and is used to compare AC and DC voltages. The rms value is a measure of voltage (also known as potential) of an AC wave though not actually the peak voltage, but rather its DC equivalent. AC motors typically have a rating of 230V rms or 460V rms. For example, the sin wave below shows a peak voltage of 648V.








The DC equivalent to a sin wave is its average or its mean. The average amplitude of the graph above is zero, so that value is useless. The graph needs to have all positive values for its average to have any meaning. To resolve this issue, one must square the original sin function. The resulting graph is shown below.








The peak value of this graph is 422,333 volts. To find the average or mean value, simply divide by two. The last step is to take the square root.








The 459.53V may be rounded up to 460V. This is the maximum rms value that could be created by a 648 volt battery pack and an AC speed controller at full throttle.

One might notice that the name of the operation is "root mean square", but that the order of operation is actually reversed, (1.square 2.mean 3.root). The order of operation is very important when doing this type of calculation.


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## mattW (Sep 14, 2007)

Good, post x, I added a bit of an intro to give it some context, but really useful for those who go with AC


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## Guest (Sep 26, 2008)

Hay, it was ok as far as you went but there is a lot more... RMS is a useful number and is calculated as you said, or by multiplying peak voltage by 0.707 and that is useful because electrical loads which convert electrical energy to heat, such as incandescent light bulbs, or heating devices, produce the same amount of heat from the 460 volts rms in your example as they would produce if 460volts DC were applied! But loads which work magneticaly react differently, they respond to the true arithmetic average of the voltage, that is calculated using the formula peak voltage times 0.636. many things electrical including motors, analog (De'Arsnoval) meters, and of course electromagnets, work magneticaly and the magnetic field strength follows the average value, not peak or RMS. Also note we are both using a "SINE WAVE" as our example, any other waveshape uses different constants to calculate RMS or Average! Oh yeah, a capacitor will charge up to peak after a couple of alternations if the voltage doesn't change in polarity. And LED light brightness follows Peak voltage and if powered by AC or Pulsating DC our human eyes remember the brightest part of the glow even if they are flickering, at any rate above 40 flashes per second. That is called "Persistance of Vision."


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