The term "RMS" stands for "Root-Mean-Squared", also called the effective or heating value of alternating current, is equivalent to a DC voltage that would provide the same amount of heat generation in a resistor as the AC voltage would if applied to that same resistor.
RMS is not an "Average" voltage, and its mathematical relationship to peak voltage varies depending on the type of waveform. The RMS value is the square root of the mean (average) value of the squared function of the instantaneous values.
Since an AC voltage rises and falls with time, it takes more AC voltage to produce a given RMS voltage than it would for DC. For example, it would take 169 volts peak AC to achieve 120 volts RMS (.707 x169).
In this example, the heating value of the 169 AC voltage is equivalent to that of a 120 volt DC source. Most multi-meters, either voltmeters or ammeters, measure RMS value assuming a pure sinusoidal waveform.
Important Terms to Remember
Peak Voltage (Vp)
The maximum instantaneous value of a function as measured from the zero-volt level. For the waveform shown above, the peak amplitude and peak value are the same, since the average value of the function is zero volts.
Peak-to-Peak Voltage (Vp-p)
The full voltage between positive and negative peaks of the waveform; that is, the sum of the magnitude of the positive and negative peaks.
RMS Voltage (Vrms)
The root-mean-square or effective value of a waveform.
Average Voltage (Vavg)
The level of a waveform defined by the condition that the area enclosed by the curve above this level is exactly equal to the area enclosed by the curve below this level.
Important Equations to Remember
- Vp x .707 = Vrms
- Vrms = 1.11 x Vavg
- 1.414 x Vrms= Vp
- Vavg= .637 x Vp
Further Reading / Sources
- RMS Voltage Calculator
- Root Mean Square
- RMS Voltage Tutorial
- Difference Between RMS and Peak
- Peak, Average, and RMS Measurements
