RMS Calculator, peak to peak and maximum value of a sine wave.

RMS Calculator. RMS, peak to peak and maximum value of a sine wave

Calculator

Known Parameter	Parameter	Value
	RMS Value
	Peak to Peak Value
	Maximum Value (peak value)

Theory

Sine waves

A sine wave or sinusoid is a periodic wave in which the amplitude is proportional to the sine of its displacement angle. The electrical voltage in our households is a sine wave, and we can find sine waves in many other fields, like sound propagation, radio transmission, etc.
Note: One interesting fact is that almost any periodic waveform can be expressed as the sum of an infinite set of sine waves (Fourier series). This is really helpful as sine waves are relatively easy to compute.

RMS Value (effective value)

The average value of a sine wave (considering a complete cycle) is zero, because the area above the horizontal axis during the positive half cycle is the same as the area below the axis during the negative half cycle, so they cancel each other out. Instead of the average value, the RMS (Root-Mean-Squared) value is usually used. In the case of a set of n values, RMS is:

RMS Equation

So, it is always a positive value, even if some X_i values are negative.

In the case of AC electrical circuits, RMS value is very useful and usually voltage and current are indicated in RMS value. The AC Ohm's law is V= I · Z, where V and I are the rms values of the voltage and current and Z is the impedance

Vp - Maximum instantaneous value (or Peak Value)

Maximum instantaneous value measured from the zero level.

Vpp - Peak to peak value

Difference between positive and negative peaks.