# Difference Between Peak to Peak and RMS

Peak to Peak vs RMS

Peak to Peak and RMS amplitudes are two measures of an alternating signal/source. Peak to peak amplitude is measured from the signal and RMS value has to be derived from the measurements.

Peak to Peak

Peak amplitude is the maximum amplitude obtained by a signal/source in a given interval. If the form of the signal is periodic and uniform, then peak values are constant throughout. Consider a sinusoidal wave as shown below.

To represent the strength of a signal, often the maximum absolute value from zero or the peak value of the signal is used. Another term used is the peak to peak value. Peak to peak value of a system is the difference between the maximum amplitude in the negative direction and in the positive direction. Again, if the wave form is uniform and periodic, the peak to peak value is a constant.

These concepts are used in audio technology, electrical engineering, and many other sub fields using alternating signals.

RMS (Root Mean Square)

RMS Amplitude or the Root Mean Square Amplitude is a derived amplitude to interpret the properties of a signal. For a sinusoidal waveform as shown above, RMS value of the signal is obtained by the formula

$A_{RMS}&space;=&space;\frac{A_{peak}}{\sqrt{2}}$

Requirement of RMS values comes from the fact that average amplitude of the wave within a period (T) is zero. The positive half of the amplitude cancels the negative half. It implies that no wave was transmitted during that period, which is not true in reality.

$A_{mean}&space;=&space;\int_{0}^{T}\left&space;(A&space;_{peak}Sin&space;\omega&space;t&space;+&space;\phi&space;\right&space;)dt&space;=&space;0$

Therefore, the amplitude values are squared (when squared, all values become positive). Then taking the average gives a positive number, but the values are much higher than the actual values. The square root of the average serves as an indicator to the average amplitude of the wave.

$A_{RMS}=&space;\sqrt{\frac{\int_{0}^{T}\left&space;(A_{peak}Sin&space;\omega&space;t&space;+&space;\phi&space;\right&space;)^{2}dt}{\int_{0}^{T}dt}}$

$=&space;\sqrt{\frac{{A_{peak}}^{2}\int_{0}^{T}1&space;-&space;cos&space;2\left&space;(&space;\omega&space;t&space;+&space;\phi&space;\right&space;)dt}{2T}}$

$=&space;\sqrt{\frac{{A_{peak}}^{2}\left&space;(&space;T&space;-&space;0&space;\right&space;)}{2T}}$

$=&space;\frac{A_{peak}}{\sqrt{2}}$

RMS voltage and RMS current are important in the AC theory of electricity. The RMS values of voltage and current give the average voltage and current in the main power supplies. The power dissipated when alternating current passes through a resistance is calculated using VRMS and IRMS.

P = VRMS IRMS

The RMS values of voltage and current produce the same power as produced by DC voltage and DC current of same values passing through a resistance.

Peak to Peak vs RMS

• Peak value is the absolute values of the maximum amplitude variation in any direction. For a uniform periodical signal, this values is a constant.

• Difference between the maximum values in the positive direction and the negative direction is known as the Peak to Peak amplitude.

• RMS amplitude is a derived amplitude, to represent the average amplitude of an alternating signal. For a sinusoidal wave, it can be given as

$A_{RMS}&space;=&space;\frac{A_{peak}}{\sqrt{2}}$