**Crest factor** is defined as the ratio of the peak value (or maximum value) to the RMS value of a waveform. It is denoted by the capital letter ‘C’. It is also known as **peak factor**. The waveform can be any quantity like current, voltage, etc.

**Contents**show

## Crest factor Formula

$\text{Crest factor}=\frac{{A_{peak}}}{{A_{rms}}}$

where,

A_{peak} is the peak or maximum value of the waveform

A_{rms} is the rms value of the waveform

### Crest factor of Half wave rectifier

Let the peak value of the rectified output be V_{m}.

The RMS value of output voltage of single-phase half-wave rectifier is given by

$V_{rms}=\frac{V_{m}}{2}$

As we know the crest factor is given by

$\text{Crest factor}=\frac{{V_{peak}}}{{V_{rms}}}$

Therefore, we get

$\text{Crest factor}=\frac{{V_{m}}}{{\frac{V_{m}}{2}}}$

∴ Crest factor = 2

The crest factor of half wave rectifier is 2

### Crest factor of Full wave rectifier

Let the peak value of the rectified output be V_{m}.

The RMS value of output voltage of single-phase full-wave rectifier is given by

$V_{rms}=\frac{V_{m}}{\sqrt{2}}$

As we know the crest factor is given by

$\text{Crest factor}=\frac{{V_{peak}}}{{V_{rms}}}$

Therefore, we get

$\text{Crest factor}=\frac{{V_{m}}}{{\frac{V_{m}}{\sqrt{2}}}}$

∴ Crest factor = √2 = 1.414213

The crest factor of full wave rectifier is √2

### Crest factor of Bridge rectifier

Let the peak value of the rectified output be V_{m}.

The RMS value of output voltage of bridge rectifier is given by

$V_{rms}=\frac{V_{m}}{\sqrt{2}}$

As we know the crest factor is given by

$\text{Crest factor}=\frac{{V_{peak}}}{{V_{rms}}}$

Therefore, we get

$\text{Crest factor}=\frac{{V_{m}}}{{\frac{V_{m}}{\sqrt{2}}}}$

∴ Crest factor = √2 = 1.414213

The crest factor of full wave rectifier is √2