Crest factor

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The crest factor of a waveform is equal to the peak amplitude of a waveform divided by the RMS value.

$C = {{x_{\mathrm{peak}} \over x_{\mathrm{rms}}}}$

It is therefore a dimensionless quantity.

DC voltages have a crest factor of 1 since the RMS and the peak amplitude are equal, and it is the same for a square wave (of 50% duty cycle).

This table provides values for some other normalized waveforms:

Wave type	Mean value (rectified)	Waveform factor	RMS value	Crest factor
Sine wave	${2 \over \pi} \approx 0.637$	${\pi \over 2 \sqrt{2}} \approx 1.11$	${1 \over \sqrt{2}} \approx 0.707$	$\sqrt{2} \approx 1.414$
Full-wave rectified sine	${2 \over \pi} \approx 0.637$	${\pi \over 2 \sqrt{2}} \approx 1.11$	${1 \over \sqrt{2}} \approx 0.707$	$\sqrt{2} \approx 1.414$
Half-wave rectified sine	${1 \over \pi} \approx 0.318$	${\pi \over 2} \approx 1.571$	${1 \over 2} = 0.5$	$2 \,$
Triangle wave	${1 \over 2} = 0.5$	${2 \over \sqrt{3}} \approx 1.155$	${1 \over \sqrt{3}} \approx 0.577$	$\sqrt{3} \approx 1.732$
Square wave	$1 \,$	$1 \,$	$1 \,$	$1 \,$

[edit] Digital multimeters

Crest factor is an important parameter to understand when trying to take accurate low frequency signals. For example, given a certain digital multimeter with an AC accuracy of 0.03 % (always specified for sine waves) with an additional error of 0.2 % for crest factors between 1.414 and 5, then the total error for measuring a triangular wave (crest factor = 1.73) is 0.03 % + 0.2 % = 0.23 %.

[edit] Applications

Electrical engineering — for describing the quality of an AC power waveform
Vibration analysis — for estimating the amount of impact wear in a bearing ^[1]
Radio and audio electronics — for estimating the headroom required in a signal chain ^[2]
- Music has a widely-varying crest factor. Typical values for a processed mix are around 4–8 (which corresponds to 12–18 dB of headroom, usually involving audio level compression), and 8–10 for an unprocessed recording (18–20 dB).^[3]^[4]^[5]^[6]
Physiology — for analysing the sound of snoring ^[7]