# What Do We Mean By Crest Factor? (For audio applications)

Working with loudspeakers, live sound or mixing and mastering audio, you may come across the term “crest factor”.

It can be very easy to define crest factor in mathematical terms, but what does it mean in the real world? And should we even be worried about crest factor?

As a general rule, crest factor is defined as the ratio of the peak value of a waveform to its root mean square (RMS) value.

Knowing how much an audio signal varies from the average value of the signal to the peak is helpful, as it can give us an indication of the characteristics of the signal.

For example, if there is not much difference between the average level of a signal and its peak, there is not much dynamics in the sound, and the sound is compressed.

But does this matter? And when does the crest factor become important?

It is possible that you can go through your entire audio career, be it as a mix and mastering engineer or someone who works with loudspeakers and live sound and never use or benefit from crest factor data of a signal.

In this article, I will share what I know of crest factor as a loudspeaker designer and mix engineer, covering:

• What do we mean by crest factor? (For audio applications)
• What does crest factor tell you?
• Why is crest factor important?
• How do you calculate crest factor?
• What is the crest factor of a speaker?

## What Do We Mean By Crest Factor? (For audio applications)

The term “Crest Factor” in the realm of audio applications refers to the ratio of the peak value of a waveform to its root mean square (RMS) value. It’s a measure that provides insights into the quality and characteristics of an audio signal.

A high crest factor indicates a signal with high peak levels and a broad dynamic range, often associated with high-quality audio. Conversely, a low crest factor suggests a more compressed signal with less dynamic range, typically in heavily processed or distorted audio.

Understanding the crest factor is crucial in audio applications as it helps optimise signal levels, reduce distortion, and preserve audio quality.

If you know how much an audio signal varies from average to peak, you will be better able to work with that audio.

For example, in mixing and mastering audio, if you know how loud your peaks are, you can apply the right amount of limiting and compression without killing the overall volume and dynamics of the track.

In loudspeaker design, you need to design your speakers so that they can pass a power test which takes in a continuous signal with a crest factor of at least 6dB according to AES standards. (Note, newer AES standards specify 12dB). This ensures that amplifiers which use your speaker can handle most audio without being driven too hard and burning out.

## What Does Crest Factor Tell You?

The Crest Factor can tell you a lot about an audio signal’s structure and quality. It provides insight into the signal’s dynamic range, the difference between a sound’s quietest and loudest parts.

An audio signal with a high crest factor has an extensive dynamic range, indicating a sound with solid peaks and lower valleys. This often translates into a more vibrant and detailed audio experience.

On the other hand, a low crest factor implies a smaller dynamic range, suggesting a sound that’s more even and less dynamic. It’s also a valuable tool for detecting possible signal clipping or distortion.

If the crest factor is too low, it could mean the signal is too loud and might be clipping, which can degrade the audio quality.

Thus, monitoring the crest factor can help ensure optimal audio performance.

I should add that audio is highly subjective. When it comes to audio and the world of mixing and mastering, there is not one crest factor number that will tell you whether a sound is good. From my experience, you need to listen and consider the crest factor in context.

If you want to know about crest factor in audio mixing and mastering, I highly recommend this article from iZotope.

## Why Is Crest Factor Important?

Crest factor holds significant importance in audio applications for several reasons. Firstly, it guides in setting appropriate amplification levels, ensuring that audio signals are not excessively amplified, which can lead to signal clipping or distortion. Sound engineers can adjust the signal level by monitoring the crest factor to prevent unwanted distortion and maintain audio integrity.

Secondly, it is a crucial factor in determining the dynamic range of a signal. A high crest factor generally implies a greater dynamic range, desirable in high-fidelity audio systems for better sound reproduction.

Lastly, the crest factor can indicate the level of processing a signal has undergone. Overly processed signals tend to degrade in quality and usually exhibit a lower crest factor.

Hence, understanding and monitoring the crest factor is fundamental to maintaining optimal audio quality and performance.

## How Do You Calculate Crest Factor?

In order to calculate the crest factor of an audio signal, two key aspects are evaluated: the peak value and the RMS (Root Mean Square) value of the signal.

The formula for calculating the crest factor is as follows:

Crest Factor = 20log (peak value / rms value)

The ‘Peak Value’ represents the absolute highest point of the waveform, while the ‘RMS Value’ is a measure of the magnitude of the waveform, or essentially, the ‘effective’ value of the total waveform. It is calculated by squaring all of the waveform’s values, finding the average of these squares, and then taking the square root of that average.

Once the Peak Value and RMS Value are determined, they are plugged into the formula, and the resulting quotient is the crest factor.

This computed crest factor then serves as a guide in audio processing and sound engineering, aiding in optimising signal levels and preserving audio quality.

## What Is The Crest Factor Of A Speaker?

When designing a speaker, it is important that your speaker can handle peaks in the audio signal without distorting the sound quality.

Loudspeaker manufacturers will apply a test signal of continuous pink noise to a new speaker design for two hours with a crest factor of at least 6dB. This is generally in line with AES standards.

The reason for this is to stress test the excursion and heat-coping capabilities of the speaker.

For example, if you have a continuous signal that suddenly has a large peak, which is in the lower frequency range (below 60Hz), you could damage a speaker as the cone and suspension try to respond to this input. Applying a frequency of 60Hz suddenly to a speaker will result in a significant movement of the speaker cone, which could mechanically damage the speaker.

A signal with a crest factor ratio of 6dB is the same as having a power factor of 4x in your amplifier. In other words, let’s assume you have an amplifier producing 200 watts continuously. It will need to produce 800 watts for the peaks of the signal.

From this test, we can determine how much power a loudspeaker can handle. As a general rule, if it can survive a continuous signal of pink noise with a crest factor of 6dB for two hours, it is fit for the market.

I should add that some audio standards specify that the test signal must have a crest factor of 12dB. Not many manufacturers use this as this is very demanding for the amplifier and speaker.

For example, a crest factor of 12dB is equivalent to a power factor requirement of 16x in your amplifier. So in the real world, if you have an input signal producing 100 watts continuously, the amplifier must be able to deliver 1600 watts for the signal peaks.

## Final Thoughts

The crest factor is pivotal in audio signal processing, design, and sound engineering. It provides crucial insights into an audio signal’s dynamic range and the degree of processing it has undergone.

This, in turn, helps maintain optimal amplification levels, prevent distortion, and preserve the overall sound quality.

Calculating the crest factor involves understanding a signal’s peak and RMS values, and using these values effectively can maximise audio performance.

Whether you’re a sound engineer, a speaker designer, or an audiophile, understanding the crest factor can significantly enhance your grasp of sound quality and manipulation.