A Beginner’s Guide to Headphone Amplifier Terms: Volume vs Gain vs Headroom

Everyone in the headphone hobby has come across the terms volume, gain, and headroom. It’s likely that most of us just smile and nod, and have a more-or-less vague understanding that these three things all somehow relate to how loud the music is, and leave it at that. Today we’re going to explore these concepts in a little more detail and discuss how each relates to music listening and to choosing a DAC, amplifier, and headphones.

On the recording side, the benefit to understanding (and properly adjusting) volume, gain, and loudness is producing clearer and higher resolution recordings, with lower noise floors and greater dynamic range (don’t worry, we’ll discuss those terms below). On the enthusiast side of music listening, understanding these concepts allows us to squeeze all the performance out of the gear we own, and to choose the right gear to pair together.

Right off the bat, I’m going to cheat a bit and include a couple more concepts in the volume section. The terms power and loudness get thrown around a lot, and it’s important to know how they are related to volume.

Volume, Power, and Loudness

We will start with the concept of volume, as it’s the most familiar and intuitive of the three. Put simply, volume is a measure of the output level of an audio system, measured in decibels (dB). Increasing the volume increases the amplitude of the audio signal.

Volume can further be differentiated between speaker driver output (which is volume) and amplifier output, which is defined as power and measured in Watts (W). Power is calculated as voltage squared, divided by load resistance (which typically refers to the impedance of the headphone driver). It’s enough to know that wattage and voltage are linked.

Loudness is the least quantifiable as it is a subjective impression of volume. What one person perceives as loud, another may not. Loudness is associated to the level of sound intensity, duration, and frequency. 

Volume, power, and loudness are all related on a logarithmic scale. In a nutshell, to double the perceived loudness, this requires a volume increase of 10dB, over 3 times the voltage, and 10 times the power. 

Loudness Compensation

You may be familiar with the ‘loudness’ button sometimes found on stereo amplifiers. Engaging this circuit alters the frequency response curve to correspond roughly with the equal loudness characteristics of the ear. In simpler terms, loudness compensation boosts low frequencies at low volume levels because the ear is less sensitive to these sounds. The Fletcher-Munson curve details how our sense of volume varies at different frequencies. 

Further complicating the concept of loudness is the psychoacoustic effect of how we perceive improvements in sonic performance (bass, soundstage, detail, extension, etc) when the volume is increased (within a reasonable range). Subjectively, we fall victim to perceiving that louder is better and often mistakenly attribute quality improvements solely based on volume mismatch when comparing two audio components.

Remember, volume takes the subjectivity out of the loudness equation. It’s a measure (in dB) of the output power of an audio system from the drivers. 

Volume = Speaker driver output level (dB)

Power = Amplifier output (W)

Loudness = Perception of the level of volume (dB)

Gain

Increasing volume makes the output audio louder. Gain also modulates the amplitude of the audio signal, but at the input stage, before it’s been processed. Adjusting the gain at the input of an audio component controls the amplitude before it goes through the circuit. Volume controls the amplitude after the audio signal has gone through the circuit.

Gain is defined as the ratio between the volume at the input and the volume at the output of an electrical circuit. 

Gain = Signal Out / Signal In

Gain may be expressed as a ratio (such as 4x) or in decibels (such as 12dB). 4x is the same as 12dB if when the volume control of the amplifier is set at maximum, the output voltage is four times higher than the input (1V input, 4V output). Typical headphone amplifiers gain settings are in the range of 2-3x (low gain) and 5-8x (high gain), although this varies by model. 

Too little gain and the headphones will not get loud enough. Too much gain and only a small range of the volume control will be usable (commonly leading to channel imbalance issues with analog volume potentiometers) and increased distortion and noise. In general, there is a common rule that states you should use the lowest gain setting that yields an acceptable listening level.

Adjusting gain affects the quality and tone of the sound but does not increase the maximum power output of an amplifier. Increasing the gain will just make an underpowered amplifier run out of clean power sooner and start to distort. Gain controls the maximum loudness inside an audio circuit before this distortion point is reached (clipping). Reducing gain can be used to limit the maximum power output to ensure that even at the maximum volume setting, the attached headphones are not overpowered or the sound is not loud enough to damage hearing.

Gain = the ratio between the volume (signal amplitude) at the input and output

Headroom

In order to understand headroom, we have to discuss a couple of other common audio terms. First up is noise floor, which is the quietest section of an audio track (where you hear hiss and hum). It’s the sum of the unwanted electrical noise in the audio signal. Reducing gain lowers the noise floor.

On the other end of the spectrum is the loudest part of the audio before the signal begins to distort. We defined it above as clipping. Increasing the gain too far drives the audio signal to clip. The space between these two points is known as dynamic range. Dynamic range is defined as the difference in decibels between the loudest and quietest portions.

Dynamic Range = Clipping Point – Noise Floor

In analog audio, peak amplitude before clipping is based on voltage. In digital audio, peak amplitude is based on bit depth.

When we record or listen to music, we strive for a level somewhere in the middle of the dynamic range (a ‘sweet spot’) to allow for musical transients to have enough space to increase without clipping (loud sounds) or to decrease without falling below the noise floor (quiet sounds). Headroom is the space between the sweet spot and the clipping point.

Headroom is the difference between the loudest portion of the audio and the loudness threshold that your sound system can handle without distortion. Think of headroom as power in reserve. It’s the available power that isn’t being used by an amplifier. If a signal is driven into clipping, there is no available headroom. Increasing gain decreases input headroom and makes it easier for a lower amplitude signal to maximize the output stage.

Conclusion

It’s tough to define terminology without getting too technical. Either the definition evolves into mathematical calculations and dense jargon, or it all remains a bit too vague to understand. Hopefully, you now feel more immersed in the basic concepts of volume, gain, and headroom and understand a little more how they are interrelated and differ from one another. 

Volume is relatively simple, as it’s a measure of the output of the audio coming from our headphones. Loudness is our perception of the volume. Gain is the ratio of the audio signal in vs out of a circuit. Adjusting the gain affects the quality of the audio signal. Too low and you will hear the noise floor. Too high and the signal will clip. Dynamic range is the space between the noise floor and clipping point. Headroom is the available space between the sweet spot within the dynamic range and the point of clipping. For amplifiers, headroom is the power on reserve to reproduce highly dynamic portions of the music without distortion.

Author Trav Wilson:  Audiophile or Audio-Phool? I don’t claim to have golden ears with magical properties, nor any ability to create music. But I do have a deep appreciation for music, founded at a young age, and curated over the years. I’m also unapologetically a gear-head and love lights, buttons, meters, switches, and especially things made from traditional wood, leather, metal, and glass materials. As with everything, take it for what it is: this is just one person’s opinion. Runs noteworthy.audio