What is a decibel?

Decibels in plain English

A decibel says how much bigger or smaller one level is than another, so on its own it has no size at all, unlike a kilogram or a volt. When a plug-in says it's boosting 3 dB, it means the output is 3 dB above the input. When a meter reads −12 dBFS, it means the signal is 12 dB below a fixed reference, in this case full scale.

The scale is logarithmic, so equal steps in decibels are equal ratios. Every 20 dB multiplies the size of a signal by ten, which makes 40 dB a hundred times, 60 dB a thousand and 120 dB a million. Your ears need a scale like that. The loudest sound you can stand has about a million times the air pressure of the quietest one you can hear, and in decibels that whole range fits between 0 and about 120.

The name comes from the bel, a unit named after Alexander Graham Bell. One bel is a tenfold change in power and a decibel is a tenth of one; bels are too coarse for everyday use, so dB is what you'll see on every meter and plug-in.

The letters after dB tell you what the reference is. dBFS is measured from the digital maximum, dBu from a set voltage and dB SPL from the quietest sound pressure a young ear can detect. Without letters, a decibel figure is a change: "turn it up 3 dB" says how far to move and nothing about where you end up.

Reading the lab

The lab is a loudness meter on a loop, with a Gain knob that adds or takes away decibels. The four meters next to the big screen read the loop in two kinds of decibel. M, S and I show loudness in LUFS, and TP shows the true peak in dBTP, the highest point the waveform reaches between the samples.

Under the meters, the whole loop is drawn as a waveform, with the original in pale ivory and your version in pink. The dashed lines are 0 dBFS. Turn the gain down 6 dB and the pink shape becomes half the height of the pale one, which is the plainest way to see what a decibel does to a signal.

The crest factor screen compares each version's peak level with its RMS level, an average, and the Right now panel works out what your settings did from the audio you're hearing. The Limiter knob pushes the loop into a ceiling at −1 dBTP. The streaming buttons are switched off on this page; the LUFS lesson covers what they do.

How to work out decibels

There are two formulas, and which one you use depends on what you're measuring. Sample values, voltages and sound pressure are amplitudes: they describe the height of a wave. For those, the level in decibels is 20 × log₁₀(ratio). Power and energy, in watts, use 10 × log₁₀(ratio). Both give the same decibel figure for the same change, because power goes up with the square of amplitude.

Say a sample in your DAW has the value 0.5, on a scale where 1.0 is full scale. Its level is 20 × log₁₀(0.5), which is −6.02 dBFS. A sample at 0.1 is −20 dBFS and one at 0.01 is −40 dBFS. Going the other way, divide by 20 and raise ten to that power: −12 dB is 10^−0.6, about 0.25, so the wave is a quarter of the height.

Amplitude is the column that matters for almost everything in a DAW, from sample values to fader moves.

Decibels add where ratios multiply, and that's most of the reason engineers use them. A 3 dB EQ boost followed by a fader 5 dB down leaves the signal 2 dB quieter overall, a sum nobody wants to do as 1.41 × 0.56. It's also why gain changes in the lab move every meter by the same number: −6 dB of gain takes 6 off the peak, the RMS and the LUFS reading alike.

Adding two sounds together

Signals don't combine the way their decibel numbers suggest. Two identical copies of a track, each peaking at −6 dBFS, sum to a wave twice the height, so the result peaks at 0 dBFS. Unrelated sounds at the same level, like two guitar takes, add up in power instead, and come out about 3 dB louder together. So a second take of a part makes it only a little louder. Stack the same sample twice, perfectly in time, and it jumps by 6 dB.

How loud is a decibel?

A change of 1 dB is about the smallest step in level most people can pick out when they compare the same music back to back. Spread over an evening, a few decibels can go unnoticed, which is how monitoring creeps up in volume during a long session.

Loudness and level don't follow the same maths. Halving the height of the wave, −6 dB, sounds clearly quieter but nowhere near half as loud. Most people hear a drop of about 10 dB as half as loud and a rise of 10 dB as twice as loud. That figure comes from the sone scale, which was built from listening tests on how loudness grows with level, and it's approximate, but it's a far better guide than the 6 dB one.

Your ears also hear some frequencies as louder than others at the same level, with their sensitivity peaking between about 2 and 5 kHz and falling away in the deep bass. A meter that reads plain decibels can't know that. LUFS meters filter the sound first to make up for it, which is how a bright synth and a sub-bass at the same peak level end up with different loudness readings.

dBFS: decibels relative to full scale

dBFS is the decibel your DAW's meters use. Full scale is the biggest number a digital file can store, so 0 dBFS is the ceiling and every level below it is negative. Silence is −∞ dBFS, because a sample of zero is no fraction of anything.

In a fixed-point file, such as a 16 or 24-bit WAV, nothing can go above 0 dBFS. A sample that tries gets stored as the maximum instead, the top of the wave is cut flat, and that's clipping. Inside most DAWs the mix runs in 32 or 64-bit floating point, which can hold values far above full scale, so a channel can read +3 dBFS without damage as long as the level comes down again before it reaches a plug-in that clips, the converter or an export.

Each bit in a fixed-point file adds about 6 dB of range. A 16-bit file has roughly 96 dB between full scale and its noise floor and a 24-bit file roughly 144 dB, more than any microphone or converter can use. So there's no prize for recording close to 0 dBFS at 24 bits: peaks around −18 to −10 dBFS leave plenty of headroom and lose nothing you could hear. The sample rate and bit depth lesson has the detail.

dBTP: decibels true peak

A peak meter in dBFS reads the samples. The sound you hear is the smooth curve a converter draws through them, and that curve can rise higher than any single sample, most often on bright, heavily limited material. dBTP is the level of that curve, measured by working out extra points between the samples as the ITU-R BS.1770 standard describes. The lab's TP meter works out four points for every sample.

The figure below shows the worst case, a tone with only four samples per cycle. Slide the timing and the samples can miss the top of the wave by 3 dB, so a sample peak meter reading −3 dBFS would be hiding a wave that reaches full scale. When a file like that is converted to MP3 or AAC, or played through a converter that can't handle overs, the hidden peaks can distort.

That's why limiters on masters have their ceiling set in dBTP. Spotify asks for masters to stay under −1 dBTP, and under −2 dBTP if they're louder than −14 LUFS. The true peak lesson goes further into how the peaks between samples come about.

dBu, dBV and analogue levels

Analogue gear measures voltage, so its decibels need a voltage reference. dBu uses 0.775 volts RMS, a figure inherited from telephone engineering, where 0.775 V across 600 ohms delivers one milliwatt. dBV uses a round 1 volt. Both are amplitudes, so the 20 × log₁₀ formula applies.

Professional line level is +4 dBu, which is 0.775 × 10^4/20, about 1.23 V. Consumer gear runs at −10 dBV, about 0.32 V. Converted to the same reference, −10 dBV is −7.8 dBu, so the two standards sit close to 12 dB apart, and a consumer output plugged into a professional input leaves you short of level.

There's no fixed link between dBu and dBFS. Each converter is set so that full scale matches a certain voltage, printed on the spec sheet as its maximum input or output level. Studios often line them up to a standard: the European broadcast recommendation EBU R68 puts 0 dBu at −18 dBFS, and SMPTE RP155 in the US puts +4 dBu at −20 dBFS. That's where the habit of mixing around −18 dBFS comes from, and many plug-ins modelled on analogue gear are calibrated so their 0 VU sits at that level. The dBFS vs dBu vs dBV comparison has more on converter levels.

dB SPL, LUFS and the other decibels

dB SPL measures sound in the air, against a pressure of 20 micropascals, roughly the quietest 1 kHz tone a young listener can hear. That's 0 dB SPL, and the threshold of pain is somewhere around 120 to 130 dB SPL. A sound level meter set to A-weighting reads dB(A), which counts low and very high frequencies for less, the way your ears do at quiet levels. The UK's Control of Noise at Work Regulations 2005 make hearing protection compulsory at a daily average of 85 dB(A), a useful figure for anyone who spends long sessions on monitors or headphones, and the protecting your hearing lesson covers safe listening.

Distance changes SPL too. In open space, every time you double your distance from a source the level drops by about 6 dB, because the same energy is spread over four times the area. Indoors, reflections from the room make that less exact.

LUFS and LU belong to the same family. A loudness unit is the same size as a decibel, and LUFS is loudness measured from full scale, so a track at −8 LUFS is 6 LU louder than one at −14 LUFS.

Peak, RMS and loudness in decibels

The same sound gives different decibel readings depending on how the meter measures it. A peak meter shows the highest point of the wave, an RMS meter averages the level over a short window, and a LUFS meter averages it after filtering to match hearing. The gap between peak and RMS is the crest factor.

A sine wave's crest factor is 3.0 dB, because its peak is 1.41 times its RMS value. Pink noise, which is random, measures about 12 dB in the lab, and the full mix 16.2 dB, because short drum hits set its peaks without adding much to its average. All three peak within a decibel of full scale, yet the sine reads −2.5 LUFS and the mix −14.1. A peak reading in dBFS tells you how close you are to clipping and very little about how loud something sounds.

Meters don't all agree on where a sine sits, either. The AES17 standard defines 0 dBFS RMS as the RMS level of a full-scale sine, so some RMS meters read a full-scale sine as 0 dB while others read it as −3 dB. Check which kind you have before comparing numbers. The LUFS vs RMS vs peak comparison goes through more examples.

How to work out decibels without a calculator

You'll rarely need the log button. A few fixed points, plus the fact that decibels add, get you close enough for any mixing decision.

1. Learn the anchors6 dB doubles the signal and 20 dB multiplies it by ten. 3 dB doubles the power, which is 1.41 times the signal.
2. Break a number into anchors26 dB is 20 plus 6, so it's ten times and then twice: twenty times the signal. 12 dB is two doublings, four times the signal.
3. Count your way backA signal a quarter of the size is two halvings, so it's −12 dB. A hundredth is two divisions by ten, so it's −40 dB.
4. Check the units matchOnly compare decibels that share a reference. A peak of −6 dBFS and a line level of +4 dBu can't be compared until you know how the converter is set.

Common decibel mistakes

Thinking −6 dB is half as loud

It halves the signal, which sounds quieter but well short of half as loud. If you want a part to sound about half as loud, pull it down 10 dB and adjust from there.

Treating 0 dB on a fader as a level

A fader at 0 dB is unity gain: it passes the signal through unchanged. A meter at 0 dBFS is a level, the top of the scale. Channels with their faders at 0 dB can peak anywhere.

Adding decibel numbers when sounds combine

Two sounds at −10 dBFS make neither −20 dBFS nor 0. Identical copies come out 6 dB higher, unrelated sounds about 3 dB higher, and two copies with opposite polarity cancel to silence.

Trusting a sample peak meter to catch every over

A sample peak meter can sit at −0.3 dBFS while the true peak is over 0. Use a true peak meter, or a limiter with true peak mode, on anything you export for release.

Comparing two versions at different levels

A version 1 dB louder often sounds better on first listen, whatever else changed. When you compare two settings, match their loudness first, by ear or with a LUFS meter.

Training your ears to hear decibels

The quiz under the lab plays two versions of the loop between 1 and 3 LU apart and asks which is louder. In most rounds A has been through a limiter, so the louder version can have the lower peaks and a peak meter would pick the wrong one. Get the 3 LU rounds right every time first, then see how often you can hear a single decibel. Your best score is kept in your browser.

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