What a decibel is, why there are so many kinds, what peak, RMS and LUFS meters actually measure, and how to set levels through a signal chain.
Prof. Thomas Posen · Interactive handout: open in a web browser, move the sliders, and press play
01What a decibel is
A decibel is not an amount; it's a ratio on a logarithmic scale. That suits our hearing, which copes with an enormous range of levels and judges changes roughly by ratio. Two formulas, depending on what you're comparing:
dB = 20 · log₁₀(A₁ ÷ A₀) amplitude: voltage, sound pressure, sample value
dB = 10 · log₁₀(P₁ ÷ P₀) power and intensity
So doubling an amplitude adds 20·log₁₀(2) = +6.02 dB, while doubling a power adds 10·log₁₀(2) = +3.01 dB. Loudness standards such as BS.1770 compute level from the mean square of the signal, a power-like quantity, so they use 10·log₁₀.1
Figure 1. A level change in dB, as an amplitude ratio (the height of the waveform) and a power ratio. Try +6, +20, −20 and −40.
02So many dBs
Because a decibel is a ratio, "dB" alone only describes a change. To state an absolute level you need a reference, which the suffix names:23
Unit
Reference (0 dB =)
Where you'll see it
dB SPL
20 µPa sound pressure, about the threshold of hearing
Acoustics, hearing safety, mic specs
dBu
0.775 V RMS (the voltage of 1 mW into 600 Ω)
Professional analog gear; pro line level is +4 dBu ≈ 1.228 V
dBV
1 V RMS
Consumer gear; consumer line level is −10 dBV ≈ 0.316 V, about 11.8 dB below pro level
dBFS
Digital full scale, the largest possible sample value
Every DAW meter and digital device
LUFS / LKFS
Loudness relative to full scale, measured per ITU-R BS.1770
Loudness meters, streaming, broadcast
LU
A loudness difference; 1 LU = 1 dB
Relative loudness, Loudness Range
03dBFS and digital headroom
In fixed-point digital audio, 0 dBFS is the largest sample value there is, so sample levels are always 0 or below. Push past it and the waveform is simply cut off: clipping.
An RMS convention to watch. The AES17 standard defines 0 dBFS as the RMS level of a full-scale sine wave. On that scale a full-scale square wave reads +3.01 dBFS RMS. Other meters use the mathematical convention, where a full-scale sine reads −3.01 dBFS RMS. Sample peaks can't exceed 0 dBFS, but RMS readings depend on which convention your meter uses.34
Bit depth and the noise floor
Each bit adds about 6.02 dB of dynamic range: for a full-scale sine against quantization noise, dynamic range ≈ 6.02·N + 1.76 dB. That's about 98 dB for 16-bit and 146 dB for 24-bit (often quoted as 96 and 144 without the 1.76).3 Real converters fall well short of 24-bit's theoretical figure because their analog circuits are noisier than that, but 24-bit still leaves far more room below the signal than you'll ever need. Apple describes 24-bit as increasing workable headroom.5
32-bit floating point, used inside most DAWs, has enormous headroom: a channel can go "over" 0 dBFS internally without clipping. The overs become real clipping only where audio is converted to fixed point: your interface's output, a fixed-point export, or a plug-in that clips internally.
04Peak, RMS and VU, PPM
Different meters answer different questions. Peak meters ask "will this clip?" Average meters (RMS, VU) and loudness meters (LUFS) ask "how loud does this sound?" The gap between peak and RMS is the crest factor. For a sine wave, RMS is the peak divided by √2, a crest factor of 3.01 dB; a drum loop's can be 15 dB or more.3
Sample peakfast attack, slow fall
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RMS300 ms average, VU-like
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MomentaryLUFS, 400 ms
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Short-termLUFS, 3 s
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Press a sound below to drive the meter.
Figure 2. A live meter that follows the audio below. Coral: sample peak. Teal: RMS (mathematical convention). Purple: loudness per ITU-R BS.1770 / EBU Tech 3341 (mono). Scale −60 to 0 dB.
Sample-peak meterShows the highest sample values. Fast, but can miss peaks between samples (see true peak, below).
True-peak meter (dBTP)Estimates the reconstructed waveform's peak by oversampling, per ITU-R BS.1770 (an oversampled rate of at least 192 kHz).2
VU meterDeveloped in 1939 by Bell Labs, CBS and NBC; standardized as ANSI C16.5-1942. Needle reaches 99% of a steady tone in 300 ms, so it shows roughly average level. 0 VU = +4 dBu (originally +4 dBm in 600 Ω).6
PPM (peak programme meter)Quasi-peak meters (IEC 60268-10) used in broadcasting: Type I integrates over 5 ms, Types IIa/IIb (BBC, EBU) over 10 ms, with a slow, steady fall-back.78
05Loudness: LUFS
Peak and RMS meters treat all frequencies equally; your ears don't. LUFS (Loudness Units relative to Full Scale, also written LKFS) is the standard loudness measure from ITU-R BS.1770, first published in 2006; the current version is BS.1770-5 (November 2023).12
K-weighting. A high shelf of about +4 dB above roughly 1.5 kHz (modeling the head's acoustics), then a high-pass filter around 38 Hz.2
Mean square in 400 ms blocks overlapping by 75%, summed across channels (the LFE channel is excluded).
Gating (added in BS.1770-2, 2011): blocks below −70 LUFS are ignored (absolute gate), then blocks more than 10 LU below the result (relative gate), so silences and quiet passages don't drag the number down.220
A constant of −0.691 dB makes a full-scale 997 Hz sine in one channel read −3.01 LUFS.2 (The meter in Figure 2 is built this way: play its full-scale 1 kHz tone and it reads −3.0 LUFS.)
Recommendations to streaming services, not mastering targets; prefers album normalization22
06Gain staging
Gain staging means setting the level at every point in the chain so each stage works in its sweet spot: far enough above its noise floor that noise isn't heard, and far enough below its clipping point that peaks get through cleanly. Get it wrong early and no later fader can fix it: noise raised with the signal stays raised, and a clipped waveform stays clipped.
The analog–digital bridge
EBU R68: 0 dBu analog = −18 dBFS, leaving 18 dB of headroom. SMPTE RP155: +4 dBu = −20 dBFS, leaving 20 dB.1516 Many DAW VU-meter plug-ins default to 0 VU = −18 dBFS.
Plug-ins that model the nonlinear behavior of analog gear may need their input at or around a particular level, commonly about −18 dBFS. Drive them hotter and they generally add more saturation.1517
Recording levels
At 24-bit there's no reason to record close to 0 dBFS: the noise floor is low enough to leave plenty of headroom. A common approach treats about −18 dBFS RMS as the equivalent of 0 VU, with peaks typically around −10 dBFS and a warning at about −6 dBFS.17 Bob Katz's K-System (K-20, K-14, K-12; JAES, 2000) formalized this idea, pairing an average-reading meter whose 0 sits 20, 14 or 12 dB below full scale with calibrated monitor levels.1819
Figure 3. A mic signal (peaking at −28 dBFS before gain) through a preamp and converter that clip at 0 dBFS and add hiss at −60 dBFS (exaggerated so you can hear it), then an analog-modeled plug-in whose nominal level is −18 dBFS, then a fader that brings the result to the same loudness every time. Bars: gray = noise floor, teal = RMS, coral tick = peak.
07Listening and review
Try it in your DAW
Put a loudness meter on your master. Play three reference tracks from a streaming service and write down their integrated LUFS and true peak.
Record the same part twice: once peaking near −20 dBFS, once near −3. Raise the quiet one to match and listen to the noise floor.
Push an analog-modeled plug-in with 12 dB more input (and 12 dB less output). Describe what changes.
Find a sound whose peak meter and loudness meter disagree the most. Why do they?
A signal's voltage doubles. How many dB is that? What if its power doubles?
Show answer+6.02 dB for amplitude (20·log₁₀2), +3.01 dB for power (10·log₁₀2).
How far apart are pro (+4 dBu) and consumer (−10 dBV) line levels?
Show answerAbout 11.8 dB (1.228 V vs. 0.316 V).
A drum loop peaks at −1 dBFS with an RMS of −17 dBFS. What's its crest factor?
Show answer16 dB (peak minus RMS).
Why does LUFS apply K-weighting before measuring?
Show answerTo approximate how loud we perceive the signal: it boosts the upper frequencies we're more sensitive to (+4 dB shelf above ~1.5 kHz) and rolls off the extreme lows (high-pass ~38 Hz).
What does the gate in an integrated LUFS measurement do?
Show answerIt ignores silence (below −70 LUFS) and passages more than 10 LU below the overall level, so quiet sections don't pull the figure down.
You recorded at 24-bit with peaks at −20 dBFS. Is that a problem?
Show answerUsually not: 24-bit's noise floor is far below that. It leaves plenty of headroom, and you can raise it later without audible noise (as long as the analog front end was quiet enough).
—Sources
ITU-R BS.1770, Algorithms to measure audio programme loudness and true-peak audio level (all versions). itu.int/rec/R-REC-BS.1770
ITU-R BS.1770-5 (11/2023), full text (PDF). itu.int (PDF)