Decibels for DJs: Logarithmic Scales, Adding Levels and Crest Factor.

Opening a meter and reading a number is easy; knowing what to do with it is another matter. Decibels are not countable units: they express logarithmic ratios, so everyday arithmetic rules do not apply directly. Two levels of 0 dB do not make 0 dB, and two speakers do not always add the same amount.

This chapter gives the minimum needed for confident work: what a decibel is and why it is logarithmic, correctly adding decibel levels, why two speakers do not automatically mean +6 dB, and crest factor, including why it matters in a mastered track. If waveform scales are unclear, first review waves, frequency, amplitude and phase.

What a Decibel Is and Why It Is Logarithmic

A decibel measures a ratio between quantities—pressure, voltage, power—against a reference on a logarithmic scale. That is the key. On a linear scale, perceiving the same rise from 10 to 20 as from 100 to 110 would require enormous absolute changes; logarithmic perception steps are conventionally read as equal.

The reference changes with the subject, the first trap: dB SPL refers to acoustic pressure against 20 micropascals, dBu and dBBV to line voltages, dBFS to the digital scale where 0 dBFS is the absolute ceiling, and LUFS to frequency-weighted, gated loudness. All are decibels; none can be added to another domain.

Practically, “90 dB sensitivity” in a manufacturer’s specification and a club’s “96 dB at the desk” are comparable only with the same reference and domain. They share the scale: a 10 dB rise sounds approximately twice as loud, although the physical value changes far more.

Adding Decibel Levels Correctly

For equal sources, total level is one source’s level plus 10 times the logarithm of source count. Two equal sources add 3 dB, four add 6 dB, eight add 9 dB and sixteen add 12 dB. This applies to equal, independent sources.

For unequal sources, add power in the linear scale, then return to decibels; the result always remains below the loudest source plus 3 dB. Never add the figures directly: 10 dB plus 10 dB is 13 dB, not 20 dB; 6 dB plus 6 dB is 9 dB, not 12 dB.

Two conditions make calculations correct. First, values must share a domain: add dB SPL only to dB SPL. Second, know whether sources are correlated, because that changes everything in the next section.

Memorise a case arising whenever processes are chained: 6 dB attenuation followed by another 6 dB totals 12 dB, because this subtracts from the same magnitude on the same scale. The trap is adding different sources’ levels, not accumulating losses.

Why Two Speakers Do Not Automatically Mean +6 dB

Every system technician faces this question; the honest answer is “it depends.” Two speakers reproducing the same signal at equal level and perfectly in phase add aligned amplitudes, doubling amplitude: 6 dB. Independent, uncorrelated sources add only power, giving 3 dB.

Everything else lies between those extremes: partial phase offsets varying by frequency, different listener paths and arrival times. Resulting level fluctuates, may rise less than 3 dB in some bands and fall in others because signal portions subtract. Correlation determines the result; it belongs to the relationship between arriving signals, not the speaker.

Two booth consequences: first, adding another system does not reliably double perceived volume; sometimes it does, sometimes not. Second, adding one track through offset paths—for example, a direct channel and a poorly adjusted effects send—can lose bass and definition where most needed.

Crest Factor

Crest factor is the ratio of a signal’s peak to RMS level in decibels. It measures peakiness: greater separation between peak and RMS means more crest factor and dynamic margin.

Typical values provide context. A pure sine wave has 3.01 dB crest factor, a triangle 4.77 dB and a square 0 dB, the extreme case without peaks above its average. Today’s commercial tracks have fairly compressed crest factors because peaks are limited to raise RMS level.

In practice, a low-crest-factor master arrives with little difference between measured level and peaks, leaving hardly any booth margin to raise it. A high-crest-factor master tolerates clean increases because its peaks are sparse. It also explains why peak and loudness meters tell different stories about the same track.

The Decibels Sharing a Booth

With the scale understood, name what each screen displays:

• dBFS: digital domain. 0 dBFS is maximum; everything else is negative. Watch this to avoid clipping.
• dBu / dBV: analogue line domain against a voltage reference, used in preamp and physical mixer specifications.
• dB SPL: acoustic pressure in air, measured by sound level meters and used by venue noise regulations.
• LUFS: weighted, gated loudness for comparing perceived track volume and streaming normalisation.

Three domains, three uses, no cross-domain addition. The guide to dBFS and LUFS meters with gain staging develops their roles in a mixing chain; acoustic metrics in the next chapter naturally follow.

Pocket Rules for Addition and Subtraction

• +3 dB = double power, or two equal independent sources.
• +6 dB = double amplitude, or four equal independent sources.
• +10 dB = ten times the power; practically, a clear perceived jump.
• −6 dB = approaching twice the distance from a source in the direct field.
• Never add decibel figures arithmetically; add powers and return to the scale.

Those five lines cover most informal calculations. For exact results with unequal-level sources, work linearly then return to decibels, as Engineering ToolBox’s equal-source addition formula describes.

Common Decibel Mistakes

Adding dB as numbers. 10 dB and 10 dB do not make 20 dB. The commonest confusion creates the most imagined noise in chains.

Confusing peaks with volume. Crest factor reminds you: peaks protect against clipping; RMS level or loudness describes what is heard.

Assuming every speaker contributes the same. Without known correlation, another system might add 6 dB or almost nothing.

Mixing domains in a calculation. dBFS plus dB SPL means nothing: different quantities with different references.

Setting level from a meter number without identifying it. Without domain and weighting, the number is incomplete information. To choose metrics for each case, continue with acoustic metrics: Leq, LAF, Lmax and percentiles.

Next Step

You can read and add levels. Next choose what to measure: averages, time weightings, peaks and percentiles, with their applications. Continue with Acoustic Metrics: Leq, LAF, Lmax, Ld, Le, Ln and Percentiles.