Decibel
Non-SI unit accepted for use · quantity: level, a logarithmic ratio
01 · Definition
A decibel measures nothing on its own. It states how many times one quantity exceeds another — and it demands that the other one be named.
A power level equals ten decimal logarithms of the ratio: L = 10 lg(P/P₀) decibels. For quantities whose square is proportional to power — pressure, voltage, current — the factor doubles: L = 20 lg(F/F₀). Hence the rule that looks odd to the uninitiated: doubling the power gives 3 dB, doubling the amplitude gives 6 dB. The unit is dimensionless and is not part of the SI, though it is accepted for use alongside the bel and the neper. The reference value is a compulsory part of the notation: without «relative to 20 µPa» or «relative to 1 mW» a figure in decibels means nothing at all.
The ear takes in sounds spanning a ratio of one to a trillion in intensity. Writing that out linearly is awkward, and it is heard logarithmically anyway: equal ratios feel like equal steps. The second reason is technical — losses along a chain of amplifiers and lines multiply, whereas in decibels they simply add up.
02 · Conversion
Enter a level and the sheet will unfold it into ratios
Every row of the table describes one and the same ratio, written differently. The bel is ten times larger than the decibel, the neper counts by the natural logarithm and lives in circuit theory, and percentages are handy when the ratio is close to unity.
Decibels from separate sources do not add up arithmetically. Two identical machines at 60 dB give 63 dB, not 120: it is the power that doubles, not the level. To sound twice as loud takes about ten decibels more — that is, ten times the power.
| Unit | Name | Value | Where it appears |
|---|---|---|---|
| {u} | {name} | {value} | {note} |
03 · Orders of magnitude
sound pressure scale, reference 20 µPa04 · Measuring instruments
What decibels are measured with
A condenser microphone, a weighting filter A, C or Z, and averaging over time. Class 1 holds a tolerance of a fraction of a decibel at mid frequencies.
It slips over the microphone and delivers a reference 94 decibels — exactly one pascal of sound pressure. Without this check before a measurement the meter's figures carry no weight.
In radio engineering the vertical axis is always in dBm: zero means one milliwatt. A cellular receiver works from −50 down to −110 dBm — six orders of magnitude in power on a single screen.
It counts not from a physical threshold but from the hearing norm at each frequency. Zero dB HL is the median of a healthy young ear, which is why the scale can go negative.
05 · Writing rules
lower-case d, upper-case B, the reference is compulsory
The upper-case B is there because the bel is named after Alexander Bell; the lower-case d is the prefix «deci». A space goes between the number and the unit. The symbol has no plural: 20 dB, never 20 dBs. Prefixes are not applied to the decibel: there is no such thing as a kilodecibel, only a thousand decibels — which never comes up in practice.
Forms like dBm, dBA, dBi and dBFS go against SI rules: letters qualifying the quantity must not be appended to a unit symbol. Metrologists suggest putting the reference in brackets after the number, but the industries hold on to the short form, and the standards tolerate it.
06 · Neighbouring units
All three level units describe one ratio but take different logarithms. The bel is decimal and large, the decibel is its tenth and the workhorse, the neper is natural and convenient in the mathematics of transients.
Reference values are set by separate standards: 20 µPa for sound in air, 1 mW for radio-frequency power, 0.7746 V for studio audio, and the converter's full scale for digital.
07 · Historical section
The units the decibel grew out of
The loss of one mile of telephone cable at 800 hertz. A measure physical to the last: to work out how much a line had lost, it was compared against a coil of wire.
The first attempt to prise the unit away from a piece of cable: a pure ratio of powers with a decimal logarithm. It coincided numerically with the decibel to come.
Named after Alexander Bell. It proved too large: nearly every practical difference fitted into single bels and fractions of one, so the tenth part came into use.
Named after John Napier, the inventor of logarithms. It counts to base e and is therefore natural in attenuation equations, but awkward in reports.
The decibel is not a unit of a quantity but a way of writing a ratio
Strictly speaking, the ratio of two powers is dimensionless, and its value equals one multiplied by a number. The International Bureau of Weights and Measures recognises the bel, the decibel and the neper as units of logarithmic ratios, but with a proviso: they are not part of the SI and are used only together with a stated reference. Hence the whole muddle with suffixes. Engineering practice appended a letter to the symbol — dBm, dBA, dBi, dBFS — and each such form implies its own reference value, although the rules of the system forbid adding anything to a unit. While the metrologists argue, the industries have been using suffixes for seventy years, and there is nothing to replace them with: the alternative demands cumbersome qualifiers on every line of a test report.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with special names, and the non-SI units that neither engineering nor everyday life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules. In 36 languages.
Non-SI units
open the decibel sheetSI base units
the decibel is dimensionless — there are no base units in itSI derived units with names of their own
in terracotta — those whose ratios are counted in decibelsSheet language
36 languages. The symbol dB and the formulas are not translated — they are the same in every locale; what is translated is the prose, the local land measures and the writing rules.