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Logarithmic unit used to describe ratios of signal levels - like power or intensity - to a reference level.

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The decibel is a logarithmic unit used to describe the ratio of a signal level - like power or intensity - to a reference level.

  • the decibel express the level of a value relative to a reference value

Decibel Definition

The decibel level of a signal can be expressed as

L = 10 log (S / Sref)                                                       (1)


L = signal level (decibel, dB)

S = signal - intensity or power level (signal unit)

Sref = reference signal - intensity or power level (signal unit)

Decibel is a dimensionless value of relative ratios. The signal units depends on the nature of the signal - can be W for power.

A decibel is one-tenth of a Bel - named after Alexander Graham Bell, the inventor of the telephone.

Note! - the decibel value of a signal increases with 3 dB if the signal is doubled (L = 10 log (2) = 3).

If the decibel value and reference level are known the absolute signal level can be calculated by transforming (1) to

S = Sref 10(L / 10)                                                      (2)

Decibel Calculator

S - signal - intensity or power level (signal unit)

Sref - reference signal - intensity or power level (signal unit)

Decibel Scale

Example - Lowest Hearable Sound Power

10-12 W is normally the lowest sound power possible to hear and this value is normally used as the reference power in sound power calculations.

The sound power in decibel from a source with the lowest sound hearable can be calculated as

L = 10 log ((10-12 W) / (10-12 W))

    = 0 dB

Example - Highest Hearable Sound Power

100 W is almost the highest sound power possible to hear. The sound power in decibel from a source with the highest possible to hear sound power can be calculated as

L = 10 log ((100 W) / (10-12 W))

    = 140 dB

Example - Sound Power from a Fan

Decibel Scale - example fan 120 dB

A fan creates 1 W of sound power. The noise level from the fan in decibel can be calculated as

L = 10 log ((1 W) / (10-12 W))

    = 120 dB

Example - Sound Intensity and Decibel

The difference in decibel between sound intensity 10-8 W/m2 and sound intensity 10-4 W/m2 (10000 units) can be calculated as

ΔL = 10 log ((10-4 W/m2) / (10-12 W/m2)) - 10 log ((10-8 W/m2) / (10-12 W/m2))

    = 40 dB

Increasing the sound intensity by a factor of

  • 10 raises its level by 10 dB
  • 100 raises its level by 20 dB
  • 1000 raises its level by 30 dB
  • 10000 raises its level by 40 dB and so on
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  • Engineering ToolBox, (2003). Decibel. [online] Available at: [Accessed Day Mo. Year].

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