Convert logarithmic sound/signal levels between decibels, bels and nepers.
Sound • 3 units
All 3 units on the Sound Level Converter are defined against the Decibel (dB), so each result is one conversion factor away from a single reference rather than the end of a chain of roundings.
The conversion this page is most often opened for is ready before you type anything: 1 dB = 0.1 B. Change either side and every row in the table recalculates with it.
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The bel was created at Bell Telephone Laboratories in the 1920s to express ratios of power on a logarithmic scale, and was named in honour of Alexander Graham Bell. In practice the bel is too large, so the decibel (one-tenth of a bel) is used almost universally. The neper is a related logarithmic unit based on natural logarithms rather than base-10.
Logarithmic units suit human perception: our ears respond to enormous ranges of sound intensity, and a 10 dB increase is perceived as roughly "twice as loud." Decibels are also used for signal gain, electronics and acoustics, so converting between decibels, bels and nepers is common in audio and telecommunications work.
Quick reference — 1 Decibel (dB) is equal to:
| Bel | B | 0.1 |
| Neper | Np | 0.115129263 |
3 units of sound level, each a fixed multiple of the dB. The table spans 10:1, from dB (1 dB) to B (10 dB). Conversion is one multiplication into the base unit and one division out of it, with no lookup table and no approximation.
value_to = value_from × (factor_from ÷ factor_to)1 dB = 1 dB1 B = 10 dB1 Np = 8.68589 dBwhere:
Assumptions: Factors are exact definitions. Full double precision is carried internally and rounding is applied only for display.
Result25 dB = 2.5 B
The decibel is a ratio rather than an amount, so a bare decibel value is an incomplete statement until the reference is named. Sound pressure levels are referenced to 20 micropascals and written dB SPL; radio and audio power is referenced to a milliwatt as dBm; digital audio counts down from full scale as dBFS. The same number in two of these means two entirely different things, and mixing them is the most common error in the whole subject.
The second trap is that decibels are defined on power, so the multiplier depends on whether the quantity being compared is a power or an amplitude. Ten times the power is 10 dB, but ten times the voltage is 20 dB, because power goes as the square of voltage. Using the wrong one puts every result out by a factor of two on the decibel scale, and it happens most often when a voltage ratio from a datasheet is treated as a power ratio.
The neper is the same idea built on natural logarithms instead of base ten, which makes one neper about 8.686 decibels. It survives in transmission-line and control theory because it falls out of the exponential decay directly, without the conversion factor that logarithms to base ten introduce. Encountering it in a paper is a sign the author was working from the underlying mathematics rather than from measurement practice.