Sound Converter

The bel, the decibel and the neper don't measure an amount: they express a ratio between two values on a logarithmic scale. A sound level in decibels compares a sound with a reference, and a gain or a loss in a cable or an amplifier compares the power out with the power in.

Every 10 dB is ten times the power, so a sound 20 dB louder carries 100 times the power. Sound levels such as 60 dB for a conversation are measured against the faintest sound a person can hear, a pressure of 20 µPa.

How to convert sound units

Type a value into any field, and every other unit is calculated at once. For example, 30 dB:

1. In bels: divide by 10.

   30 / 10 = 3 B

2. In nepers: multiply by 0.115129.

   30 * 0.115129 = 3.454 Np

A power ratio in decibels is 10 * log(P2/P1), so 30 dB is a power ratio of 10^(30 / 10) = 1,000.

Common conversions

What a level in decibels means as a ratio. Power and intensity follow 10 * log, and amplitudes such as voltage or sound pressure follow 20 * log:

Sound units

Bel (B)

The Bel is a logarithmic unit used to express the ratio between two quantities, typically power or intensity. It is named after Alexander Graham Bell, the inventor of the telephone.

The Bel is defined as the logarithm to the base 10 of the ratio of two power or intensity levels. The level in bels is L = log(P2/P1), where P2/P1 represents the power ratio.

Decibel (dB):

Since the Bel is a rather large unit, it is not useful for precise measurements. Usually a smaller unit, the Decibel or dB, is used. The Decibel represents one-tenth of a Bel.

Decibels (dB) = 10 * log(P2/P1)

The conversion factor to convert from Bel to Decibel is:

1 Decibel (dB) = 0.1 Bel

Neper (Np)

The Neper is another logarithmic unit used to express the ratio between two quantities. It is named after John Napier, a Scottish mathematician. The Neper is commonly used in engineering and mathematics but is less prevalent in the field of sound measurement.

The neper is defined in terms of ratios of field quantities, also called root-power quantities (for example, voltage or current amplitudes in electrical circuits, or pressure in acoustics), whereas the decibel was originally defined in terms of power ratios. A power ratio 10 * log(ratio) dB is equivalent to a field-quantity ratio 20 * log(ratio) dB, since power in a linear system is proportional to the square of the amplitude. Hence the decibel and the neper have a fixed ratio to each other:

1 Np = 20 * log(e) dB = 8.685889638 dB

and

1 dB = 1/20 * ln(10) Np = 0.115129255 Np