# dB converter

## Decibels to watts, volts, hertz, pascal conversion calculator

Convert dB, dBm, dBW, dBV, dBmV, dBμV, dBu, dBμA, dBHz, dBSPL, dBA to watts, volts, ampers, hertz, sound pressure.

1. Set the quantity type and decibel unit.
2. Enter the values in one or two of the text boxes and press the corresponding Convert button:

## Decibels unit definition

The decibel (symbol: dB) is a relative unit of measurement corresponding to one tenth of a bel (B). It is used to express the ratio of one value of a power or root-power quantity to another, on a logarithmic scale. A logarithmic quantity in decibels is called a level. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately 1.25893) or (sometimes equivalently) an amplitude (field quantity) ratio of 10​1⁄20 (approximately 1.12202).

The unit is used to express a change in value (e.g., +1 dB or −1 dB) or an absolute value. In the latter case, the numeric value expresses the ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 volt, a common suffix is "V" (e.g., "20 dBV").

Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm in base 10. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude.

The definition of the decibel originated in the measurement of transmission loss and power in telephony of the early 20th century in the Bell System in the United States. The bel was named in honor of Alexander Graham Bell, but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.

The decibel is used in a wide range of applications. Decibels are especially used, when a referring to power or a derived measure, which values can vary in a wide range. The most prominent usage of decibels is in sound volume. So, for example a sound of 0dB is barely hearable, whereas a vaccum cleaner on average has 75dB and a rock concert reaches about 110dB.

In class, you often find the following definitions for something in decibels

XdB=10log10(XlinXref).${}_{}{}_{}\frac{{}_{}}{{}_{}}$

This equation transforms quantity Xlin${}_{}$ from linear scale to a quantity in dB scale XdB${}_{}$. In order to do that, first the linear quantity is related to a reference quantity Xref${}_{}$ and the ratio of both is transformed into the log-domain. Apparently, XdB${}_{}$ does actually have no unit and we artificially add dB to make clear we are in logarithmic scale. When Xlin${}_{}$ equals the reference level, the dB-scale becomes zero:

XdB=10log10(XlinXref)

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