A **bel** (symbol **B**) is a unit of measure of ratios of power levels, i.e., relative power levels. It is mostly used in telecommunication, electronics and acoustics. Invented by engineers of the Bell Telephone Laboratory, it was originally called the *transmission unit* or *TU*, but was renamed in 1923 or 1924 in honour of the laboratory's founder and telecommunications pioneer Alexander Graham Bell.

The bel is a logarithmic measure. The number of bels for a given ratio of power levels is calculated by taking the logarithm, to the base 10, of the ratio. Therefore, one bel corresponds to a ratio of 10:1. Mathematically, the number of bels is calculated as B = log_{10}(*P*_{1}/*P*_{2}) where *P*_{1} and *P*_{2} are power levels. The neper is a similar unit which uses the natural logarithm.

The bel is too large for everyday use, so the **decibel (dB)**, equal to 0.1 B, is more commonly used. One decibel is equivalent to a ratio of about 1.259:1.
It is defined as 10 log_{10}(*P*_{1}/*P*_{2}) where *P*_{1} and *P*_{2} are the powers.

The decibel is a dimensionless "unit". The decibel is not an SI unit, although the CIPM has recommended its inclusion in the SI system.

Table of contents |

2 Typical abbreviations 3 Common misconception: +3 dB means "times two" 4 References |

The reason for using the decibel is that the ear is capable of hearing a very large range of sound pressures. The ratio of the sound *pressure* that causes permanent damage from short exposure to the limit that (undamaged) ears can hear is more than a million. Because the *power* in a sound wave is proportional to the square of the pressure, the ratio of the maximum power to the minimum power is more than one trillion. To deal with such a range, logarithmic units are useful: the log of a trillion is 12, so this ratio represents a difference of 120 dB.

Psychologists have found that our perception of loudness is roughly logarithmic, see Weber-Fechner Law. In other words, you have to multiply the sound intensity by the same factor to have the same increase in loudness. This is why the numbers around the volume control dial on a typical audio amplifier are related not to the absolute power amplification, but to its logarithm.

Various frequency weightings are used for acoustical measurements to approximate the changes in sensitivity of the ear to different frequencies at different levels. These include the dB(A), dB(B), and dB(C) weightings.

Sounds above 85 dB are considered harmful, while 120 dB is unsafe and 150 dB causes physical damage to the human body. Windows break at about 163 dB. Jet airplanes are about 133 dBA at 33 m, or 100 dBA at 170m. Eardrums pop at 190 to 198 dB. Shock waves and sonic booms are about 200 dB at 330 m. Sounds around 200 dB can cause death to humans and are generated near bomb explosions (e.g. 23 kg of TNT detonated 3 m away). The space shuttle is around 215 dB (or about 175 dBA at 17m). Nuclear bombs are 240 dB to 258 dB (distance unknown). Even louder are earthquakes, tornados, hurricanes and volcanoes.

In radio electronics, the decibel is used to describe the ratio between two measurements of electrical power. It can also be combined with a suffix to create an absolute unit of electrical power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". 0 dBm is one milliwatt, and 1dBm is one decibel greater than 0 dBm, or about 1.259 mW.

Although decibels were originally used for power ratios, they are nowadays commonly used in electronics to describe voltage or current ratios. In a constant resistive load, power is proportional to the square of the voltage or current in the circuit. Therefore, the decibel ratio of two voltages *V*_{1} and *V*_{2} can be defined as 20 log_{10}(*V*_{1}/*V*_{2}), and similarly for current ratios. Thus, for example, a factor of 2.0 in voltage is equivalent to 6.02 dB (not 3.01 dB!).

This practice is fully consistent with power-based decibels, provided the circuit resistance remains constant. However, voltage-based decibels are frequently used to express such quantities as the voltage gain of an amplifier, where the two voltages are measured in different circuits which may have very different resistances. For example, a unity-gain buffer amplifier with a high input resistance and a low output resistance may be said to have a "voltage gain of 0 dB", even though it is actually providing a considerable power gain when driving a low-resistance load. Although this is pedantically deplorable, it is actually a very common practice and seems likely to persist.

- dBm - dB(mV/m²) - millivolts per square metre - signal strength of a radio signal
- dBμ
*or*dBu - dB(μV/m²) - microvolts per square metre - strength of a radio signal - dBf - dB(fW) - femtowatts - amount of power required to drive a radio receiver
- dBW - dB(W) - watts - amount of power transmitted by a low-power radio station
- dBk - dB(kW) - kilowatts - amount of power transmitted by a broadcast radio station
- dBV - dB(V) - volts - amplitude of an audio signal in a wire
- dBv
*or*dBu - dB(0.775V) - same as dBV but referenced to 0.775 volts instead of 1 volt - dBm - dB(mW@600Ω) - in analogue audio, milliwatts into a 600-ohm load

- dBA, dBB,
*or*dBC - different weightings of the human ear's response to sound - dBd - dB(dipole) - effective radiated power compared to a dipole antenna
- dBi - dB(isotropic) - effective radiated power compared to an imaginary isotropic antenna
- dBfs
*or*dBFS - dB(full scale) - amplitude of a signal (usually audio) compared to the maximum which a device can handle before clipping occurs

To contrive a more serious example, consider converting a large decibel figure into its linear ratio, for example 120 dB. This is correctly calculated as a ratio of 10^{12} or one trillion. But if we use the assumption that 3 dB means "times 2", we would calculate a ratio of 2^{120/3} = 2^{40} = 1.0995 × 10^{12}, for a 10% error.

- Martin, W. H., "DeciBel – The New Name for the Transmission Unit",
*Bell System Technical Journal*, January 1929.